Ground moving target indication with synthetic aperture radars for maritime surveillance

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In the using or citation of parts of the thesis it’s obliged to indicate the name of the author Departament de Teoria del Senyal i Comunicacions GROUND MOVING TARGET INDICATION WITH SYNTHETIC APERTURE RADARS FOR MARITIME SURVEILLANCE Ph.D. Thesis GROUND MOVING TARGET INDICATION WITH SYNTHETIC APERTURE RADARS FOR MARITIME SURVEILLANCE Author EDUARDO MAKHOUL VARONA Thesis advisor Prof. Antoni Broquetas Ibars Ground Moving Target Indication with Synthetic Aperture Radars for Maritime Surveillance Author Eduardo Makhoul Varona Thesis Advisor Prof. Antoni Broquetas Ibars A thesis submitted to the Universitat Polit` ecnica de Catalunya (UPC) in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Ph.D. program on Signal Theory and Communications Remote Sensing Laboratory (RsLab) Group Barcelona, March 2015 Eduardo Makhoul Varona Ground Moving Target Indication with Synthetic Aperture Radars for Maritime Surveillance Ph.D. program on Signal Theory and Communications This work has been supported by FPU Research Fellowship Program, Ministerio de Educaci´on, contract AP2009-4590; by FI-AGAUR Research Fellowship Program, Generalitat de Catalunya, contract 2010FI EM051757; by the Spanish Ministry of Science and Innovation (MICINN) under projects TEC2011-28201-C02-01, TEC2008-06764-C02-01 and CONSOLIDER CSD2008-00068; and by European Commission under FP7-SPACE Projects NEWA Ref. 241630 and SIMTISYS Ref. 263268. Copyright ©2015 by Eduardo Makhoul Varona, TSC, UPC, Barcelona, Spain. All rights reserved. Reproduction by any means or translation of any part of this work is forbidden without permission of the copyright holder. Acta de qualificació de tesi doctoral Curs acadèmic: Nom i cognoms Programa de doctorat Unitat estructural responsable del programa Resolució del Tribunal Reunit el Tribunal designat a l'efecte, el doctorand / la doctoranda exposa el tema de la seva tesi doctoral titulada __________________________________________________________________________________________ _________________________________________________________________________________________. Acabada la lectura i després de donar resposta a les qüestions formulades pels membres titulars del tribunal, aquest atorga la qualificació: NO APTE APROVAT NOTABLE EXCEL·LENT (Nom, cognoms i signatura) President/a (Nom, cognoms i signatura) Secretari/ària (Nom, cognoms i signatura) Vocal (Nom, cognoms i signatura) Vocal (Nom, cognoms i signatura) Vocal ______________________, _______ d'/de __________________ de _______________ El resultat de l’escrutini dels vots emesos pels membres titulars del tribunal, efectuat per l’Escola de Doctorat, a instància de la Comissió de Doctorat de la UPC, atorga la MENCIÓ CUM LAUDE: SÍ NO (Nom, cognoms i signatura) President de la Comissió Permanent de l’Escola de Doctorat (Nom, cognoms i signatura) Secretari de la Comissió Permanent de l’Escola de Doctorat Barcelona, _______ d'/de ____________________ de _________ 2014/2015 Eduardo Makhoul Varona Teoria del Senyal i Communicacions Teoria del Senyal i Communicacions Ground Moving Target Indication with Synthetic Aperture Radars for Maritime Surveillance To my father Issa, my mother Montserrat and my sisters Jeannette and Ingrid. To my beloved Aglaia. The sea, once it casts its spell, holds one in its net of wonder forever. Jacques Yves Cousteau Preface Em costa creure que estigui escrivint aquests l´ınies, que son les ´ultimes d’una llarga historia que ja fa m´es de cinc anys que va comen¸car. Com de segur totes i tots els que han passat per aquesta experi`encia, estaran d’acord amb mi que aquesta etapa que es tanca la podr´ıem definir com una aut`entica muntanya russa; amb molts d’alts i baixos, per`o una viv`encia ´unica que m’ha perm`es cr´eixer com a persona i gaudir de molts bons moments acompanyat sempre d’aquelles persones amb qui he confiat i que han cregut en mi. Es per aix`o que aquestes l´ınies intenten ser un agra¨ıment sincer a totes aquelles persones que sense el seu suport no hauria pogut arribar fins aquest prec´ıs moment. En primer lloc vull agrair al meu director de tesi, el professor Antoni Broquetas, per haver-me donat l’oportunitat de poder realitzar aquesta tesi doctoral i pel seu recolzament. Els seus consells i els seus coneixements t`ecnics m’han ajudat a desenvolupar el meu propi cam´ı en aquesta tesi. Tamb´e li vull agrair l’oportunitat de poder participar en diferents projectes que m’ha perm`es estar en contacte directe amb la industria aeroespacial europea i altres grups d’investigaci´o. Tamb´e vull aprofitar aquest espai per agrair als diferents professors del departament el seu recolzament durant la realitzaci´o de la tesi doctoral; en especial al professor Carlos L´opez pel seu inter`es, recolzament i les discussions t`ecniques que en la ultima etapa de la tesi m’han perm`es ampliar els meus coneixements cap a una vesant del SAR, la polarimetria, abans desconeguda per mi; i tamb´e voldria agrair als professors Albert Aguasca, Jordi Mallorqui i Xavier F`abregas que sempre han estat disponibles per qualsevol consulta o discussi´o. From my stay in Germany I keep many and very pleasing memories, thanks to all the people I met for the second time in the Microwaves and Radar Institute. First of all I thank Dr. Gerhard and Dr. Marwan Younis for giving me that opportunity. I would like to specially thank my collegue Dr. Stefan Baumgartner, who has helped me during my stay and for his dedication in all our discussions on SAR-GMTI. I would like to take the opportunity to thank also Dr. Josef Mittermayer and Marc Rodriguez. I have to mention also my friends Nikola and Mariano, with them I have shared very good moments, making my stay there much more comfortable and funny. No em puc oblidar dels meus companys (“ex-UPCeros”), Sergi, Ricardo i Marivi, que tan be em van acollir a Munich i amb els quals em vaig divertir tant (iala, iala !!!), i amb els quals vam implantar l’esperit TSCero dels cafes postlunch al DLR. El que ha fet ´unica aquesta experi`encia ha sigut el gran grup d’amics i companys que m’he trobat durant aquests anys i amb els quals he compartit tants bons moments i vii experi`encies, a m´es de despatx. Hem esdevingut una gran fam´ılia que de tant en tant es torna a ajuntar per nadal o al estiu i fem alguna trobada masienca, per gaudir i expandir la nostra cultura gastron`omica. Tot i ser un “intr´us”, els “anteneros” m’han acollit molt i molt be en el seu cercle, i es per aix`o que els hi estic molt i molt agra¨ıts pels bons moments gaudits, moltes gr`acies nois i noies: Marc, Santi, Enrique, Marta, Maria, Gemma, Dani i Edgar. En aquesta familia “TSCera” no hi poden faltar els meus companys “SARistas”, Dani, Giuseppe, Rub´en, Pep i Alberto que m’han ajudat quan ho necessitava i amb els que tantes rutes de la tapa he compartit. No em vull oblidar ni de l’Alba ni del Guillem, uns intrusos Camineros, que s’han afegit al cercle vici´os del caf`e matiner/postlunch al ´ultim tram de la tesi. Voldria dedicar unes paraules especials d’agra¨ıment per en Santi, que amb molta paci`encia sempre estava disposat a donar un cop de m`a i ajudar-me a resoldre problemes de qualsevol tipus; tots estem en deute amb tu, Santi. Gr`acies al Rol i a la Veva, per haver-me acollit com un m´es de la fam´ılia G´omez- D’Alessandro i per tots els dinars i sopars a casa vostra on he apr`es a tenir un visi´o m´es cr´ıtica de les coses. Ser quien soy y llegar a donde he llegado se lo debo a mi familia que siempre me ha demostrado su apoyo y cari´no sin condiciones, y han cre´ıdo en mi. No hay suficientes palabras para expresar la inmensa gratitud a mis padres, Issa y Montserrat, que me han transmitido ese esp´ıritu de trabajo y lucha por lo que uno m´as anhela y desea: tu como siempre lo sacar´as adelante ten paciencia. Estar´e siempre en deuda con vosotros. A mis hermanas, Jeannette e Ingrid, por su amor incondicional y soporte moral, a ellas que han estado a mi lado siempre que lo he necesitado y han cuidado de su hermano pequeÃśo, muchas gracias hermanitas. A mis cu´nados Mario y Eduard porque han sabido lidiar con un personaje tan especial como yo, les doy mis m´as sinceras gracias. Finalment voldria dedicar aquestes ´ultimes l´ınies a l’Aglaia, que m’ha suportat, pacient, dia a dia durant tota aquesta etapa, sense esperar res a canvi i que m’ha ajudat a relativitzar els meus problemes i buscar les estrat`egies m´es adequades per avan¸car en aquest cam´ı sinu´os. Gr`acies pel teu suport incondicional, per ser la persona que ets i compartir la teva vida juntament amb mi. viii Contents 8 Conclusions 193 8.1 Maincontributions............................... 194 8.2 Mainconclusions................................ 196 8.3 Futureresearchlines.............................. 197 A GMTI literature review 201 B Multichannel SAR (MSAR) signal formulation 215 B.1 Targetsignalmodel .............................. 216 B.1.1 1D (azimuth) signal modeling . . . . . . . . . . . . . . . . . . . . . 216 B.1.2 2D signal modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 B.2 Discussion on theoretical clutter signal modeling . . . . . . . . . . . . . . 232 B.3 SARprocessing................................. 235 B.3.1 Chirpscaling .............................. 235 B.3.2 Range Compression, RCMC and SRC . . . . . . . . . . . . . . . . 240 B.3.3 Azimuth focusing and phase correction . . . . . . . . . . . . . . . . 241 B.4 Mathematical derivations and approximations . . . . . . . . . . . . . . . . 243 B.4.1 Quadratic range phase in range-frequency Doppler domain . . . . 243 B.4.2 Range dependent phase after chirp scaling in Doppler domain . . . 245 Acronyms 247 Nomenclature 251 Bibliography 257 List of Figures 287 List of Tables 293 List of Publications 295 JournalArticles.................................... 295 ConferenceArticles.................................. 295 MasterThesisSupervised .............................. 297 Participation in R&D Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 xv Chapter 1 1Introduction This chapter is devoted to the describe the motivations that have led to the study carried out within this doctoral activity and the related main objectives to be fulfilled. The structure of this doctoral dissertation is also presented to point out specifically which are the main contributions of each chapter and how they are linked to the fundamental goals. 1 Chapter 1. Introduction 1.1 Motivation of the thesis More than 70 per cent of the Earth’s surface lies beneath the sea; phenomenas ongoing in, on and above the oceans have a direct consequence on our lives. Water is the principal component of Earth’s hydrosphere, is integral to all known life, makes part of the carbon cycle and influences climate and weather patterns. Therefore, monitoring the human related activities in the ocean is of key importance to prevent and mitigate their impact on this global ecosystem. The ocean is the habitat of 230.000 known species, and so an important source of food with 13 million tonnes of fish and seafood consumption in 2011 according to Food and Agriculture Organization (FAO) [1]. The Ocean has historically been one of the most important means of transport. Unlike in the past, ships currently carry goods rather than people. In the last decades, the globalization of the economy and the related increase of consumerism has lead to a tremendous expansion of the shipping market and flow [2]. According to latest available statistics from the European Commission (EC) [3], in 2012 a total of 1401 billion tonne-kilometer (tkm) of goods were transported by sea, only in 28-member European Union (EU); being the second most important mode after road transport (1692.6 billion tkm). It must be noted that maritime transport represents the most efficient mean with 13.9 percent of total CO2emissions from fuel consumption compared to the 71.9 percent of road transportation, the 12.8 % of civil aviation (with 3 billion tkm transported) and 0.6 % of railways (with 407 billion tkm) according to the EC statistics in 2012. Such figures demonstrate and justify the increasing importance of the sea in the global economy. This situation leads to newly emerging concerns, from the ecological, economical, social and geopolitical points of view; which define specific requirements for globally surveilling seas and oceans. Two main global human activities are jeopardizing the ocean ecosystems and consequently resources and our quality of life. Overfishing and the related overexploitation constitute one of the mainstream of ocean endangering problems. Many conservation organizations, such as World Wide Fund (WWF) and Save Our Seas Foundation (SOSF), have led studies to analyze the fishing patterns concluding that illegal, unregulated and unreported fishing accounts for an estimated 20 percent of the world’s catch and as much as 50 percent in some fisheries [4,5]. Moreover, a related problem is that an important part of the fishing catch is made of unwanted fish and other marine life, in a way that between 8 and 25 percent of the total global catch is discarded [6]. Another important thread for the ocean ecosystem are the marine spills of oil, chemicals and other hazardous substances, which have a dramatic ecological impact but also economic and political costs. The demand of the industrial nations and newly-industrializing emerging economies of energy and mineral resources have led to increasing quantities of oil (and related substances) being transported through oceans and seas. Oil tanker spills amounted 22 thousand tonnes during the last four years (2010-2013) according to not-for-profit organization International Tanker Owners Pollution Federation (ITOPF) [7]. Taking into account that more than 90 percent of the World’s trade goods and more than 70 percent of global crude oil are transported by sea, the maritime security becomes an issue of utmost importance. Due to the excessively increasing shipping traffic there is more likelihood of accidents and associated environmental damage and economic loss, but there is also spread of piracy attacks, smuggling and organized crime. In the same 2 1.1 - Motivation of the thesis way illicit activities, such as illegal fishing/overexploitation, weapon movement and illegal immigration are phenomenas of growing concern in the new millennium. In this framework, the governmental authorities all over the world have pointed out the necessity of setting up specific regulations on human activities in and over the seas and oceans to protect the marine environment and to ensure the related economical outcomes. However, such regulations require from entities that ensure their accomplishment by means of monitoring the vessels and ships’ activities. The first strategies for vessel monitoring were and still are mostly based on specific radio-frequency transponders located in the vessel that provide real-time information of the position, course and speed of ships. Among these, automatic identification system (AIS) [8], vessel traffic services (VTS) [9] and vessel monitoring system (VMS) [10] are widely used for ship monitoring (especially in coastal areas). Nonetheless, this sort of technology is not fully reliable since the vessels do not always transmit radio-frequency signals, precisely those intent on avoiding notice. In this sense, remote sensing has become a valuable procedure to gather and to analyze information about the Earth’s properties and dynamics. In a broad and simpler sense, remote sensing is understood as the distant acquisition of information about an object without being in physical contact. It refers to the science of collecting, processing and interpreting data resulting from the interaction between electromagnetic signal and matter. Satellite or spaceborne Earth observation (EO) has become crucial for remote sensing since it can grant the monitoring of the environment at a global scale, preventing and managing natural or industrial catastrophes, anticipating conflicts and administering crises. Protection and preservation (related to humanitarian, natural or technological risks) are mainstream fields of application for EO-based geoinformation services. The exploitation of radar technology for spaceborne remote sensing of the ocean has indisputable benefits since it provides an all-weather, all-day (independent of the solar light) wide-swath monitoring of the sea. The continuous advances in synthetic aperture radar (SAR) coherent systems, which provide high-resolution two-dimensional reflectivity images of tens of kilometers, has demonstrated the suitability of this technology for EO and particularly for maritime monitoring and surveillance. The launch in 1978 of SEASAT [11] represented an inflexion point for the oceanographic spaceborne remote sensing and for SAR-based missions. Since then, more than 15 spaceborne SAR missions have been operated with 10 more planned to be launched in the next few years. ground moving target indication (GMTI) is devoted to the detection of moving objects on the Earth’s surface (cars, trucks, ships and alike). The integration of GMTI modes in SAR allows additionally high-resolution imagery of the detected vessels when proper processing strategies are considered. Mainly, three different SAR-based approaches can be used for vessel surveillance: reflectivity-based SAR methods using single channel configurations, polarimetry and multichannel GMTI. Single channel SAR systems exploit the fact that vessels in general have greater reflectivity than the sea itself. Such systems are limited to the detection of vessels with high signal-to-clutter-and-noise ratio (SCNR) and they fail to identify moving vessels hidden by the sea returns, also referred to sea clutter as the ocean backscattering represents the unwanted signal. Migration towards multidimensional or multichannel SAR systems represents a more powerful approach. In this context, polarimetric SAR (PolSAR) exploits polarimetric 3 Chapter 1. Introduction diversity based on the different backscattering response of sea and vessels for detection of the latter. Nevertheless, there is no effective sea clutter cancellation, meaning that subclutter visibility for small boats cannot be accomplished. Moreover, it is not feasible to estimate velocity and direction of motion of the vessels with high accuracy. Multichannel SAR-GMTI take profit from the spatial diversity to suppress the interfering clutter signals before target detection can be performed; based on the associated inter-channel phase differences, which are distinct for clutter and moving targets. Target parameters of the detected vessels (e.g. along- and across-track velocities) can be also estimated. Extensive research in the multichannel GMTI field, driven mainly by military requirements, has resulted in the development of fully operational airborne GMTI systems for detecting land targets. Nonetheless, these manned aircraft-based sensors will not provide economically viable data sources for civilian applications, where the wide-area coverage is also a driven requirement. Spaceborne SAR-GMTI radars can overcome the spatial coverage of airborne platforms. To date, both the required technology and the related processing techniques, which could enable operative space-based SAR-GMTI missions, are not fully available. However, the rapid development in efficient, compact satellite design and in active phased array antenna (APAA) have changed the paradigm for SAR-GMTI, reducing capital costs and attracting investment in commercial satellites. Currently, there is no civilian spaceborne radar system with an operational GMTI mode; but state-of-the-art SAR missions, such as RS2 (C-band) and TSX (X-band), make use of the APAA technology to experimentally demonstrate the GMTI capabilities from spaceborne SAR instruments. These instruments are based on dual-receive antenna configurations, and with appropriate antenna switching and/or toggling strategies up to four virtual channels can be configured. Such missions have limited detection capabilities, especially when imaging small and slow moving targets with subclutter visibility. The operation of spaceborne SAR-GMTI has been widely evaluated for detecting land targets, with special interest on road traffic management; and a lot of effort has been devoted to the analysis and definition of the related processing strategies and algorithms. Nevertheless, multichannel SAR-GMTI is not yet being extensively employed in the maritime surveillance field for vessel detection. As a consequence, this thesis is mainly devoted to the study of the limitations of current SAR-GMTI missions when operated in maritime scenarios and the proposal of optimal multichannel SAR-GMTI architectures that allow subclutter detection of slow moving small (reduced reflectivity) vessels. Performance evaluation of such missions is key to the doctoral activity here considered, where both classical GMTI techniques as well as promising optimum algorithms have been tested. The limited access and availability of real spaceborne multichannel SAR-GMTI data, and the necessity of cost-effectively mission prototyping resulted in the development of flexible simulation tools to demonstrate the validity of the proposed mission architectures. Processing experimental multichannel SAR-GMTI data sets from airborne (F-SAR) and spaceborne platforms (TSX) over maritime scenarios has been also carried. The main goal is to foresee the peculiarities of processing real data with special emphasis on the inter-channel calibration, evaluating the most adequate processing strategies based on existing classical and promising GMTI algorithms. When evaluating SAR-GMTI capabilities over maritime scenarios, the lack of an accurate modeling of the complex sea clutter background results on one of the main limita- 4 1.2 - Objectives of the thesis tions to properly understand the real GMTI performance from spaceborne SAR missions. The interfering sea clutter has specific differential characteristics when compared to inland regions, where the internal clutter motion could be a limiting factor, producing additional decorrelation. In this sense, the availability of spaceborne polarimetric data over maritime scenarios from TSX has been exploited along the thesis, for a preliminary transversal characterization of the sea clutter returns when imaged by an X-band SAR sensor. A radiometric, statistical and polarimetric study has been carried out, emphasizing the system-driven limitations when modeling the ocean returns. It has been also demonstrated how to properly accommodate such system influences (thermal noise and temporal decorrelations) in the widely assumed Bragg surface model for the sea backscattering, exploiting the polarimetric dimension. The great advance in APAA, central for the further development of the SAR missions, and in particular of the SAR-GMTI sensors, allows a great degree of flexibility in the acquisition mode’s operation; but to fully exploit this kind of systems proper calibration strategies are mandatory. This doctoral activity has devoted special effort to the analysis of the current internal calibration methodologies on-board the SAR sensors based on APAA, proposing alternative methodologies to reduce the impact of internally-monitored errors on the final radiometry of the image. 1.2 Objectives of the thesis The encompassing objective of this doctoral work is the study and analysis of GMTI capabilities with spaceborne SAR sensors for maritime surveillance purposes; based on a transversal study going from the system proposal, passing by processing strategies evaluation, performance assessment and sea clutter characterization, to calibration methodologies recommendation. A detailed enumeration of the main objectives of the thesis follows: •Study and review of state-of-the-art in the GMTI field with special emphasis in the frame of spaceborne radar systems, which allows the derivation of a map of the current GMTI framework providing insights in the readiness and maturity of the actual SAR-GMTI systems and the applied techniques. •Development of flexible simulation tools for accurate SAR-GMTI performance evaluation and mission prototyping. The driven requirements are flexibility, modularity and integrability in the design of such software-based tools. Limited access to real multichannel spaceborne SAR-GMTI data requires a realistic simulation environment that can provide SAR-GMTI raw data for a user-defined system configuration/acquisition, supplying the means to evaluate the current GMTI techniques. •Analysis and evaluation of the GMTI capabilities of current state-of-the-art spaceborne SAR missions when operating over maritime scenarios, showing their limited efficacy for vessel subclutter visibility detection. Proposal of alternative multichannel SAR-GMTI missions exploiting the optimal GMTI processing strategies to enhance the detection of small and slow moving vessels masked by the sea clutter response, validating their potential improvement using proper realistic simulation environments. Assessment of the impact of imaging high-speed boats with SAR systems and how adequate processing strategies can be used to recover the induced 5 Chapter 1. Introduction degradation in terms of SAR-GMTI performance. •Evaluation of classical and optimum adaptive processing GMTI techniques applied to real data over marine environments acquired with airborne and spaceborne SARGMTI systems, in order to foresee the peculiarities of working with experimental data sets. Proposal of adequate processing strategies that provide the best performance possible. Validation of the refocusing capabilities of the adaptive SAR focusing algorithm integrated in the GMTI processing chain. •A characterization of the sea background in terms of mean power reflectivity, statistics and polarimetric behavior due to the lack of exhaustive studies to provide realistic modeling on the complex sea clutter scenarios. •Study and proposal of (internal) calibration strategies to minimize the impact of system-dependent errors in the final products’ radiometry of current spaceborne SAR missions, based on APAA. 1.3 Structure of the thesis This doctoral dissertation is organized in eight chapters. Additional information is also distributed in two appendices at the end of the thesis. This first chapter introduces the motivation and states the main goals of this work. Chapters 2 to 7contain the main contributions of this doctoral research. Each chapter focuses on one of the six main objectives previously detailed: •Chapter 2 gives a general overview of the GMTI framework recently exploited by spaceborne SAR missions. A brief review of the general concepts and the techniques is provided. Moreover, a theoretical-based model of the multichannel SAR-GMTI signals is developed at image level, fundamental for a proper theoretical performance evaluation. The exhaustive literature study introduced in appendix A represents the basis of the structured historical review presented in this second chapter. A detailed derivation of the moving target multichannel SAR raw data signal is reported in appendix B. •Chapter 3 describes and presents three simulation tools developed in the frame of this doctoral activity, which have been used to evaluate the GMTI capabilities of current SAR-GMTI missions as well as to propose alternative optimal GMTI spaceborne architectures for maritime surveillance. •Chapter 4 carries out an exhaustive SAR-GMTI performance evaluation using the implemented simulation tools, comparing current state-of-the-art SAR missions, such as TSX and TDX, with a new multichannel configuration using non-uniformly distributed receive phase centers and intended for GMTI applications over maritime scenarios, with the aim of detecing small and slow boats in subclutter visibility. •Chapter 5 is devoted to the GMTI processing of real multichannel SAR data using acquisitions over marine environments from airborne (F-SAR) and spaceborne (TSX) instruments, considering different state-of-the-art GMTI techniques. The refocusing capabilities of the integrated adaptive SAR processor when imaging moving vessels has been also demonstrated. Special emphasis is being placed on the appropriate inter-channel calibration or balancing and how this could impair the GMTI 6 1.3 - Structure of the thesis performance. •Chapter 6 presents a detailed characterization of the sea/ocean clutter returns at X-band imaged by TSX mission, using polarimetric data sets, and in a three-level basis: radiometric, statistical and polarimetric descriptors. The validity of different theoretical models has also been assessed; particularly, the impact of system-related limitations (as thermal noise and temporal decorrelation induced by the acquisition mode) in the physical backscattering model (X-Bragg) has been analyzed, proposing an extension known as X2-Bragg. •Chapter 7 introduces a novel approach in the instrumental error analysis of SAR systems based on active phased array antenna (APAA), defining a new term referred as post-calibration residual errors. Alternative (to the more widely used) internal global calibration strategies are proposed to reduce the impact of such errors. The document is concluded in chapter 8, summarizing the main results and contributions presented along the document as well as providing some insights on the eventual continuations of the present research. 7 2.2 - Moving targets in SAR imagery resolution imaging capabilities. MIMO operation provides more virtual phase centers and with larger baselines compared to the real array. Therefore, MIMO-SAR systems have higher sensitivity to slowly moving targets and at the same time provide improved clutter cancellation capabilities, [65], since this suppression is performed both in transmission as well as in reception [66]. Waveform design with adequate cross-correlation properties is a key point in the study of MIMO radars, since channel decorrelation is quite dependent on the quality of the waveforms [65]. From the GMTI point of view, channel decorrelation is critical for a proper operation as stated in [50] and observed from the studies carried out in Chapter 4. Reliable separation of the radar echoes from the simultaneous use of multiple transmit signals is mandatory for proper operation of future SAR-MIMO systems. The interested reader is referred to [64] for discussions on this topic. A step forward in the field of GMTI radars is the so called cognitive radar approach, intuitively described by Guerci in [67]. This type of system is a fully adaptive (transmit/receive) MIMO radar with knowledge-aided processing, where a dynamic (“learning”) database integrated in the real-processor chain uses both endogenous and exogenous information. In this way, the radar achieves some cognitive characteristics as “perceiving/sensing”,“remembering/database” and “thinking/adaptive algorithms”. This means that, e.g., in the case of maritime surveillance a low-complexity real-time GMTI processor on-board the platform could provide a preliminary detection. Then, for a region where an event is present the system redirects the resources towards that specific area of interest improving the detection with (possibly) higher resolution imaging capabilities. This historical review of the GMTI has been based on an exhaustive bibliographic research and study carried out during the initial phase of the thesis and it has been accordingly updated. In appendix A Table A.1 compiles more than 200 bibliographic references from early 80s, till 2014 specifying different classification concepts, giving a snapshot of the GMTI context and the related state-of-the-art. 2.2 Moving targets in SAR imagery SAR systems achieve high resolutions in the range direction through pulse compression of the wave-encoded chirp signal and the fine resolution in azimuth by means of crosscorrelating the theoretical stationary target’s phase response with the received data [23]. Hence, the SAR image formation requires to accurately model the imaging system, the transmitted signal, the acquisition geometry and its evolution through time. In case of moving targets the assumption of stationary world matched filter (SWMF) is not valid any more (filter mismatch), leading to non-correctly focused moving targets in the SAR image, which can become completely masked by clutter and noise. The study of the different impacts of imaging a moving object with a SAR sensor was originally developed by Raney in [25] and since then a lot of work has followed. For the interested reader comprehensive and intuitive descriptions as well as the mathematical foundations are thoroughly presented in the work of Sharma [68,69] and Baumgartner [70]. In the following lines a general review of the main impairments on moving target SAR imaging is reported. The aim is to stress the need to identify those effects and their origins, in order to developed proper processing SAR-GMTI strategies. In Chapter 4, where an optimized SAR-GMTI mission proposal is evaluated, the integration of target kinematics in the SAR processing step proves to be fundamental for the detection of 15 Chapter 2. GMTI with multichannel SAR (MSAR) systems (a) (b) (c) Figure 2.1: Moving vessels in SAR imagery: (a) F-SAR (X-band) image over the Elbe Mouth (19.11.2009), (b) ONERA BUSARD (Ka-band) image over Fos-sur-Mer close to Marseille (18.10.2012) and (c) TerraSAR-X acquisition over the Strait of Dover (01.05.2010). slowly moving targets; but even more important for high-speed boats, where the induced dynamics could ruin the performance due to SCNR degradation. In Chapter 5, where real experimental data has been processed, section 5.2.1 is devoted to the description of an adaptive SAR processor based on a MFB using the range-Doppler (RD) algorithm. High-resolution images of moving vessels have been recovered for F-SAR airborne data, where the longer integration time degrades their response when imaged with a SWMF. When performing conventional SAR processing under the assumption of SWMF, moving targets appear in general defocused/blurred and displaced from their actual position. In Figure 2.1, these effects can be observed when imaging moving vessels with different sensors. Fig. 2.1a corresponds to a high-resolution image (65 cm by 6 cm, range-azimuth) close the Elbe Mouth obtained with the airborne sensor F-SAR [71], where the vessels are sailing along the river. Azimuth defocusing on the vessels can be recognized probably induced by the along-track velocities and/or across-track accelerations over the long 16 2.2 - Moving targets in SAR imagery SWMF Moving target signal Backfolding moving target signal (a) SWMF (b) SWMF (c) Figure 2.2: Doppler histories (in time-frequency) of a moving target with different motion parameters (in blue) and of the SWMF (in red): (a) across-track velocity vz; (b) along-track velocity vx, across-track acceleration axand vertical (elevation) acceleration ay; (c) alongtrack acceleration ax;TSA and BCrefer to synthetic aperture time and clutter bandwidth, respectively (figures adapted from [70]). integration time (around 6 seconds). A high-resolution image of two tankers close to Marseille imaged by the Ka-Band SAR DRIVE [72] is shown in Fig. 2.1b. In this case, defocusing effects are not so evident probably because the vessels are anchored at the port of Fos-sur-Mer. In Fig. 2.1c, a TSX image over the Strait of Dover, the so called “ship-of-the-wake” effect can be clearly recognized, such that the across-track velocity (its projection to the line-of-sight) produces an azimuth displacement w.r.t the corresponding wake due to the induced Doppler shift, taking into account that SAR processors image the scene at its zero Doppler position. Compared to the airborne F-SAR case, azimuth defocusing is negligible for typical spaceborne synthetic aperture times TSA around 1 second. A schematic representation of the Doppler histories of a moving target in the timefrequency domain are depicted in Fig. 2.2. These graphs help understanding the impact of different motion parameters in the final SAR images. The vertical axis corresponds to the Doppler frequency and the horizontal to the slow-time (azimuth time). The signal of the moving target is represented as solid blue lines and the corresponding time-frequency representation of the SWMF is also included as solid red lines. Fig. 2.3 shows the impact of different motion parameters on the azimuth point spread function (PSF) of a simulated point-like target for the X-band system considered in Table 4.1. The target is located at an incidence angle of 33.17 degrees. Each motion parameter has been independently analyzed considering 150 MHZ and 2.8 KHz of processing bandwidths in range and azimuth, respectively, with a Kaiser spectral weighting of 2.5. In the following subsections the major impacts of the different motion parameters are briefly described. 2.2.1 Across-track velocity The projection of the across-track velocity into the line-of-sight, known as radial velocity, produces a wrong positioning (azimuthal shift) of the target in the final image. This misplacement is denoted by ∆ttin Fig. 2.2a, which corresponds to the azimuth time 17 Chapter 2. GMTI with multichannel SAR (MSAR) systems -440 -430 -420 -410 -400 Azimuth shift [m] -40.0 -30.0 -20.0 -10.0 0.0 Norm. to fixed target [dB] vz=10 m/svz=10 m/svz=10 m/s (a) -20 -10 0 10 20 Azimuth shift [m] -40.0 -30.0 -20.0 -10.0 0.0 Norm. to fixed target [dB] Fixed vx=10 m/s vx=20 m/s Fixed vx=10 m/s vx=20 m/s Fixed vx=10 m/s vx=20 m/s (b) -20 -10 0 10 20 Azimuth shift [m] -40.0 -30.0 -20.0 -10.0 0.0 Norm. to fixed target [dB] Fixed az=0.5 m/s2 az=5 m/s2 Fixed az=0.5 m/s2 az=5 m/s2 Fixed az=0.5 m/s2 az=5 m/s2 (c) -20 -10 0 10 20 Azimuth shift [m] -40.0 -30.0 -20.0 -10.0 0.0 Norm. to fixed target [dB] Fixed ax=0.5 m/s2 ax=10 m/s2 Fixed ax=0.5 m/s2 ax=10 m/s2 Fixed ax=0.5 m/s2 ax=10 m/s2 (d) Figure 2.3: Impact of different motion parameters on the azimuth PSF of a simulated point-like target for the X-band system defined in Table 4.1 at an incidence angle γ0of 33.17 degrees: (a) across-track ground velocity vz, (b) along-track velocity vx, (c) across-track ground acceleration and (d) along-track acceleration ax; the PSF of a fixed target in solid black line is also included for comparison purposes except in (a) (150 MHz and 2.8 KHz azimuth and range processing bandwidths using a Kaiser window with spectral weighting of 2.5). where the target is imaged. Ill-positioning in azimuth can be also caused when the target’s radial velocity is higher than half the PRF, due to Doppler aliasing: in this case the target is imaged at different positions (“real” target and its related ambiguities, known as “ghosts”). In Fig. 2.2a, ∆tamb corresponds to the time at which the ambiguous (backfolded) portion of the target is imaged. As the across-track velocity increases the spectral overlap between the target’s Doppler history and the SWMF decreases producing a widening of the PSF as well as degradation on its peak response. Therefore, the full Doppler bandwidth determined by the PRF should be considered in the processing to avoid filtering out fast moving targets. 2.2.2 Along-track velocity Along-track velocity produces defocusing of the azimuth impulse response since this motion parameter changes the quadratic part of the target’s range history (evolution of the distance during the acquisition time), which translates into a variation of the Doppler rate 18 2.3 - MSAR data model swath width antenna beam antenna footprint azimuth range swath far range near range x Elevation cut Figure 2.4: Multichannel SAR (MSAR) acquisition geometry. (slope) compared to SWMF. This effect is sketched in Fig. 2.2b, where negative alongtrack velocities vxand vertical accelerations ayas well as positive across-track ground accelerations azproduce an increase of the Doppler rate compared to the SWMF. The change on the range history curvature produces also a residual range cell migration (RCM) not properly compensated in the common SAR processors, such that the energy is spread among several range cells producing additional azimuth defocusing and range smearing. Fig. 2.3b presents comparatively the azimuth PSF when using a SWMF, assuming a fixed target as well as the same target with different along-track velocities vx. Similar effects are also obtained when changing the across-track acceleration as shown in Fig. 2.3c. Along-track velocity and across-track accelerations produce non-distinguishable effects and cannot be separated using only the Doppler slope information. In the same line and as analyzed in Chapter 4, vertical accelerations contribute to the radial acceleration, analogous to the across-track ones and hence these two components cannot be decoupled. 2.2.3 Along-track acceleration Along-track accelerations produce third-order phase errors in the range history or equivalently a deflection in the Doppler history as schematically represented in Fig. 2.2c, which become important for longer integration times like in the case of airborne systems. The major impact is a non-symmetric behavior on the sidelobes of the azimuth PSF as shown in Fig. 2.3d for an extreme and improbable acceleration of ax=10 m/s2. 2.3 MSAR data model In the following section a general data model at SAR image pixel level is described, required to understand the related operation of the different GMTI techniques working 19 Chapter 2. GMTI with multichannel SAR (MSAR) systems directly on SAR images, such as DPCA, ATI and EDPCA. This mathematical modeling is used in the theoretical performance evaluation presented in Chapter 4 for different SAR-GMTI missions and it is of key importance to properly interpret and analyze the obtained results. For GMTI techniques, such as ISTAP, working with range-compressed data in the Doppler domain and prior to image formation, this theoretical model can be extended to the range-Doppler domain as briefly described in section 2.4.2.2. Consider a general multichannel SAR configuration, consisting of Mparallel receivers (RXs) collocated in the along-track direction x, which are displaced {dxi}M i=1 from the transmit (TX) reference phase center as depicted in Fig. 2.4. A flat Earth geometry is assumed, such that the satellite, orbiting at Horb, moves with an effective velocity ve, [73]. The detection of the moving target, whose multichannel signal is denoted by s(ϑt), can be understood as a hypothesis testing problem H1:x=s(ϑt) + c(ϑc) + n H0:x=c(ϑc) + n(2.1) driven by the presence of interference q, which consists of background clutter c(ϑc) and thermal noise n.ϑt=vx, vz, R0, σ2 tand ϑc=vxc, vzc, R0, σ2 care parameter vectors of the moving target and clutter, respectively; where the first two elements of the vectors correspond to the along- and across-track velocities, with R0the slant range of closest approach (for the stationary scene) and the related power levels indicated by the sigma terms. 2.3.1 Signal The target, modeled as a single-like point scatter moves on the ground plane (y= 0) with a uniformly accelerated movement in both along-track (x) and across-track ground (z) directions, as generally assumed in the literature [16,69]: x(t) = x0+vxt+ax 2t2 z(t) = z0+vzt+az 2t2(2.2) where tstands for slow time (or azimuth time). At t= 0 the target is located at x0 and z0, which corresponds to the along- and across-track coordinates, respectively. The along- and across-track velocities of the target are represented by vxand vz, whereas their associated accelerations are axand az. The mutlichannel signal of the moving target, at resolution cell level, can be formulated using vectorial notation as: s(ϑt) = αt∆ATI (ϑt) (2.3) where it is assumed that the different SAR images have been properly co-registrated and balanced, [74]. It is well-known that the target RCS varies with the aspect angle for road traffic [26] as well as for maritime targets [75,76]. In case of a deterministic target model the RCS it is assumed to be constant during the synthetic aperture formation, such that for calibrated images, αtis directly related to the RCS square root. In (2.3), the term ∆ATI (ϑt) collects the ATI phase for the different channels at the displaced image position 20 2.3 - MSAR data model of the moving target: ∆ATI (ϑt) =    exp {ψt1(ϑt)} . . . exp {ψt1(ϑt)}   (2.4) when considering a focusing function matched to the quadratic part of the moving target’s range equation. In (2.2), as it is widely considered in literature [53,69], x0= 0 is assumed for simplicity in the mathematical notation without losing generality. Then, the interferometric phase component of the ith channel can be expressed as [69] ψi(ϑt) = πdxivr λ·1 ve−vx−ve v2 rel (ϑt)(2.5) where λis the carrier wavelength; vrrefers to the radial velocity, i.e., line-of-sight projection of the ground range velocity vr=vzsinγ0, where γ0is the incidence angle; and the relative velocity term vrel is expressed as: vrel (ϑt) = s(vx−ve)2+v2 z1−z2 0 R2 0+z0az(2.6) A more realistic modeling, which accounts for the target’s random variability on the radar response, is a zero-mean complex Gaussian scattering center, [77], i.e. αt∈C∼ N0, σ2 t=RCS. Then, the multichannel target signal s(ϑt) is characterized by its covariance matrix Rt=Ens(ϑt)s(ϑt)Ho=      σ2 t1. . .ρt1,M qσ2 t1σ2 tMe∆ψt1,M . . ..... . . ρt1,M qσ2 t1σ2 tMe−∆ψt1,M . . . σ2 tM     (2.7) where (·)His the Hermitian and complex conjugate operator; and E{·} the statistical expectation. Decorrelation effects induced either by the own movement of the target or by the internal clutter motion (ICM), [78,79], can be modeled through the correlation coefficient between each pair of channels ρti,j . ∆ψti,j refers to the ATI phase between the ith and jth channels. 2.3.2 Interference GMTI processing intends to detect moving targets masked by the presence of interference, consisting of the background clutter c(ϑc) and the unavoidable thermal noise nof the receiver2. The latter is generally modeled as a zero-mean complex Gaussian process, n∈C∼ N (0,Rn). The noise has neither a temporal nor a spatial structure, Rn=σ2 nI, 2In the Military field Jammers are sources of additional interference, but are not considered through the thesis. 21 Chapter 2. GMTI with multichannel SAR (MSAR) systems where Istands for identity matrix (unitary diagonal matrix). For calibrated SAR images the noise mean power is related to the noise-equivalent sigma zero (NESZ) and the ground resolution cell area. The clutter has specific temporal and spatial correlations, which account for both temporal and spatial variability of its radar returns. As it is extendedly considered in the literature [29,44,45, 80], the clutter is assumed to have a stationary zero-mean complex Gaussian distribution c(ϑc)∈CMx1∼ N (0,Rc). This hypothesis breaks down when considering realistic scenarios that may contain highly heterogeneous terrains, such as urban or industrial areas [50]. In the maritime case, it has been widely assumed that a K- distribution (compound model) fits well the sea clutter returns [81,82]. In Chapter 6, the statistical characterization of an X-band sea clutter using TSX polarimetric data shows a good fitting of the K-distribution to the magnitude. In this regard and to complement the mission performance evaluation carried out in Chapter 4 a K-distributed sea clutter has been also considered in order to understand the impact of non-Gaussian statistics. A way to provide a more realistic maritime scenario is two-folded: account for specific clutter decorrelation between the different channels induced by the ICM and the inclusion of an ATI phase, which can be related to a mean surface velocity on the sea structure. In this sense, the covariance matrix of the clutter Rccollects those parameters as Rc(ϑc) = Enc(ϑc)c(ϑc)Ho=    σ2 c1. . .ρc1,M pσ2 c1σ2 cMe∆ψc1,M . . ..... . . ρc1,M pσ2 c1σ2 cMe−∆ψc1,M . . . σ2 cM   (2.8) where σ2 cirefers to the clutter power for the ith channel, which is related to the normalized radar backscattering coefficient σ0and the ground resolution cell area. For maritime scenarios, this coefficient can be obtained from several semi-empirical models given specific system parameters (frequency, polarization, incidence angle) and scenario conditions (sea state or wind velocity). For further details the reader is referred to section 6.2.1, where a brief review of the most extendedly used σ0models is presented. The phase term ∆ψci,j in (2.8) represents the ATI phase between channels iand jdue to a mean Doppler velocity induced by the clutter scattering points within a resolution cell [83]. This mean Doppler velocity includes the current surface (line-of-sight or radial) velocity of the sea, as well as two other components [83]: the phase velocity of radially traveling Bragg-resonant surface waves (major backscattering mechanism) and the orbital velocity of the gravity waves. In (2.8), the correlation coefficient ρci,j between channels iand jtakes into account the temporal decorrelation induced by the ICM and is related to the (baseline) time-delay τi,j between those two channels (equivalent two-way phase center). From [79] and under the assumption of Gaussian distributed clutter, the ρci,j has a Gaussian-like shape: ρci,j = exp (−τi,j τc2)= exp     −   (dxi−dxj)·ve 2·v2 rel(ϑc) τc   2    (2.9) 22 2.3 - MSAR data model Figure 2.5: Grid of clutter patches: main clutter patch (in red) and the related ambiguous clutter patches (in green) due to the combined range-azimuth ambiguities. where τcis the clutter correlation time, which for an X-band system can vary between 10 to 60 ms, depending on the sea conditions and system resolution, [83,84]. As the radar measures range and (Doppler) velocity ambiguously, the moving target competes also with ambiguous clutter patches. Therefore, for the main non-ambiguous clutter patch (Fig. 2.5 in red), a grid of ambiguous clutter responses (Fig. 2.5 in green) should be also considered when modeling the clutter [26,27,29,44,45]: c(ϑc) = αc∆ATI (ϑc) + Namb X k,l αck,l ∆ATIk,l (ϑc),(k, l)∈Z2\{0,0}(2.10) where αcand αck,l refer, respectively, to the reflectivity of the main clutter and the ambiguous k, lth clutter patch (associated to the kth range and lth azimuth ambiguity). In (2.10), (k, l)∈Z2\{0,0}denotes the set of those whole-numbered index pairs of admissible range-azimuth ambiguities except for k=l= 0, which refers to the nonambiguous clutter patch of interest. The vectors ∆ATI (ϑc) and ∆ATIk,l (ϑc) collect the ATI-phases induced by the clutter’s mean Doppler velocity, accordingly. Considering a homogeneous (stationary) complex Gaussian sea clutter surface and uncorrelated ambiguities, the interference covariance matrix can be expressed as Rq(ϑc) = Rc0(ϑc) + Namb X k,l Rck,l (ϑc) + Rn,(k, l)∈Z2\{0,0}(2.11) where Rc0(ϑc) is the covariance matrix for the main3clutter patch [as expressed in (2.8)]. Assuming the same sea correlation properties as for the main patch, the covariance matrix for the k, lth ambiguous patch is analogously defined by Rck,l (ϑc) = Enck,l (ϑc)ck,l (ϑc)Ho=      σ2 ck,l 1 . . .ρc1,M qσ2 ck,l 1 σ2 ck,l M e∆βl 1,M . . ..... . . ρc1,M qσ2 ck,l 1 σ2 ck,l M e−∆βl 1,M . . . σ2 ck,l M     (2.12) 3From now on the subindex 0 refers always to the main clutter patch. 23 Chapter 2. GMTI with multichannel SAR (MSAR) systems The off-diagonal phase terms of Rck,l (ϑc) are modeled as ∆βk,l i,j = ∆ψci,j −2π·l·PRF ·dxi−dxj·ve 2·v2 rel (ϑc)(2.13) The first term in (2.13) accounts for the interferometric phase ∆ψci,j induced by the clutter’s mean Doppler velocity. The second term models the residual phase due to wrong channel coregistration on the ambiguities as pointed out in [29]. This spatial alignment (coregistration) is accomplished by time-shifting the signals of the different channels via interpolation, efficiently performed applying a phase ramp in the Doppler domain. Due to partial backfolding of the different Doppler ambiguities, this phase ramp produces a residual constant phase error [52], modeled by the second phase term in (2.13). This residual error vanishes when the DPCA condition holds, i.e., the satellite’s displacement between pulses is a multiple of the baseline separation between the involved channels. For simplicity the main clutter and the related ambiguous patches are assumed to have equal radar backscattering coefficient σ0(homogeneous open sea conditions). In this case, the power of the k, lth ambiguous patch for the ith channel can be expressed as σ2 ck,l i=σ2 ci·CRAASRk,l (2.14) where CRAASRk,l refers to the combined-range-azimuth-ambiguity-to-signal ratio for the k, lth ambiguity. This new defined metric provides a single SAR ambiguity performance metric that combines the definition of both the azimuth-ambiguity-to-signal ratio (AASR) as well as the range-ambiguity-to-signal ratio (RASR) [23] for the grid of Namb ambiguities4: CRAASR = Namb X k,l CRAASRk,l,(k, l)∈Z2\{0,0} = Namb X k,l R3 0·sin(γ0)·|D2−w(θk,l, φk,l)|2 R3 k,l ·sin(γk,l)·|D2−w(θ0, φ0)|2·RBa/2 −Ba/2|P2−w(fd+l·PRF)|2df RBa/2 −Ba/2|P2−w(fd)|2df (2.15) where R0and Rk,l correspond to the slant range for the main and the k, lth ambiguous clutter patches, respectively; γk,l refers to the incidence angle for the k, lth ambiguous clutter patch. The impact of the two-way antenna patterns is accounted for in the D2−w(θk,l, φk,l) term, where θk,l and φk,l are the spherical angles in the antenna coordinate system for the specific ambiguous clutter patch. The term P2−w(fd) models the Doppler spectrum, including the antenna pattern and the azimuth window used in SAR focusing for a specific (azimuth/Doppler) processing bandwidth Ba. 4In case of AASR only the impact of the (azimuth) ambiguities with the same iso-range as the patch of interest is included in the definition (varying l6= 0 for fixed k= 0 in CRAASR definition). Analogously for RASR, solely the ambiguities from broadside (zero-Doppler) and at different ranges w.r.t the patch of interest are considered (varying k6= 0 for a fixed l= 0 in CRAASR definition). In this sense, and taking into account that a grid of Namb ambiguities around the main clutter patch exist, the different combinations of range-azimuth ambiguity pairs are accounted for in the CRAASR definition, which are accordingly weighted by the two-dimensional antenna pattern. Therefore, in the CRAASR not only the two main axial ambiguities (as considered by AASR and RASR) are included in the ambiguity performance but also any other possible combination in the two-dimensional plane around the main non-ambiguous clutter patch. 24 2.4 - GMTI processing techniques 2.4.2.3 Extended DPCA (EDPCA) EDPCA is an adaptive optimum processing technique proposed by Cerutti et. al in [29]. EDPCA is an extension of the classical DPCA and ATI algorithms for architectures with more than two receiving channels, exploiting a sub-optimal STAP algorithm, which uses only the spatial DoF. The different steps of the EDPCA algorithm can be traced from the flow chart of the implemented SAR-GMTI processor at image level, in Fig. 5.13, integrating EDPCA, DPCA and ATI techniques, and used for real data evaluation. After range compression, the different channels are spatially coregistrated and (if necessary) balanced/calibrated. In order to maximize the target SCNR (before clutter cancellation), an adaptive SAR processing (for every channel) is performed via a MFB, where the different kinematic parameters are properly considered in both range cell migration correction (RCMC) and azimuth focusing steps9as described in section 5.2.1. The required number of filters to be integrated in the MFB depends on the accepted loss in SCNR when compared to the ideal case. Some insights are given in section 4.3.2, when considering the case of imaging high-speed boats with vertical and horizontal accelerations. According to [13,67,101], the weights of the clutter cancellation filter that maximize the SCNR at EDPCA processor’s output, y=wH(ϑt)x, are : w(ϑt) = βR−1 q(ϑc)d(ϑt)∈CMx1(2.25) where d(ϑt) refers to the spatial beamformer adapted to the target parameters, such that phase differences between the channels are compensated d(ϑt) = ∆ATI (ϑt)∈CMx1(2.26) The theoretical interference covariance matrix Rqcan be pre-computed if system, instrument and clutter parameters are perfectly characterized a priori. Otherwise, Rqis replaced by its maximum likelihood (ML) estimation (sample covariance matrix) b Rq(ϑc,ϑt) = 1 P P X p=1 xp(ϑc,ϑt)xH p(ϑc,ϑt)∈CMxM (2.27) where {xp(ϑc,ϑt)}P p=1 correspond ideally to Pindependent and identically distributed (i.i.d.) pixels of training data over an homogeneous region, where no target is present, avoiding the so called moving target self-whitening. As pointed out in [105] “a rule of thumb” to achieve a minimum degradation of 3 dB in the SCNR performance, requires the number of i.i.d. Psamples to be greater than 2M. The dependency of b Rqwith ϑt has been included to point out that the estimation is performed over the MSAR images adapted to specific target kinematic parameters, i.e., for a given iteration of the MFB. In order to have CFAR test statistics at the EDPCA processor’s output, the scalar 9No compensation of the Doppler shift (azimuth shift) is carried out, since, otherwise, the target will appear at different azimuth positions for different vzof the filter bank, posing difficulties to efficiently compare the outputs of the bank of filters. 31 Chapter 2. GMTI with multichannel SAR (MSAR) systems term βin (2.25) is properly chosen as: β=1 qdH(ϑt)b R−1 q(ϑc,ϑt)d(ϑt) (2.28) ensuring a unitary power residual interference. Similar to DPCA, the output’s magnitude is compared against a threshold for a given Pfa. 2.4.2.4 Imaging STAP (ISTAP) In classical GMTI operation STAP is operated as filter with no image formation process. In this sense, Cerutti has proposed in [28] the ISTAP algorithm, efficiently integrating a post-Doppler STAP in the SAR processing chain, such that well-focused SAR images of moving targets are obtained. The clutter cancellation is performed in the Doppler domain and per Doppler bin only using the spatial DoF. This approach works well under the assumption of interference decoupling between the different Doppler bins, which for moderate synthetic aperture times is fulfilled [44,45]. Contrary to classical factored STAP techniques, ISTAP does not perform any segmentation of the acquisition time into short coherent processing intervals (CPIs), but instead processes the whole integration time (through SAR focusing) maximizing the output SCNR. A full processing chain integrating ISTAP with a SAR processor based on a MFB has been implemented for real data operation, see flow chart in Fig. 5.14. Contrary to EDPCA, in ISTAP the interference covariance matrix is estimated once and not for every filter of the MFB. This means also that clutter cancellation (by means of R−1 q) is performed only once. Moreover, SAR processing (per each adaptive filter) is applied over a single range-compressed and clutter canceled image, while in EDPCA Mindependent SAR images should be processed per MFB iteration. From these considerations, it is clear that ISTAP is computationally more efficient. In this case the Doppler-dependent interference covariance matrix is estimated for each Doppler bin averaging over a set of Prange cells, as done in post-Doppler STAP: b Rq(fd,ϑc) = 1 P P X p=1 xp(fd,ϑc)xp(fd,ϑc)H∈CMxM (2.29) The ISTAP Doppler-dependent weights before SAR focusing can be written as w(fd,ϑt) = b R−1 q(fd,ϑc)d(ut, fd,ϑt) qdH(ut, fd,ϑt)b R−1 q(fd,ϑc)d(ut, fd,ϑt)∈CMx1(2.30) where d(ut, fd,ϑt) corresponds to the steering vector, which compensates for the phase differences between the different channels for that moving target, incorporating the twoway receive antenna pattern information. This beamformer corresponds to the product of diagonal matrices D(fd,∆fd,ϑt) (antenna pattern) and ψ(fd,∆fd,ϑt) (beamformer phase) as defined in (B.32) and (B.33). Such a formulation can be traced from the detailed mathematical derivation of the multichannel SAR raw data signal of a point-like moving target presented in Appendix B. After SAR processing (RCMC and azimuth-compression) for each filter in the MFB the magnitude at ISTAP output is compared against a threshold for a given Pfa. 32 2.5 - Concluding remarks 2.5 Concluding remarks A general picture of the GMTI framework has been described in this chapter, based on a comprehensively review of the GMTI state-of-the-art. In this way, it is easier to understand the limitations of current SAR missions to detect slow and small moving objects with especial emphasis on the maritime scenario and the need to define optimized SAR-GMTI configurations to this purpose. The level of maturity and readiness of the SAR-GMTI for spaceborne operation is low; there is still a lot of work to be done, especially in the case of maritime surveillance from space platforms. The impact of moving targets on SAR imagery has been briefly reviewed. The knowledge about these effects is essential for the proposal of adequate processing strategies: the induced image and radiometric degradations of moving targets when imaged by a SWMF could ruin GMTI performance if the related kinematics are not properly considered. A multichannel SAR data model at image level has been also derived. This mathematical formulation constitutes the basis of the theoretical performance evaluation of any SAR-GMTI mission when considering GMTI techniques that operate at image level, such as DPCA, ATI and EDPCA. In this derivation it has been stressed the need to properly account for the ambiguities’ impact, which could play an important role in the expected SAR-GMTI performance. In this sense, the CRAASR has been defined to unify the impact of the combined range-azimuth ambiguities in a single ambiguity metric. Classical dual channel GMTI techniques, such as DPCA and ATI, have been described, since they are of special interest for current SAR-GMTI missions, equipped at most with two parallel receivers. Such configurations provide limited detection capabilities and additional spatial diversity (additional phase centers) is required to exploit the optimum adaptive techniques based on STAP, resulting in enhanced GMTI performance. A brief description of STAP concepts has been also carried out, with special emphasis on the sub-optimum post-Doppler technique that has received lately special attention by the SAR community. Based on the data model at image level, a simplistic formulation in the range-compressed Doppler domain has been derived, which demonstrates to be useful for preliminary validation of some mission when using a post-Doppler approach. The promising SAR-GMTI techniques as EDPCA and ISTAP, which exploit optimally the spatial DoF, have been also reviewed. Lately, the efforts in the GMTI research are directed to rethink the operation of GMTI in combination with promising modes as HRWS SAR and MIMO SAR. This would allow a wide area surveillance system with high-resolution imaging capabilities. Therefore, new processing algorithms should be proposed, where system complexity and computational load reductions are the driven requirements. 33 Chapter 3 3Multichannel SAR (MSAR) simulation tools To understand the limitations of current state-of-the-art SAR-GMTI missions as well as to evaluate the applicability and performance of different GMTI processing techniques on new mission concept designs, the implementation of flexible simulation tools plays a pivotal role in the research carried out through this thesis. The restricted access to experimental raw data and the limited number of spaceborne SAR sensors with GMTI capabilities has suggested the necessity to define and develop different simulation systems (with different levels of complexity). These tools facilitate the transversal assessment and validation of SAR-GMTI missions from the architectural configuration to the processing techniques, passing by the appropriate modeling of the calibration requirements. This chapter describes the three main simulation tools developed within this doctoral activity. The first part is devoted to introduce the multichannel SAR raw data simulator (MSARRDS). In the second part of the chapter, a SAR-GMTI mission performance tool is presented, based on theoretical characterization of both SAR and GMTI operation. Finally, a Monte Carlo (MC) like performance simulator is described. 35 Chapter 3. Multichannel SAR (MSAR) simulation tools Moving targets Sea clutter Moving targetsSpaceborne radar Figure 3.1: Schematic representation of the spaceborne GMTI paradigm. 3.1 Introduction The prohibitive cost of constructing and testing spaceborne radar prototypes for future missions has motivated the necessity to further develop simulation technologies that can help in the development process. The rapid evolution of the electronic technology, allowing powerful computing resources in general-purpose machines, jointly with the availability of precise mathematical models for the spaceborne radar paradigm, Fig. 3.1, enables the implementation and validation of radar missions in reasonable times. A lot of effort has been devoted to the proper simulation of radar operation from the research/academic point of view [31, 106–110] to the commercial one [111–114], where fidelity and speed are the main driven parameters. The conceptual definition, design and implementation of radar simulation environments is a complex process, which requires the merging of multidisciplinary knowledge (system engineering, mission performance, signal processing and algorithms’ coding). In this sense, proper design strategies are required to deal with sophisticated simulation environments; some guidelines to emulate radar systems can be found in reference textbooks as [115–117]. With proper conditioned simulation tools, spaceborne SAR-GMTI radar missions (or general purpose radar) can be accurately modeled, such that a complete and exhaustive performance evaluation can be carried out under different design parameters, operating system and scenario conditions, considering the related trade-offs. In this way, they can be used to design optimized radar system configurations, and at the same time to test potential processing algorithms. The schematic representation of the spaceborne GMTI paradigm, shown in Fig. 3.1, allows understanding the general problem of emulating and modeling the operation of an imaging radar that should be able to detect moving targets on the Earth surface. Fig. 3.1 helps breaking down this complex conglomerate into different macro conceptual modules that can be separately modeled and designed, which in turn can be used either as an integral part of a hierarchical-like simulator or as an isolated simulation entity. The flying platform that carries the sensor should be properly modeled and parametrized, taking into account the basic operational parameters (frequency, bandwidth, PRF, re- 36 3.2 - Multichannel SAR raw data simulator (MSARRDS) ceiver noise and alike), the number of receiving channels and the antenna pattern integration. This latter plays an important role when considering the accurate impact of radar ambiguities and possible system-dependent errors in the SAR-GMTI performance evaluation. The acquisition geometry and so the coordinate system should be properly characterized upon a given level of complexity, especially when a realistic orbital simulation is expected. Accuracy and fidelity on modeling realistic environments (scenarios) to validate the GMTI capabilities of any radar mission, is one of the most demanding and complex topics to be faced when implementing such simulation tools. The environment model includes both moving target and background clutter; and for the particular case of SAR-GMTI over maritime scenarios, additional considerations to account for the internal motion of the sea clutter should be made. Different approaches have been proposed to properly emulate the radar response of sea clutter, following a physical (electromagnetic) description [118–121], or as in [49,122–124] trying to extrapolate the electromagnetic interaction between the radar signal and the sea to a stochastic process. A statistical-like approach has been considered in the different implemented simulation tools to model the impact of background clutter (for given spatial and temporal correlations), since one of the main objectives of the thesis is the validation of SAR-GMTI missions using different processing algorithms. Further research and discussions on sea clutter statistics and characterization at SAR image level are carried out in Chapter 6, with experimental data from the spaceborne TSX mission. The design of any radar simulation tool should be flexible enough to accommodate different design options in terms of system configurations and processing algorithms so that different system/techniques can be optimized. At the same time it should be able to simulate selectable scenario conditions (using a data base of target models and clutter parameters), such that the performance of any SAR-GMTI mission/processing technique can be fully characterized and compared in a wide variety of realistic acquisition scenarios. 3.2 Multichannel SAR raw data simulator (MSARRDS) One of the objectives of this thesis is to evaluate the applicability and performance of GMTI techniques using spaceborne SAR platforms in order to understand their limitations, allowing the proposal of optimized system configurations as well as adequate processing strategies. In the framework of this doctoral activity, a raw data simulation tool is defined and developed, providing SAR-GMTI data sets for user-defined scenarios and system configurations. With this tool the different GMTI processing/detection techniques can be assessed and validated, for any given configuration and system parameter specifications, at any time and with a reduced cost. The requirements defined for this SAR-GMTI simulator tool are: •Flexibility in the system configuration, acquisition and scenarios definition •Emulation of realistic potential scenarios 37 Chapter 3. Multichannel SAR (MSAR) simulation tools Process condition? ANTENNA PATTERN GENERATOR SENSOR/SYSTEM DEFINITION SCENARIO DEFINITION SIMULATION DEFINITION BUS (Parameters exchange) Yes No Process condition? RAW DATA GENERATOR Yes No Process condition? PROCESSING STAGE Yes No INPUTSOUTPUTS Antenna Pattern file Raw data files SAR images SAR-GMTI images Detection maps Monte Carlo Figure 3.2: Block diagram of the multichannel SAR raw data simulator (MSARRDS). •Mono- and multistatic acquisition configurations •Integration of GMTI as well as SAR processing techniques •Evaluation and performance analysis of the different GMTI techniques The software implemented in this thesis sets the basis for the development of part of the SImulator for Moving Target Indicator SYStem (SIMTISYS) [31], an FP7 Copernicus research project to support EU’s maritime surveillance with the aim of improving citizen security and environmental monitoring. The SIMTISYS simulator will be a useful and powerful tool, which will assist users (coast guard authorities) with the detection and tracking of vessels in the context of pre-defined scenarios. The SIMTISYS consortium is formed by seven partners from three European countries with extensive experience in the field of Maritime radar surveillance and spacebased simulation tools. 3.2.1 Simulator structure definition and design During this thesis special effort has been devoted to develop a system-level simulator, whose basis is flexibility, modularity and interoperability at both system configuration and processing stages. In this way, different levels of complexity can be easily incorporated when modeling/defining both raw data generation as well as processing. Single and multichannel acquisitions can be configured, such that additional operational modes can be efficiently integrated. Emulating realistic clutter is a key point for proper evaluation of the SAR-GMTI missions along with the involved processing algorithms. In this sense, maritime environments represent challenging scenarios to be simulated. Therefore, an adequate clutter modeling is required, enabling a versatile operation, while keeping efficiency as a driven characteristic of the generation process. Fig. 3.2 shows a simplified high-level description of the simulator flow chart. Four main components can be differentiated: (i) the input interface, where the system configuration, scenario and simulation options are defined; (ii) the interconnecting bus, where the different information is accordingly exchanged between the different entities of the 38 3.2 - Multichannel SAR raw data simulator (MSARRDS) simulator and it is also in charge of managing the workflow, i.e., the sequence of tasks to carry out a simulation activity; (iii) the core of the simulator, which consists of three main modules (antenna pattern generator, raw data generator and the processing stage); and (iv) the output interface, where the different results (intermediate and final products) are provided to the user in terms of figures or text files. 3.2.1.1 Inputs definition As an input to the simulator three main definition blocks are specified (sensor, scenario and simulation), encapsulated as independent structures of parameters. Sensor definition The configuration of the flying platform is characterized in terms of: •Radar and operation mode parameters: frequency of operation, pulse duration, bandwidth, PRF, incidence angle, platform, spot and effective velocities1. •Instrument hardware configuration: number of transmit and receive channels, antenna configuration and type, tilt and squint angle acquisition2. •Antenna tapering configuration, indicating the type of tapering both in the vertical and horizontal dimensions of the antenna, being subswath and pulse sequence (toggling/switching modes) dependent. •Polarization configuration, either HH or VV. •Front end: transmitted peak power, noise figure and receiver/transmitter losses. Scenario definition The scene/environment to be simulated is described by means of: •Ground extension (in range and azimuth), beam of operation, and incidence angles at center, near and far range. •Clutter type (land or sea), azimuth and range separation of the scattering points, radar backscattering coefficient model, and temporal/spatial correlation properties. •Moving target parameters: ground (along-, across-track and vertical) velocities and accelerations, positions w.r.t the center of the scene and RCS. At this point it must be noted that one of the main difficulties in modeling sea clutter, aside from its simulation (section 3.2.1.3) and statistical description (analyzed in chapter 6), has been to find an appropriate model of sea radar backscattering coefficient σ0. The fundamental requirement was to find a mathematical model properly parametrized in order to allow a certain degree of flexibility when simulating different operating and scenario conditions. Moreover, the model should be able to provide realistic values of σ0for spaceborne SAR imaging acquisitions. Due to the high variability and randomness of the 1The different parameters in the mode of operation structure can be defined as subswath dependent, when operating with different beams to cover different incidence angles. 2The antenna configuration (length, height, number of elements in TX/RX for an active array, separations, physical positions of receiver channels) can be specified for each TX/RX channel for each subswath, and for each pulse sequence when using toggling/switching modes of operation, [45]. 39 Chapter 3. Multichannel SAR (MSAR) simulation tools ocean conditions, a theoretical (analytical) description of its reflectivity using microwave frequencies is not yet available. A lot of effort has been devoted to develop semi-empirical models that could relate the σ0to radar parameters, acquisition geometry and sea conditions. The most representatives are: the Georgia Institute of Technology (GIT) [125], the Hybrid (HYB) [126], the Technology Service Corporation (TSC) [127] and the Naval Research Laboratory (NRL) [128]. The TSC and NRL models have been integrated in MSARRDS, since they provide the widest range of incidence angles, covering most radar bands of interest. Further discussions on the available σ0models can be found in section 6.2.1. Simulation definition In the simulation parameters definition block specific operation conditions and flags are activated and/or inputed giving control over the simulation process and its different stages. In this manner, the raw data generation block can be activated/deactivated, with the possibility to pass specific external (raw) data files to the processing stage. It also incorporates flags to consider the inclusion, one by one, of moving targets, clutter and/or thermal noise. As it is discussed in section 3.2.1.3, there are different selectable ways to generate raw data for the clutter. Like for the raw data generation, the antenna pattern computation stage can be turned on/off, feeding the current simulation with a new antenna pattern or using one already generated. The simulator includes also the option of running different trials as part of a Monte Carlo performance evaluation approach, such that different sets of raw data are generated and accordingly processed. The type of processing to be carried out can also be chosen, specifying the SAR processing parameters (processing bandwidths and windowing type), GMTI technique (DPCA, ATI, EDPCA and ISTAP) and multilooking. As a pre-processing operation, channel balancing/calibration and coregistration are optional operations. The CFAR detection approach can be also selected, using a sliding window approach or selecting a portion of the image for interference statistical parameters’ estimation. Once the detection map has been generated the detected pixels can be clustered for further post-processing purposes. If desired, the user, through the simulation definition block, can indicate whether intermediate figures and/or data products, mostly related to the processing stage, should be saved for their further inspection and analysis. 3.2.1.2 Antenna pattern generation A dedicated module, Fig. 3.3, has been implemented to accurately model the antenna patterns of any multichannel configuration, based on the specified input antenna structure. The output of the module is also a data structure containing for each channel: (i) the two-dimensional gain pattern in transmission and reception, as a function of the antenna angles θand φ; (ii) the elevation and azimuth antenna pattern cuts and (iii) the related 3 dB beamwidths for TX and RX. It must be noted that in case of toogling/switching operations [45], the corresponding antenna patterns are also computed, since the antenna configuration can be modified from pulse-to-pulse. The user can indicate the step size 40 3.3 - MSAR-GMTI mission theoretical performance tool 3.2.1.4 Processing stage The raw data cube is passed to the processing stage, see Fig. 3.7, providing different final products: (i) a stack of SAR images, per channel and per iteration, in case of MFB processing; (ii) the SAR-GMTI images, for each selected processing technique; and (iii) the corresponding detection maps. Both SAR and SAR-GMTI images can be expressed in terms of SCNR metrics to facilitate the performance comparison of the different GMTI techniques. The simulator integrates an adaptive range-Doppler processor, based on a MFB, to compensate for the induced imaging degradations, maximizing the moving target response. A detailed description of such a processor is presented in section 5.2.1. Processing bandwidths, spectral windowing and MFB’s specifications are input parameters that can be selected. Three main GMTI processing techniques can be selected to obtain the aforementioned products: DPCA, ATI, EDPCA and ISTAP. For the classical dual-channel techniques (DPCA and ATI), the user indicates which channel combinations to be used (for more than 2-receiver configurations). Processing chains similar to the ones depicted in Fig. 5.13 and Fig. 5.14 have been incorporated to the processing stage, for further details the reader is referred to sections 5.2.2 and 5.2.3. 3.3 MSAR-GMTI mission theoretical performance tool To complement the raw data SAR simulator a modular performance analysis tool has been developed. The aim of this flexible software is to evaluate the potentiality of general purpose multichannel SAR missions, with emphasis on the GMTI capabilities, such that the expected performance can be anticipated with reduced computational cost, based on a theoretical modeling and description of the SAR-GMTI operation. In this regard, an efficient optimization of the SAR-GMTI mission can be accomplished for a given set of mission requirements. Fig. 3.8 depicts a high-level description of this performance tool, where the input parameters and specifications are based on data structures (loaded to a bus for their exchange), profiting from the same definitions considered in the raw data simulator. A similar conceptual architecture to the MSARRDS has been defined. Three main input blocks can be distinguished: •Sensor definition: configuration parameters (frequency, number of channels, baselines, antenna type, noise factor and alike) and access range (number of beams and the related incidence angles to be operated). •GMTI processing: technique to be selected (DPCA and EDPCA in current version), channel combination and processing bandwidths (and windowing type). •Scenario definition: –Target: type (deterministic or complex Gaussian), velocity, RCS and coherence time for Gaussian target modeling. –Clutter: radar backscattering coefficient σ0, coherence time and mean surface velocity. 47 Chapter 3. Multichannel SAR (MSAR) simulation tools Process condition? ANTENNA PATTERN GENERATOR GMTI PROCESSING SCENARIO DEFINITION SENSOR/SYSTEM DEFINITION BUS (Parameters exchange) Yes No SAR PERFORMANCE SAR-GMTI PERFORMANCE INPUTS OUTPUTS NESZ AASR RASR CRAASR Eigenvalue distribution SCNR Probability of detection TIMING ANALYSIS / OPTIMIZATION Timing diagram PRFs Figure 3.8: Block diagram of the MSAR-GMTI mission theoretical performance tool. The core of the simulator is composed by three performance modules: timing analysis/optimization, SAR and SAR-GMTI performance. For a given orbit height a timing analysis (based on the diamond diagram computation) is performed to determine the selectable PRFs for the different subswaths (beams) to be operated covering the specific access range. PRF definition has a direct impact on the ambiguity performance and consequently on the SAR-GMTI performance. This information is inputed to the SAR performance module, which is in charge of computing different SAR metrics. Characterization of such metrics requires an accurate modeling of the antenna patterns for the different beams to be operated. The antenna diagrams can be obtained from the antenna pattern generator, already implemented in the raw data simulator, or loaded from external files. The SAR performance module computes NESZ, AASR, RASR and combinedrange-azimuth-ambiguity-to-signal ratio (CRAASR) for the different subswaths, where the corresponding number of combined range-azimuth ambiguities to be included is a selectable parameter. The SAR-GMTI performance module exploits the outcome of the SAR performance stage, and based on a theoretical description, provides detection metrics in terms of SCNR at the processor’s output as well as probabilities of detection Pdfor the different set of velocities, RCS and operational beams. It can also provide the eigenvalue distribution as a function of the incidence angle. This metric is a useful indicator of the predominant (interference) mechanism, against which the moving targets should compete. 3.4 Monte Carlo (MC) MSAR-GMTI simulator tool The detection capabilities of any GMTI system can be statistically quantified through the probability of detection Pd. In this sense, MC simulations provide a very useful tool to asymptotically characterize this probability for specific system and scenario conditions. A flexible SAR-GMTI performance simulator tool, based on MC simulations at image level, has been implemented to provide the statistical metrics Pdand Pfa. This tool avoids 48 3.5 - Concluding remarks TARGET SIGNAL GENERATOR NOISE RANDOM GENERATOR CLUTTER RANDOM GENERATOR +MGMTI PROCESSING CFAR DETECTOR ITERATIVE TRIAL GENERATION GMTI PROCESSING SCENARIO DEFINITION SENSOR/SYSTEM DEFINITION SAR PERFORMANCE METRICS Probaility of detection Figure 3.9: Block diagram of the Monte Carlo (MC) MSAR-GMTI performance tool. generating and processing iteratively synthetic raw data for a given system/scenario to characterize the Pd, which otherwise could be time-consuming. A flow chart of the MC simulator is depicted in Fig. 3.9. This flexible tool enables the analysis of any type of configuration/GMTI technique, for any given scenario definition. Range values can be specified simultaneously for up to nine different scenario parameters: RCS, ground radial velocity, target type (deterministic or Gaussian), target correlation, clutter reflectivity, clutter correlation and clutter mean velocity. The system is defined through antenna configuration/baselines, NESZ, CRAASR, PRF and resolutions. Three different SAR-GMTI techniques are integrated in the performance tool: ATI, based on a 2D (phase-magnitude) parametric (Gaussian clutter case) CFAR detector; DPCA and EDPCA using both a magnitude-based parametric CFAR detector. It is also possible to specify a multilook processing, indicating both the number of looks to be used as well as in which looks the target is present. Then, an exhaustive data base of probability of detections can be properly parametrized for a given SAR-GMTI mission and easily extrapolated to any configuration with proper parameter scaling to avoid re-computation. 3.5 Concluding remarks Special effort and dedication has been devoted to the definition, design and implementation of different software simulators through this doctoral activity. The development of these tools is crucial for the evaluation, analysis and proposal of an optimized SAR-GMTI mission as discussed in the next chapter. The MSARRDS is the most complete simulator among the developed ones. The potentiality of this simulator is its capability to generate multichannel SAR raw data with a realistic emulation of the acquisition process. Its modular design enables easily the integration of further updates that can provide a much more accurate and complex modeling of the SAR operation, e.g., orbital model of the platform or system dependent errors. Different from the other simulators, MSARRDS provides final SAR image products, at expense of more demanding computational cost and memory allocation. 49 Chapter 3. Multichannel SAR (MSAR) simulation tools MOVING TARGET RAW DATA GENERATOR SAR R/D PROCESSOR CLUTTER GENERATOR [Gaussian, K-distribution] NOISE GENERATOR PSF FILTERING RADAR/SYSTEM CONFIGURATION SCENARIO CONFIGURATION + SBR MODULE MULTICHANNEL SAR IMAGES [Target, clutter, noise] Pd EXTRACTOR Pd MAP GENERATOR SAR GMTI PROCESSOR [DPCA,ATI,EDPCA] MTI MODULE OFF-LINE GMTI PERFROMANCE CHARACTERIZATION GMTI PERFORMANCE DATA BASE CFAR DETECTION [ATI-2D, OS-CFAR] Pd MAPS SAR-GMTI IMAGES DETECTION MAPS Figure 3.10: Flow chart of the simulator tool developed by the UPC team in the frame of SIMTISYS project. The mission theoretical performance simulator and the MC based one are a perfect complement to the MSARRDS since they can be used as a forecasting tools to anticipate the capabilities of a given configuration when processed with a specific technique. The reduced computational load of the theoretical performance simulator is its most appealing characteristic. Nevertheless, its range of application is limited to the ability to theoretically define (in a closed form) the operation of a given SAR-GMTI technique under given scenario conditions. The SAR-GMTI metrics computed by the theoretical performance simulator are exploited by the MC like simulator to properly assess the operation of a given mission. The MC tool provides a complete data base of probabilities of detection sampling a wide range of different scenario parameters, avoiding the high computational cost and memory allocation of doing so with the MSARRDS. Such data base can be used to complement the information on the final SAR-GMTI products provided by the MSARRDS, i.e., indicate the expected Pdfor the different detected targets on the output images. The experience gained in the development of the different software simulation radar tools, has been exploited in the design, as a part of a team, of the SIMTISYS simulator [31]. The block diagram corresponding to the part implemented by the UPC team is shown in Fig. 3.10, where two main modules can be differentiated: first, the SBR (spaceborne radar) stage, is responsible for the generation of the synthetic multichannel SAR images, taking advantage of the basis of the MSARRDS. The second stage carries out the GMTI processing, providing SAR-GMTI synthetic images as well as detection maps, where the probability of detection is obtained from the developed off-line Monte Carlo MSAR-GMTI simulator. 50 Chapter 4 4Performance evaluation of SAR-GMTI missions This chapter compares current state-of-the-art SAR missions, such as TerraSAR-X (TSX) or TanDEM-X (TDX), with a new multichannel configuration based on non-uniformly displaced phase centers, intended for GMTI applications over maritime scenarios. The GMTI capabilities of the different configurations are analyzed in a three-level performance approach. The expected theoretical performance of the optimized SAR-GMTI mission is first evaluated. In a second step, an intensive numerical simulation evaluation, based on MC trials, is carried out in order to characterize the probabilities of detection under different system parameters as well as scenario conditions. Different GMTI techniques, DPCA, ATI and EDPCA, are assessed. Finally, synthetic simulated SAR data, obtained in a study case scenario, is used to demonstrate the potential improvement of the proposed multichannel configuration compared to the current SAR missions, providing subclutter visibility for maritime surveillance of small and slow moving boats1. 1This chapter includes figures and text fragments, sometimes verbatim, of the author’s publication [JA1]. 51 Chapter 4. Performance evaluation of SAR-GMTI missions 4.1 Introduction SAR systems for remote sensing applications have been gaining special interest during the last decade, as testified by the increased number of recent and forthcoming missions: TSX, TDX, CSK, RS2, Sentinel-1 and PAZ. Some of them include an experimental mode that adds GMTI capabilities from spaceborne platforms, which allows covering the requirements on the so called Situation Awareness. The objective of the SAR-GMTI is to detect moving targets on the Earth surface (cars, trucks, ships,...) and focus them into high resolution synthetic aperture images. This kind of missions will provide a powerful tool to globally monitor road and maritime traffic (fisheries management, coastal and maritime security). Single channel GMTI systems operate high PRF and narrow antenna beamwidths, limiting the detection to fast targets with strong reflectivity [68]. However, several shortcomings derive from this method especially when they are applied in spaceborne platforms, where PRF is quite restrictive in order to achieve the desired trade-off between azimuth resolution and unambiguous swath width, [23]. In single channel SAR systems there is an intrinsic ambiguity between radial velocities and azimuth location in SAR images [44]. This ambiguity problem can be solved by means of multiple receive channels, which provide improved detection capabilities thanks to the increased spatial diversity. Current SAR missions, as TSX, TDX and RS2, equipped with two parallel receivers, have limited capabilities to detect weak and slow moving targets, as could be the case of small boats in the sea. For these dual receive antenna (DRA) mode configurations, conventional SAR/GMTI processing techniques operating on the SAR processed images can be applied, based on either phase subtraction, ATI, or simultaneous phase and amplitude subtraction, DPCA. In order to obtain adequate performance, by means of STAP, more than two receive antennas are required [44]. One way to obtain additional spatial diversity, without increasing the system complexity, is based on the use of suitable antenna switching and toggling modes [45]. These kinds of approaches imply an antenna effective area reduction, resulting in a degradation of the SNR and increased PRF requirements to reduce azimuth ambiguities [15,45]. The evolution to multichannel approaches based on the deployment of SAR constellations could provide better performances (angular and Doppler resolutions) thanks to extended apertures. Two different GMTI strategies can be followed: (i) a coherent GMTI processing, where moderate baselines (a few hundreds of meters) with highly overlapping antenna footprints are required, [27,54]; (ii) an incoherent GMTI processing, where the train of satellites’ temporal gap can vary from seconds up to minutes, [47]. In the latter case, sub-clutter detection is not possible as the critical baseline separations, [27], have been overcome and hence neither of the coherent processing techniques exploiting multichannel configurations can be used. Therefore, coherently operating constellations permit large but sparse antenna apertures and so potential GMTI improvement. However, such configurations suffer from a high number of grating lobes, creating numerous blind velocities. Moreover, the technological complexity and cost of maintaining a constellation of satellites is rather high. From these considerations, the current chapter comparatively evaluates an architecture based on a multichannel monostatic satellite with non-uniformly spaced phase centers, briefly discussed in [135]. The goal of this mission 52 4.1 - Introduction SENSOR/SYSTEM DEFINITION SCENARIO DEFINITION SIMULATION DEFINITION BUS (Parameters exchange) INPUTSOUTPUTS SAR images SAR-GMTI images Detection maps MSARRDS Monte Carlo MSAR-GMTI simulator Probability of detection MSAR-GMTI mission theo. performance NESZ AASR RASR CRAASR Eigenvalue distribution SCNR Probability of detection Figure 4.1: Block diagram of the simulation environment used in the SAR-GMTI mission performance evaluation. is to provide sub-clutter visibility for maritime surveillance of small slow moving boats. This optimized multichannel configuration in combination with the new optimum GMTI processing techniques, such as ISTAP and EDPCA, is expected to provide improved SAR-GMTI performance [28,29]. The objective of this chapter is the GMTI performance evaluation of the current state-of-the-art SAR missions in comparison to the proposed multichannel configuration. GMTI capabilities are analyzed and characterized in terms of probability of detection, based mainly on intensive numerical simulations (MC) at image level, which are complemented with processed (simulated) synthetic raw data. Fig. 4.1 shows a high-level description of the simulation environment used in the performance evaluation of the different configuration-techniques: the three simulation tools presented in Chapter 3 have been considered. The theoretical SAR-GMTI capabilities are mainly based on the derived data model presented in section 2.3. Through the chapter a Gaussian-like model for the sea clutter is assumed. Nevertheless, and as it has been verified with experimental TSX data over maritime scenarios (see chapter 6), this hypothesis breaks down depending on system, acquisition geometry and sea conditions. It has been observed that in some cases K- distribution provides a good fitting on the sea clutter magnitude at SAR image level. In this sense, and for analysis completeness, additional processed simulated raw data results are included when considering a non-Gaussian sea clutter based on K-distribution. It is clear that the scope of the new optimized SAR-GMTI mission is to detect small and slow moving targets. However, from an operational point of view in maritime surveillance applications great interest is reserved to the detection of small boats with high-speed and complex motion. In this very case, and as briefly discussed in section 2.2, high induced target dynamics could produce severe degradation in the imaging quality (defocusing and smearing); but more importantly a reduction on the effective SCNR, which, could ruin 53 Chapter 4. Performance evaluation of SAR-GMTI missions the detection performance, if target dynamics are not properly accounted for in the processor. A preliminary study on the impact of SAR imaging high-speed boats (with large vertical and horizontal accelerations) has been also carried out using simulated raw data. To this end a complete SAR-GMTI processing chain has been implemented, integrating a matched filter bank (MFB) based on an adaptive RD processor, as proposed in section 5.2.1 for real data. The aim is to demonstrate that the proposed SAR-GMTI mission in combination with an appropriate processing strategy will be able to detect also this high-speed moving targets. Therefore, high-resolution images of the moving vessels can be obtained, as validated with airborne real data in section 5.2.1, of key importance for post-processing recognition/classification purposes. Three SAR-GMTI processing techniques operating directly on SAR images have been considered in the performance evaluation: the classical DPCA and ATI for dual-channel systems and the new promising adaptive EDPCA technique. Clutter homogeneity plays an important role in the estimation of the interference covariance matrix performed by ISTAP and EDPCA, and so directly affects the GMTI performance. In this sense, the EDPCA processing is preferred on maritime scenarios since it operates at image level, allowing selection and processing of homogeneous patches. Moreover, the performance characterization of the ISTAP via MC simulations would require its evaluation in the range-Doppler domain, leading to a computationally much more costly approach compared to the efficient one presented in section 3.4, which operates at image level. Both ISTAP and EDPCA provide the same GMTI performance when the DPCA condition is fulfilled; otherwise, ISTAP gives improved results as pointed out in [28]. 4.2 Mission analysis 4.2.1 Multichannel configurations State-of-the-art SAR missions, as TSX, RS2 and TDX, equipped with two receivers, have limited GMTI capabilities to detect slow moving targets, due both to a reduced number of channels and to the short baselines (2.4 m one way) that determine the minimum detectable velocity (MDV). The deployment of coherently operating SAR constellations, as TDX, provides improved performance in terms of Doppler (velocity) and angular resolution, but at the expense of a reduced range of unambiguous velocities (1.4 m/s), caused by the longer baselines (around 200 m). In maritime scenarios, where sea coherence time could reach tens of milliseconds [83, 84], depending on the sea conditions, the channel coherence (for the longer baseline) could drop off dramatically, and so would the capability of clutter rejection. Therefore, a trade-off solution, is to consider a monostatic multichannel configuration with non-uniformly spaced receivers, taking advantage from baseline diversity to ensure high sensitivity to slow moving targets (with the largest baseline), and simultaneously alleviating the Doppler ambiguities (with the shorter ones); in a way that channel coherence could be kept high enough to ensure proper detection capabilities. From these considerations, a three-channel configuration is proposed, where the two external antennas are deployed using a telescopic boom, as originally suggested in [135], and an unfolding system, respectively. The number of channels has been selected to limit the system complexity and at the same time to fulfill the required degrees of freedom 54 4.2 - Mission analysis TX RX 4.8 m 14.4 m 4.8 m Unfolding Boom xx x 4.8 m (a) TX RX 4.8 m 200 m xxxx 4.8 m X-DRA (b) Figure 4.2: Schematic representation of the different configurations to be analyzed: (a) proposed Boom configuration and (b) Tandem (two flying X-DRA satellites); transmit (TX) phase center denoted by the solid circle, receive (RX) by the triangle symbol and effective two-way (2-W) by the cross symbol. driven by the eigenvalue distribution of the interference covariance matrix, as discussed in section 4.2.2. The length of the boom has been selected to deliver a probability of detection (Pd) close to one for a 1 m2RCS target, whose ground range velocity is greater than 5.5 m/s when processing the three-channel data cube with EDPCA. The boom length is a multiple of the antenna length assuming a telescopic structure will be used for deployment. The system operates in X-band, equipped with a configurable 4.8 m-length phased-array antenna, with 32x12 transmit receive modules (TRMs). The main radar mission parameters, similar to TSX, are summarized in Table 4.1. From now on the proposed configuration will be referred as Boom system, and its SAR-GMTI performance will be compared against two different systems that emulate current state-of-the-art SAR missions: a 4.8 m-length single satellite operating in DRA mode (2.4 m per receiver), named as X-DRA; and a Tandem configuration, where two X-DRAs fly in formation (only one TX)2with a baseline of 200 m, as schematically represented in Fig. 4.2b. At this point it must be noted that perfect time and frequency (coherence) synchronization between the two satellites is assumed. It is well known that TSX and TDX do not fly in a train-like configuration but rather in a HELIX formation [55] and hence there is an across-track baseline coupled with the along-track of interest. In this sense, it is assumed that the across-track baseline could be perfectly compensated (or coregistrated), [48]. 4.2.2 SAR-GMTI expected performance An orbital height of 514 Km has been selected to ensure an incidence range coverage from 14-60 degrees (swath ground extension of 640 Km), intended to be covered with 27 subswaths, whose extension is in the order of 30 Km. PRF is a key parameter in the operation of any SAR-GMTI mission: from the GMTI operation point of view, the highest PRF possible is required to ensure that the fastest ground velocity to be detected is not ambiguous. However, the higher the PRF, the smaller the unambiguous (range) swath extension. Fig. 4.3 shows the timing (diamond) diagram as a function of PRF and incidence angle for a fixed pulse duration of 45 µs, and indicates whether the echo delay is such that the signal doesn’t superimpose either on the transmit instances (gray strips) or on the nadir 2In [54] Gierull refers to this configuration as classic coherent tandem concept, where one satellite transmits and both receive the backscattered signal simultaneously. 55 Chapter 4. Performance evaluation of SAR-GMTI missions Table 4.1: Radar system parameters. Parameter Value Units Satellite velocity 7604.8 m/s Spot (ground) velocity 7311.6 m/s TX (transmit) antenna length 4.8 m RX (receive) antenna length Boom/Tandem 4.8/2.4 m TX/RX antenna height 0.7 m Number of TRMs 32x12 Carrier frequency 9.65 GHz Peak transmitted power 2.2 KW Polarization HH Noise factor 4.3 dB Transmitter losses 2 dB Receiver losses 2 dB 2000 3000 4000 5000 6000 PRF [Hz] 14 23 33 42 52 61 Incidence angle [deg] 121 202 293 403 546 755 ground range [Km] Figure 4.3: Timing (diamond) diagram for an orbit height of 514 Km and a fixed pulse duration of 45 µs: the restrictions on the receive echo window due to transmit instances (grey strips) and nadir echoes (green strips) are shown. The extension of the 27 different subswaths for the selected PRFs is shown on top of the image as colored polygons. returns (green strips). From beam 1-19 the highest possible PRF has been selected, while for beams 20-27 (with higher incidence angle) a trade-off between azimuth and range ambiguities level has been considered to choose the PRF. Fig. 4.4a represents the NESZ metric of the Boom system, i.e., a measure of the system’s sensitivity to areas of low radar backscatter. This metric indicates the normalized radar backscattering coefficient σ0that provides a unitary SNR, [23]. NESZ as a function of slant range R0(or equivalently w.r.t incidence angle γ0) has been computed according to the formulation in [136] like NESZ = 2 (4π)3PnPRF c0λ2PavGT X GRX ·Naz sin γ0 δaz ·1 PNaz i=1 D2−w(θ0i, φ0i)/R2 0(θ0i, φ0i) 2(4.1) 56 4.2 - Mission analysis SCNR (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 5 10 15 20 [dB] Boom 14.4 m Boom 28.8 m Boom 57.6 m XDB 14.4 m Boom 14.4 m Boom 28.8 m Boom 57.6 m XDB 14.4 m Boom 14.4 m Boom 28.8 m Boom 57.6 m XDB 14.4 m Figure 4.10: SCNR as a function of ground range velocity (at center of subswath 8) for EDPCA technique considering different variants of the Boom configuration, assuming a deterministic target (RCS of 0 dBm2) and a sea state 4 (σ0NRL model) Gaussian clutter with 10-ms coherence time; XDB corresponds to a Boom configuration where the two first channels are X-DRA like (2.4 m separation with no unfolding) and the third one (2.4 m antenna length) is located on a 14.4 m mast. SCNR X-DRA -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 2.17 1.08 0.0 -1.08 -2.17 Doppler [KHz] (a) SCNR Tandem -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 2.17 1.08 0.0 -1.08 -2.17 (b) SCNR Boom -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 2.17 1.08 0.0 -1.08 -2.17 -47.0 -37.0 -27.0 -17.0 -7.0 [dB] (c) Figure 4.11: Post-Doppler STAP SCNR for system configurations in Fig. 4.2 with radar parameters defined in Table 4.1: (a) X-DRA configuration, (b) Tandem and (c) Boom; deterministic target with RCS of 0 dBm2and a sea state 4 (σ0NRL model) Gaussian clutter with no temporal decorrelation are assumed. and the third antenna is deployed with a mast of 14.4 m. The proposed configuration (red solid line) provides an overall improved SCNR compared to the alternative systems. Increasing the mast separation allows a slightly narrower notch response (around zero velocity), at the expense of additional steeper secondary notches. Moreover, there is a progressive degradation in the SCNR peaks due to clutter decorrelation higher impact. For XDB a generally reduced SCNR is observed since the antenna dimensions are half of the Boom architecture. Secondary notches, much steeper, are located at slightly higher velocities because of effective shorter baselines. To give some insight in the operation of STAP-like algorithms, the SCNR at the output of a post-Doppler STAP (as in ISTAP) is represented in Fig. 4.11 as a function of the target’s ground range velocity (vz) and the Doppler frequency (at which the target 63 Chapter 4. Performance evaluation of SAR-GMTI missions PdEDPCA (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 14 26 38 49 61 Incidence angle [deg] (a) PdEDPCA (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 14 26 38 49 61 (b) PdEDPCA (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 14 26 38 49 61 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (c) Figure 4.12: Boom Pdmap (as a function of incidence angle and ground range velocity) for EDPCA processing under different scenario conditions: (a) deterministic target with no clutter decorrelation; (b) deterministic target with 10-ms clutter coherence time and (c) Gaussian target with 10-ms clutter coherence time (sea state 4 under σ0NRL model and target with 0 dBm2of RCS). PdEDPCA (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 14 26 38 49 61 Incidence angle [deg] (a) PdEDPCA (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 14 26 38 49 61 (b) PdEDPCA (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 14 26 38 49 61 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (c) Figure 4.13: Tandem Pdmap (as a function of incidence angle and ground range velocity) for EDPCA processing under different scenario conditions: (a) deterministic target with no clutter decorrelation; (b) deterministic target with 10-ms clutter coherence time and (c) Gaussian target with 10-ms clutter coherence time (sea state 4 under σ0NRL model and target with 0 dBm2of RCS). is detected) for the different configurations. This SCNR has been computed according to the model presented in (2.24). No decorrelation of the Gaussian sea clutter has been considered. As expected, the STAP filter forms a notch along the clutter trajectory at vz=0. Comparatively, the Tandem configuration provides the steeper main notch, i.e., higher sensitivity to slow motion, with increased number of blind velocities. In this sense, the proposed Boom configuration shows a good compromise between ambiguous velocities and sensitivity to slowly moving targets with an improved SCNR (before azimuth focusing) for a much greater extent in the Doppler-velocity plane (ideally a complete dark-red plane would be desirable). As the synthetic aperture is formed the target and clutter pass through the beam and the corresponding directions and slant ranges vary and consequently the directing cosine of the related ambiguous clutter. In this case, the SCNR 64 4.2 - Mission analysis Pd (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch (a) Pd (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch (b) Pd (RCS=0dBm2) -50 -40 -30 -20 -10 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch X-DPCA X-EDPCA T-EDPCA B-EDPCA X-Single-ch T-Single-ch B-Single-ch (c) Figure 4.14: Pdas a function of the ground range velocity for different system-technique combinations at beam center of subswath 8 (33.17 degrees) and for different scenario conditions: (a) deterministic target with no clutter decorrelation; (b) deterministic target with 10-ms clutter coherence time and (c) Gaussian target with 10-ms clutter coherence time (sea state 4 under σ0NRL model and target with 0 dBm2of RCS). would correspond to the integration of the one in (2.24) along the Doppler frequency, once an appropriate adaptive SAR processing (to the moving target of interest) is performed, similar to the ISTAP operation [28]. Analogous to the SCNR maps presented in Fig. 4.7 and Fig. 4.8, probability of target detection Pdcharts can also be theoretically obtained as shown in Fig. 4.12 and Fig. 4.13 for Boom and Tandem configuration, respectively, when processed with EDPCA. Pdhas been theoretically computed considering CFAR detectors ensuring a Pfa of 1 ·10−5for different scenario conditions: Fig. 4.12a and Fig. 4.13a consider a deterministic target model with no clutter decorrelation; Fig. 4.12b and Fig. 4.13b show the reference scenario results (deterministic target and 10-ms clutter coherence time); and a worse case scenario is assumed in Fig. 4.12c and Fig. 4.13c, where a Gaussian target model (completely correlated) and 10-ms coherence time have been considered. The different trends on the Pdmaps can be easily extrapolated from the SCNR results. Generally speaking, Boom mission with EDPCA processing provides better detection capabilities all over the range 65 Chapter 4. Performance evaluation of SAR-GMTI missions of incidence angles (14-60 degrees) and for the different scenario conditions, especially when some sea clutter decorrelation is assumed. For the worse case scenario, where the target is modeled as complex Gaussian process and considering a 10-ms clutter coherence time, the detection capabilities are degraded for both configurations, with Boom EDPCA outperforming Tandem architecture. For analysis completeness and to show the improved SAR-GMTI performance obtained with the proposed Boom configuration, Pdcuts as a function of vzat beamcenter of subswath 8 (γ0=33.17 degrees) for different system-technique combinations and scenario conditions are reported in Fig. 4.14. Boom architecture with EDPCA technique provides in general a better Pdfor realistic scenario operation when compared to the rest of systemtechnique combinations. When considering a Gaussian target modeling, Fig. 4.14c, a lower average Pdis obtained with a flatter response as a function of the ground range velocity. Nevertheless, it must be noted that for |vz|<20 m/s, where Pdis below 0.3, target randomness provides slightly improved performance compared to the deterministic target, which is easily recognized for DPCA and EDPCA with X-DRA as well as for the single-channel detection performance. Table 4.2: Monte Carlo (MC) simulation parameters. Parameter Value Units RCS -10 to 20 dBm2 vz0 to 50 m/s Target type Deterministic/Gaussian - Target correlation -/10 ms Sea state 4 - Clutter correlation -/10 ms Mean clutter velocity 0.0 m/s γ0(incidence angle) 33.17 deg MC trials 5 ·106- Pfa 1·10−5- Looks 1/4 - Looks per target 1/4 - 4.3 Simulation results: performance evaluation In this section the theoretical performance of the proposed boom system is validated through simulation results. As depicted in the simulation environment (see Fig. 4.1), two different methodologies are considered: first, intensive Monte Carlo (MC) simulations are carried out to obtain the probabilities of detection; in a second step, and complementing the MC approach, multichannel synthetic raw data sets, generated using the MSARRDS simulator tool, are processed for the different configurations and techniques. 66 4.3 - Simulation results: performance evaluation Pd X-DRA DPCA -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (a) Pd X-DRA ATI -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (b) Pd Tandem EDPCA -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (c) Pd Boom EDPCA -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (d) Figure 4.15: Pdmaps (as a function of RCS and ground range velocity) obtained from MC simulations assuming a deterministic target model (RCS of 0 dBm2) and a Gaussian-like sea clutter (sea state 4 under σ0NRL model) with 10-ms coherence time: (a) X-DRA DPCA, (b) X-DRA ATI, (c) Tandem EDPCA and (d) Boom EDPCA. 4.3.1 Monte Carlo (MC) approach For the MC simulations presented in this section some hypothesis have been assumed: (i) clutter is a zero-mean complex Gaussian process with given spatial (along different channels) correlation properties; (ii) SAR processing has been adapted to the target kinematic parameters7; (iii) the residual phase error (due to coregistration mismatch) defined by the second term of (2.13) has been included for the first 440 combined rangeazimuth ambiguities; and (iv) the target (either deterministic or Gaussian) is correlated from look to look, while clutter has been assumed uncorrelated. Table 4.2 summarizes the different parameters of the MC simulations considering the center of subswath 8 with an incidence angle of 33.17 degrees. Fig. 4.15 shows probability of detection maps as a function of RCS and ground range velocity for different system-techniques combinations, when considering a deterministic target and 10-ms clutter coherence time (with no multilook processing). Boom system in combination with EDPCA, Fig. 4.15d, provides improved performance compared to the rest, especially in the region of slow and low reflectivity moving targets. DPCA technique 7Discussion about SAR focusing mismatch on fast moving boats is considered in 4.3.2. 67 Chapter 4. Performance evaluation of SAR-GMTI missions Pd X-DRA DPCA -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (a) Pd X-DRA ATI -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (b) Pd Tandem EDPCA -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (c) Pd Boom EDPCA -10 -5 0 5 10 15 20 RCS [dBm2] 0 10 20 30 40 50 Ground range velocity [m/s] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (d) Figure 4.16: Pdmaps (as a function of RCS and ground range velocity) obtained from MC simulations assuming a Gaussian target model (RCS of 0 dBm2) and a Gaussian-like sea clutter (sea state 4 under σ0NRL model) with 10-ms coherence time: (a) X-DRA DPCA, (b) X-DRA ATI, (c) Tandem EDPCA and (d) Boom EDPCA. applied to X-DRA data shows the worst Pdin this region, Fig. 4.15a. However, the joint 2D phase-magnitude ATI detector on the X-DRA system, Fig. 4.15b, gives comparatively a better performance, close to the EDPCA applied to Tandem system, Fig. 4.15c, where the induced higher clutter decorrelation is the driven parameter; but still EDPCA on Tandem has a threshold RCS, approximately 5 dB below the ATI case. In Fig. 4.15d, the secondary notch around 20 m/s and for RCS below 0 dBm2is related to the degradation in SCNR, caused by the sensibility loss associated to the longer baseline. In Fig. 4.16 a worst case scenario has been considered, where the target is modeled as a complex Gaussian process. A general degradation in the Pdis obtained for the different system-technique configurations, with a smoother transition as a function of RCS. Moreover, for a given fixed ground range velocity a higher RCS is required to obtain the same Pdas in Fig. 4.15. Fig. 4.17a and Fig. 4.17b show cuts of the Pdfor the different system-technique combinations as a function of across-track ground velocity (for a RCS of -5 dBm2) and versus RCS (for vz= 1 m/s), respectively. Two sea clutter coherence times (∞and 10 ms) are reported for each system-technique combination to illustrate the impact of clutter decor- 68 4.3 - Simulation results: performance evaluation 0 10 20 30 40 50 Ground range velocity [m/s] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (a) -10 -5 0 5 10 15 20 RCS [dB] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (b) Figure 4.17: System-technique comparison of the Pdobtained from MC simulations assuming a deterministic target and for different clutter correlations (τc= inf and 10-ms): (a) cut at RCS of -5 dBm2as a function of ground velocity and (b) cut at vz= 1 m/s as a function of RCS; no multilook processing is considered (X refers to X-DRA system, T and B to Tandem and Boom configurations, respectively). 0 10 20 30 40 50 Ground range velocity [m/s] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (a) -10 -5 0 5 10 15 20 RCS [dB] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms X-ATI τc=inf,10 ms X-DPCA τc=inf,10 ms T-EDPCA τc=inf ms T-EDPCA τc=10 ms B-EDPCA τc=inf ms B-EDPCA τc=10 ms (b) Figure 4.18: System-technique comparison of the Pdobtained from MC simulations assuming a complex Gaussian target and for different clutter correlations (τc= inf and 10 ms): (a) cut at RCS of -5 dBm2as a function of ground velocity and (b) cut at vz= 1 m/s as a function of RCS; no multilook processing is considered (X refers to X-DRA system, T and B to Tandem and Boom configurations, respectively). relation. For a completely correlated sea clutter the Tandem configuration with EDPCA processing (solid blue line) provides the highest sensitivity to slow moving targets, at the expense of a reduced unambiguous range of velocities. However, for realistic scenario operations clutter decorrelation impairs especially the performance of the Tandem system (solid blue line with asterisk); while Boom configuration shows a robust behavior (comparing red dashed lines with and without asterisk markers), providing the best detection capabilities as a function of the across-track velocity for a small target. ATI (dotted black line) and DPCA (dash-dot-dot green line) for X-DRA prove to have very limited capabilities to detect boats with reduced reflectivity (-5 dBm2), being almost insensitive to clutter decorrelation since X-DRA has the smallest baseline, 2.4 m. When considering the 69 Chapter 4. Performance evaluation of SAR-GMTI missions 0 10 20 30 40 50 Ground range velocity [m/s] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI l=1 lt=1 X-ATI l=4 lt=1 X-ATI l=4 lt=4 B-EDPCA l=1 lt=1 B-EDPCA l=4 lt=1 B-EDPCA l=4 lt=4 X-ATI l=1 lt=1 X-ATI l=4 lt=1 X-ATI l=4 lt=4 B-EDPCA l=1 lt=1 B-EDPCA l=4 lt=1 B-EDPCA l=4 lt=4 X-ATI l=1 lt=1 X-ATI l=4 lt=1 X-ATI l=4 lt=4 B-EDPCA l=1 lt=1 B-EDPCA l=4 lt=1 B-EDPCA l=4 lt=4 (a) 0 10 20 30 40 50 Ground range velocity [m/s] -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Pd X-ATI l=1 lt=1 X-ATI l=4 lt=1 X-ATI l=4 lt=4 B-EDPCA l=1 lt=1 B-EDPCA l=4 lt=1 B-EDPCA l=4 lt=4 X-ATI l=1 lt=1 X-ATI l=4 lt=1 X-ATI l=4 lt=4 B-EDPCA l=1 lt=1 B-EDPCA l=4 lt=1 B-EDPCA l=4 lt=4 X-ATI l=1 lt=1 X-ATI l=4 lt=1 X-ATI l=4 lt=4 B-EDPCA l=1 lt=1 B-EDPCA l=4 lt=1 B-EDPCA l=4 lt=4 (b) Figure 4.19: Pdas a function of ground velocity for different multilook processing (llooks), no multilook (1 look) and four looks (target present in a single look lt=1 and in all of them lt=4); Gaussian sea clutter with and 10-ms coherence time and target with -5 dBm2of RCS (a) deterministic model and (b) Gaussian model. performance as a function of RCS for slow moving boats (vzof 1 m/s), DPCA technique for X-DRA provides the worst results, unable to detect targets even with moderate to high reflectivity. For the same configuration, ATI 2D detector gives much better results, and gets closer to the Boom-EDPCA, which still requires lower RCS to obtain the same Pd. In this regard, and even for a 10-ms coherence time, Tandem configuration provides the lowest threshold RCS value, since the boat velocity is still in the range of vz=±1.5 m/s, where as already observed in Fig. 4.9b the Tandem SCNR is around 3 dB higher. Analogously, Fig. 4.18 shows the same Pdcuts but for a worse case scenario, where the target has been modeled as a complex Gaussian process (completely correlated from channel to channel). Comparing both situations, Fig. 4.17 and Fig. 4.18, target randomness provides in average a smaller Pdas a function of vz, smoothing the trend of Pdas a function of the RCS. For the Gaussian target and for Pdbelow a threshold level of 0.3, improved performance is obtained w.r.t. a deterministic case, whereas for Pdabove this value there is a global degradation. The impact of data averaging (multilook processing) on Pdis presented in Fig. 4.19 for a 10-ms clutter coherence with a deterministic target, Fig. 4.19a, and completely correlated Gaussian target, Fig. 4.19b. It can be observed that the performance improves as the number of looks increases, whenever the target occupies a sufficient number of single-look resolution cells to avoid degradation in the effective SCNR after multilook processing. It has been assumed that each scattering point of the target located at each resolution cell has the same RCS, and assumed to be correlated from look to look, while clutter and noise are decorrelated. Hence, it is expected that if the target size is so that the moving object lies in the different single-look cells to be averaged, a clear improvement is obtained, since the effective SCNR increases. On an opposite situation, if the target is present only in one of the looks this SCNR gets reduced (even compared to the singlelook case) and so an important degradation in the performance is expected. Therefore, multilook processing should not be discarded as notable improvement can be obtained, but the boxcar size for multilook processing should be properly selected depending on the size of the expected targets, [50]. 70 4.3 - Simulation results: performance evaluation Table 4.3: Scene parameters. Parameter Value Units Scene extension (in ground) 1 x 1 Km x Km γ0(center scene) 33.17 deg Sea state 4 - Mean clutter σ0-15.1 dB Clutter temporal correlation 10 ms 4.3.2 Synthetic SAR data approach To complement the MC simulations, synthetic multichannel data is generated using the flexible MSARRDS simulator tool described in section 3.2, where different systems, modes of operation and scenarios can be easily configured. In order to provide an analogous metric to the probability of detection, several raw data simulations (20 trials) have been carried out, such that a frequency of detection can be extracted. A complete processing chain has been implemented integrating a MFB (based on a RD processor) with the different GMTI techniques, similar to the ones proposed in [29,41]. The block diagrams of both adaptive RD algorithm and the complete SARGMTI processor (including ATI, DPCA and EDPCA algorithms) are described presented in Fig. 5.13 in section 5.2.2. Each filter of the MFB performs an adaptive SAR processing, at both RCMC and azimuth focusing steps, for a specific set of kinematic parameters (vz, azand vx), trying to recover a well focused moving object. No compensation of the Doppler shift (azimuth shift) is carried out, since, otherwise, the target will appear at different azimuth positions for different vzof the filter bank, posing difficulties to efficiently compare the outputs of the bank of filters. The scenario parameters considered in the raw data simulator are summarized in Table 4.3. In a first approach, a zero-mean complex Gaussian reflectivity for sea clutter has been assumed, in a downwind acquisition. To complement these results, and for the same sea conditions, a K-distributed clutter has also been considered, trying to emulate more realistic maritime scenarios. Six deterministic moving targets are included in the scenario as indicated in Table 4.4, where two different types of vessels (ramshackle T1 and a civil cargo T2) have been modeled as a collection of point-like targets. The electromagnetic modeling and RCS extraction of these vessels have been carried out by the company Telespazio Vega UK, in the cooperation frame of the European Commission FP7 funded Project SIMTISYS, [31]. In a first approximation, targets were simulated as rigid bodies. Targets T3 and T4 are single scattering points modeling low reflectivity slow moving targets in order to prove the potential improvement of the proposed Boom configuration. High-speed boats can reach velocities between 40 and 70 Knots (20.6-36 m/s) experiencing longitudinal and/or vertical accelerations up to several g-forces, depending on sea conditions, [137]. Point-targets T5 and T6 represent high-speed boats moving in along- and across-track directions, respectively, with vertical accelerations ay of 0.35gm/s2and longitudinal ones, ax= 0.25gm/s2(T5) and az= 0.25gm/s2(T6). 71 Chapter 4. Performance evaluation of SAR-GMTI missions Table 4.4: Target parameters (coordinate system defined in Fig. 2.4; aiand vicorrespond to acceleration and velocity in the ith dimension, respectivley). Target Type Scatterers mean RCS max. RCS vxvzaxayaz [dBm2] [dBm2] [m/s] [m/s] [m/s2] [m/s2] [m/s2] T1 Ramshackle 53 4.5 17 -1.12 6.25 -0.69 0.0 -0.30 T2 Civil cargo 102 28.2 40 -6.73 3.0 -0.22 0.0 -0.29 T3 Point target 1 -5 -5 0 5 -0.69 0.0 -0.4 T4 Point target 1 0 0 0 2.5 -0.69 0.0 -0.4 T5 Point target 1 5 5 20.6 0.0 2.45 3.43 0.0 T6 Point target 1 5 5 0.0 20.6 0.0 3.43 2.45 IF of MFB over SWMF 0 10 20 30 40 vx[m/s] -7.5 -6.2 -5.0 -3.8 -2.5 az[m/s2] 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 [dB] (a) 0 10 20 30 40 vz[m/s] -5.0 -4.0 -3.0 -2.0 -1.0 0.0 az[m/s2] 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 [dB] IF of MFB over SWMF (b) Figure 4.20: Improvement factor (IF) of the MFB with respect to SWMF: (a) target T5, vxversus azmap; (b) target T6, vzversus azmap. It is well-known that if target kinematic is not accounted for in the SAR processor, severe degradations are observed in the SAR image and this in turn prevent proper SARGMTI detection, especially for small and fast moving objects. Fig. 4.20a and Fig. 4.20b show the IF maps provided by the MFB w.r.t. a SWMF for T5 and T6, respectively. In case of T5, with a purely along-track movement and no azaccelerations, MFB can provide up to 13 dB of improvement for a set of az-vxpairs, as denoted by the diagonal strip in Fig. 4.20a. Two conclusions are extracted from these results: first, vertical acceleration ay on T5 produces equivalently similar effects as an azacceleration from the SAR processing point of view, since aycontributes also to a radial acceleration (line-of-sight projection); second, there is a coupling between across-track acceleration azand along-track velocity vx, giving rise to indistinguishable effects. For a fixed vx, a MFB step size below 0.5 m/s2 on az, produces losses on peak response below 3 dB. Analogously, for a fixed azthe step on vxis below 13 m/s. The impact of ax, inducing third-order phase errors, produces mainly an asymmetric sidelobe response for the considered acquisition time (under one second). 72 4.4 - Concluding remarks the K-distributed clutter when a 2D-CFAR detector under the assumption of Gaussianlike interference is used. Similarly, EDPCA processing on Tandem and Boom present a higher Pfa (especially Tandem due to higher impact of clutter decorrelation) when using a Rayleigh CFAR detector for the K-distributed scenario; but it gets reduced for the most appropriate K-distributed CFAR scheme. Sikaneta et. al proposed in [139] a solution to the problem of high false alarm rates in heterogeneous terrain. It considers an adaptive CFAR detector that does not depend on terrain heterogeneity, avoiding the definition of a parametric texture distribution. This alternative is based upon a mutliplicative noise model rather than a texture (compound) model, assuming high correlation between the noise-free clutter measurements. Such hypothesis should be further investigated in the case of sea clutter, taking into account the impact of sea decorrelation. 4.4 Concluding remarks The GMTI performance of different multichannel SAR missions using state-of-the-art GMTI techniques (ATI, DPCA and EDPCA) has been evaluated in this chapter over maritime scenarios. A new multichannel SAR configuration, based on non-uniformly displaced receive phase centers, has been compared with TSX and TDX like missions. With such a multichannel configuration it is possible to discern small slow moving vessels, usually undetected with present SAR systems. Under certain hypothesis (homogeneous open sea), the proposed mission tries to maximize the SAR-GMTI performance by minimizing the noise contribution, in terms of NESZ, and ambiguities’ level in the region of interest (20-40 degrees of incidence angle), while keeping a low system complexity with an optimized number of channels. Boom system has been designed trying to keep the new ambiguity metric CRAASR as low as possible in the region of operation. In the far range region (40-60 degrees) the impact of range ambiguities increases and so does CRAASR. Therefore, the performance is expected to degrade for the case of nonhomegeneous ambiguous returns, especially close to coastal areas. A way to circumvent these impairments is to consider a future SAR-GMTI mission concept exploiting azimuth phase coding (APC) in combination with digital beamforming, such that a high-resolution wide-swath (HRWS) mode can be operated [140]. The proposed architecture has been evaluated comparatively in a two-level simulation performance approach over maritime scenarios. In a first step, the probability of detection has been characterized through intensive MC simulations under different scenario conditions. Several synthetic multichannel SAR raw data sets have been processed iteratively to complement MC simulations for a realistic maritime scenario. The different simulations’ results indicate the potential improvement provided by the proposed Boom configuration when using adaptive processing approaches such as EDPCA. The simulations results are in good agreement with the theoretical expected performance. Boom configuration has been designed, such that it is slightly affected by internal clutter motion and at the same time enables high sensitivity to low reflectivity slow moving targets, alleviating Doppler (velocity) ambiguities thanks to its baseline diversity. It must be pointed out that this configuration can be scaled down (in terms of size) for a higher operating frequency, with the appropriate modification of the sea clutter modeling. The performance evaluation of the proposed mission has been carried out assuming a complex Gaussian model for the sea clutter. Additional raw data simulations assuming a 79 Chapter 4. Performance evaluation of SAR-GMTI missions K-distributed sea clutter have been performed, showing the robustness of Boom configuration when processed with EDPCA. For ATI, where no clutter cancellation is performed, a new formulation of the 2D-CFAR detector should be derived to consider a K-distributed sea clutter. The impact of SAR imaging high-speed boats has been preliminarily analyzed, showing the need to properly account for target kinematics in the SAR-GMTI processing chain via a MFB since, otherwise, the induced image degradation could impair the GMTI performance, particularly for small and fast boats. From these considerations, it can be stated that experimental campaigns over maritime scenarios are mandatory to understand and validate a sea clutter model (for the usual range of SAR incidence angles), in terms of its statistics and mean power reflectivity, and at the same time try to grasp the impact of realistic target kinematics. 80 Chapter 5 5 Experimental MSAR-GMTI over maritime scenarios This chapter is devoted to the SAR-GMTI evaluation of real multichannel SAR data over maritime scenarios. Two different type of data sets have been evaluated: (i) airborne X-band data from the F-SAR sensor and (ii) spaceborne X-band data from TerraSAR- X German satellite. The capability of refocusing moving vessels with an adaptive SAR processor is demonstrated. The impact of channel balancing/calibration on the GMTI performance is analyzed with special interest throughout the chapter. The chapter starts with an overview of the sensors’ configuration, followed by the description of the GMTI techniques used to process the experimental data sets and integrated in the implemented processing chains. In the second part of the chapter the different results of SAR-GMTI processing experimental data are presented first for the airborne case (F-SAR) and then for the spaceborne TerraSAR-X mission1. 1This chapter includes figures and text fragments, sometimes verbatim, of the author’s publication [JA2]. 81 Chapter 5. Experimental MSAR-GMTI over maritime scenarios 5.1 Sensor configurations 5.1.1 F-SAR airborne system The increasing demand on air-to-ground surveillance and reconnaissance multi-task systems, with high resolution and long range imaging capabilities, poses stringent requirements on the design of new radar sensors. A clear example is the development of an efficient traffic monitoring system, driven by the dramatical increase of road traffic, which allows to monitor large areas at once at any time (day/night) and under any weather conditions. In this sense, radar systems represent an ideal tool for efficient and continuous traffic monitoring, being the airborne sensors the precursor of such GMTI capabilities. From the operational point of view, the airborne platforms are more attractive, thanks to the higher flexibility, shorter revisit times and longer acquisitions, at expenses of a reduced spatial coverage compared to the spaceborne sensors. During the last decade there has been a continuous development of airborne radar system trying to fulfill these requirements. At European level three main research groups are working towards this end: 1. The French aerospace laboratory ONERA has a wide experience in the development of airborne SAR and GMTI systems, with special emphasis on defense applications. From the knowledge gained on the RAMSES system a new compact radar concept for SAR-GMTI operation is being developed, the so called CURACAO [18,19]. 2. The Fraunhofer-Institut f¨ur Hochfrequenzphysik and Radartechnik (FHR) has designed a multimodal and multichannel experimental airborne radar system PAMIR that delivers high resolution SAR and Inverse SAR (ISAR) images, integrating the GMTI operation on the basis of five parallel receiving channels [15,141,142]. This GMTI mode is designed to rapidly monitor wide areas using a narrow antenna in a scanning operation, such that the revisit time is reduced and the detection capability for a given target can be increased as it can be seen from different angles during the scanning, [14]. 3. The Institut f¨ur Hochfrequenztechnik und Radarsysteme (HR), at the Deutsches Zentrum f¨ur Luft- und Raumfahrt (DLR), is responsible for the development of the airborne SAR system F-SAR, contributing to the demonstration/validation of new technologies and applications. The F-SAR system is the successor to the wellknown E-SAR, providing the capability to acquire different wavelengths and polarizations simultaneously [71,143]. An experimental GMTI mode, with four receiving channels, is being used to assess different GMTI algorithms with respect to their capabilities for traffic monitoring [16,17], in the frame of two main projects, TRAMRAD [26] and VABENE [144]. The airborne F-SAR sensor is a multichannel and multifrequency polarimetric system. It can operate in X- (8-12 GHz), C- (4-8 GHz), S- (2-4 GHz), L- (1-2 GHz) and P-bands (250-500 MHz) with simultaneous polarimetric capability and single-pass polarimetric interferometric capability only in X- and S-bands. The SAR-GMTI mode is an experimental one, where at most four receiving channels can be used when operating in switched aperture dual-receive X-band mode. In Fig. 5.1a, the multichannel F-SAR configuration and operation mode are depicted. The receive and transmit antennas have 20 cm length and are co-located in the along- 82 5.1 - Sensor configurations X31VV ADC X32VH X1V X2H X32VV ADC X31VH X2V X1H 10 cm 10 cm 10 cm X32VV ADC X31VH X2V X1H X31VV ADC X32VH X1V X2H 10 cm 10 cm 10 cm Odd pulses Even pulses Flight direction (a) Figure 5.1: F-SAR sensor SAR-GMTI acquisition configuration in the switched dual-receive mode (effective two-way baselines are indicated). track or flight direction. The front-end of the system integrates only two analog-to-digital converters (ADCs), such that only two antennas can receive simultaneously. In order to obtain a 4-channel configuration, the system is operated in a switched receive mode as sketched in Fig. 5.1a, and hence the per-channel PRF is half of the operational one. The original channel nomenclature has been preserved, such that for odd pulses channels X31VH and X31VV are acquired, while for even pulses X32VV and X32VH. At this point it must be noted that the sensor was configured in VV polarization, i.e., vertical transmit and receive polarizations. 5.1.1.1 Data set description As a part of the doctoral studies, a short stay as visiting researcher has been carried out at the DLR-HR institute. During this period, multichannel airborne F-SAR data has been processed over maritime scenarios. The different available data sets were collected in 2009 in the frame of the DLR internal project Ocean SAR, and they correspond rangecompressed products with and without MOtion COmpensation (MOCO). Due to the lack of precise antenna pattern measurements for the configuration that acquired those data takes, the antenna patterns in elevation and azimuth were not compensated to avoid introducing artifacts on the data. Unfortunately, no ground truth was available for this campaign, and so no information on the scenario (vessels’ velocities and sea conditions) can be used to support the SAR-GMTI processing. An acquisition over the Elbe’s Mouth (09tdxsim0104), see Fig. 5.2, has been selected for SAR-GMTI processing evaluation. In this data take, a large land portion in the image is available. It can be used as a reference patch for proper channel balancing or calibration, co-registration (if required) and antenna pattern estimation (in case of ISTAP technique). The main acquisition and processing parameters for this data take 83 Chapter 5. Experimental MSAR-GMTI over maritime scenarios Figure 5.2: SSC image of the F-SAR GMTI acquisition 09tdxsim0104 over the Elbe’s mouth in the North Sea: AOIFSAR denotes the sea patch of interest to be processed delimited by a green box; the red solid box delimits the reference land patch CALFSAR for calibration purposes (channel balancing) and region COVFSAR, confined by the light blue solid rectangle, could be used as a reference patch for interference covariance matrix estimation. Parameter Value Units vs(sensor velocity) 85.814 m/s H0(sensor altitude) 2497.476 m Ψ (squint) 9.039 deg PRF (per-channel) 2016.129 Hz Ba(azimuth processed bandwidth) 1832.844 Hz Br(range processed bandwidth) 300 MHz Hanning spectral weighting 0.54 - Table 5.1: F-SAR acquisition and processing parameters for the 09tdxsim0104 data take over the Elbe’s mouth in the North Sea. are summarized in Table 5.1. A single look slant range complex (SSC) image of the data take produced by the DLR is shown in Fig. 5.2. The figure also indicates several regions of interest: AOIFSAR represents the region of interest to be processed containing three vessels V1, V2 and V4; a reference sea patch COVFSAR, free of vessels, which could be used for covariance matrix estimation when processing with EDPCA or ISTAP; and a reference calibration land patch CALFSAR, covering the same slant range variation as AOIFSAR, to extract the channel balancing weights. 5.1.2 TerraSAR-X spaceborne system The successful TSX satellite, launched in summer 2007, is the first German radar satellite implemented under a public-private partnership between DLR and EADS Astrium GmbH [145]. TSX is equipped with a phased array antenna of 4.8 m length that allows for multimodal operations: conventional SAR stripmap, SCanSAR and Spothlight. Two different multichannel acquisition concepts in along-track configuration have been implemented as schematically depicted in Fig. 5.3. The first one is the so called aperture 84 5.1 - Sensor configurations TX n RX nx TX n RX nx TX n RX nxx AS DRA TX n RX nxx TX RX ch1 RX ch2 Figure 5.3: TSX-ATI modes: aperture switching (AS) and dual-receive antenna (DRA); transmit (TX) phase center denoted by the solid circle, receive (RX) by the triangle symbol and effective two-way (2-W) by the cross symbol (figure adapted from [46]). switching (AS), where the whole antenna is used to transmit, while the fore and aft parts of the antenna are alternatively activated to receive in a pulse-basis sequence [146]. In this AS mode, the effective PRF per channel is half of the operational one. For the second concept, known as dual receive antenna (DRA), the whole antenna is also used to transmit but is split into two halves that receive simultaneously [147]. The availability of two receiving channels provides TSX some GMTI capabilities, with special interest on traffic monitoring [46,47,148] and current field measurements [91,92]. In the DRA mode, TSX uses the redundant receiver unit to sample the second channel, such that the fore and aft channels are combined through the hybrid coupler providing the sum and difference data. For SAR-GMTI purposes the fore and aft channels should be reconstructed using proper algorithms, such that hardware impact (gain and phase errors) is compensated minimizing channel imbalances [74,148]. In collaboration with the DLR and in the frame of the scientific project proposal, Study of Spaceborne GMTI Algorithms Using DRA Data (Ref. MTH1971), several TSX data sets are available for SAR-GMTI evaluation purposes. This data corresponds to a dedicated DRA acquisition mode campaign carried out from April to May 2010. Experimental ATI products are acquired in stripmap single polarization mode. These level-1b products are SSC, containing three images: the single receive antenna (SRA) channel, processed as a nominal strimap product and two DRA images, DRAFore and DRAAft. These latter are processed using the full azimuth bandwidth (limited by the PRF) with neither azimuth nor range windowing. Therefore, the impact of ambiguities is expected to be high, due also to the widening of the receive antenna (half of the TX). These effects can be observed in Fig. 5.4, which corresponds to the color composite image (SRA, DRAFore and DRAAft channels) over the Strait of Dover, and where the ambiguities show up as yellow coded pixels. 5.1.2.1 Data set description From the different data sets of the TSX-DRA campaign for ATI configuration (April-May 2010), an acquisition over the Strait of Dover has been selected for SAR-GMTI processing evaluation, see Fig. 5.4. The main acquisition and processing parameters for this data 85 Chapter 5. Experimental MSAR-GMTI over maritime scenarios AOITSX CALTSX V3 V2 V1 V4 COVTSX Range Azimuth V5 V6 Figure 5.4: SSC color composite image of the TSX-DRA acquisition over the Strait of Dover in the North Sea: AOITSX denotes the sea patch of interest to be processed indicated as green box; red solid box delimits the reference land patch CALTSX for calibration purposes (channel balancing); and region COVTSX, confined by the light blue solid rectangle, could be used as reference patch for interference covariance matrix estimation. Parameter Value Units vs(sensor velocity) 7682.782 m/s vg(spot/ground velocity) 7065.511 m/s PRF (per-channel) 3807.03 Hz Ba(azimuth processed bandwidth) 3807.03 Hz Br(range processed bandwidth) 150 MHz Hamming spectral weighting 1.0 - Table 5.2: TSX-DRA acquisition and processing parameters for a data take over the Strait of Dover in the North Sea. take are summarized in Table 5.2. A quicklook SSC image of the data take produced by the DLR is shown in Fig. 5.4. The figure also indicates a number of regions relevant to processing and evaluation: AOITSX represents the region of interest to be processed containing six vessels; a reference sea patch COVTSX, free of vessels, which could be used for covariance matrix estimation when processing with EDPCA or ISTAP; and a reference calibration land patch CALTSX. 86 5.2 - SAR-GMTI processing schemes 5.2 SAR-GMTI processing schemes This section describes the algorithms and processing chains used for the SAR-GMTI evaluation of the different experimental data over maritime scenarios. The objective is to provide flexible and fully integrable processing modules such that any type of data, either airborne or spaceborne, can be assessed with different GMTI techniques providing both SAR-GMTI images as well as detection maps. 5.2.1 Adaptive SAR processor In the near future, SAR-GMTI systems are required to detect slowly moving targets with low radar reflectivity (low RCS) in subclutter conditions and at the same time image them in high-resolution SAR images. Therefore, the intrinsic imaging degradation of the moving targets on SAR images, when focusing with stationary world matched filter (SWMF), should be properly compensated. An adaptive SAR processing, which includes the target kinematic parameters, allows image quality and SCNR degradation recovery, especially important when imaging low reflectivity targets. Several approaches can be followed to properly focus the moving targets in SAR images, e.g., autofocusing techniques [37,38] or matched filter bank (MFB) [40,69,149] among others. Assuming no a priori information regarding the target motion, a MFB has been used, based on a range- Doppler (RD) algorithm [73], which takes into account adaptive range cell migration correction (RCMC) and azimuth reference function. Following a similar approach as in [28,29, 41], this processor has been integrated in the different SAR-GMTI processing chains. The different effects of moving targets on SAR imagery were first analyzed by Raney in [25]. Further detailed studies can be also found in [68, 70]. In chapter 2, the impact of different target kinematics have been evaluated by means of processing raw data simulations. Hereafter, a brief mathematical formulation of the moving target slant range history is reported, pointing out how the target motion impairs the SAR focusing. Let’s assume a flat earth geometry in the SAR acquisition as depicted in Fig. 2.4, where the platform moves at constant height Horb and effective velocity vealong the azimuth (along-track) direction. As extendedly assumed in the GMTI literature, the motion of the target can be simplified to a linear movement with constant acceleration (in both azimuth and ground range) during the formation of the synthetic aperture, which is fairly true for spaceborne platforms, where the integration time is in the order of one second: x(t) = x0+vxt+ax 2t2 z(t) = z0+vzt+az 2t2(5.1) In (5.1), tstands for slow time (or azimuth time). At t= 0 (mid-acquisition time) the target is located at x0and z0, which corresponds to the along- and across-track coordinates, respectively. The along-track and across-track velocities of the target are represented by vxand vz, whereas the associated accelerations are axand az. For simplicity on the mathematical formulation, the target is assumed to be moving in the y= 0 plane without any vertical (elevation) movement. 87 Chapter 5. Experimental MSAR-GMTI over maritime scenarios The slant range distance between the target and the SAR sensor can be expressed as R(t, ϑt) = rH2 orb +x0+vxt+ax 2t2−vet2+z0+vzt+az 2t22(5.2) where ϑtis the vector of target parameters ϑt= [x0, z0, vx, vz, ax, az, αt]. A second order Taylor’s series expansion of (5.2) around t= 0 allows to understand the impact of imaging moving targets with SWMF compared to the stationary case2: R(t, ϑt)≈R0+z0vz R0 t+v2 rel (ϑt) 2R0 t2 =R0+z0vz R0 t+1 2R0(vx−ve)2+v2 z1−z2 0 R2 0+z0azt2(5.3) where R0is the slant range at t= 0 and vrel the relative velocity. In (5.3) it has been assumed x0= 0 without loss of generality. The moving target’s Doppler frequency, obtained as the time derivative of the azimuth phase ϕ(t, ϑt) = −4π λR(t, ϑt) (for the monostatic case), can be expressed as fd≈ − 2 λR0{z0vz}− 2 λR0(vx−ve)2+v2 z1−z2 0 R2 0+z0azt =fDC +Ka(ϑt)t(5.4) where Ka(ϑt) refers to the target’s azimuth (Doppler) chirp rate. In a more general case, the Doppler centroid fDC can eventually include the impact of a squint angle Ψ, between the antenna’s broadside and the perpendicular to the platform’s path fDC ≈ −2 λ(vx−ve) sin Ψ + z0vz R0(5.5) From (5.4) two main effects on the SAR image due to target motion will be present. The across-track velocity vzproduces a shift of the Doppler centroid fDC, in a way that the target is imaged at a displaced position respect to its original one. This displacement can be computed as [70]: ∆ximg =−fDC KaSWMF ve(5.6) with KaSWMF as the Doppler rate for the stationary (SWMF) case. Across-track accelerations azand along-track velocities vximpair on the Doppler rate, i.e., a variation on the quadratic term of the slant range history (5.3), which translate into smearing or defocusing in the azimuth dimension, when imaging with a SWMF. Hence, this filter mismatch produces a degradation in the azimuth resolution as well as in the moving target’s signal intensity after focusing due to the reduced coherent integration. When considering the RCMC, an across-track velocity increases the range walk (linear component of the RCM), such that a residual RCM is present for a SWMF-RCMC, [70]. 2A detailed mathematical derivation of the bidimensional MSAR signals before and after SAR processing can be found in Appendix B. 88 5.2 - SAR-GMTI processing schemes V1 (vx=0.0 m/s, az=0.0 m/s2) -50 0 50 Azimuth w.r.t center scene [m] 604.200 604.220 604.240 604.260 Slant range [km] (a) V1 (vx=8.0 m/s, az=0.0 m/s2) -50 0 50 Azimuth w.r.t center scene [m] 604.200 604.220 604.240 604.260 -40.0 -30.0 -20.0 -10.0 0.0 [dB] (b) V3 (vx=0.0 m/s, az=0.0 m/s2) -200 -100 0 100 200 Azimuth w.r.t center scene [m] 604.820 604.840 604.860 604.880 604.900 604.920 604.940 Slant range [km] (c) V3 (vx=5.0 m/s, az=0.0 m/s2) -200 -100 0 100 200 Azimuth w.r.t center scene [m] 604.820 604.840 604.860 604.880 604.900 604.920 604.940 -40.0 -30.0 -20.0 -10.0 0.0 [dB] (d) Figure 5.11: TSX-DRA processed images (DRAFore channel) using the implemented adaptive RD processor on vessels V1 and V3 over the Strait of Dover [see Fig. 5.4]: (a) SWMF over V1; (b) adaptation on the along-track velocity vx=8.0 m/s over V1; (c) SWMF over V3; (d) adaptation on the along-track velocity vx=5.0 m/s over V3 (three range lines extracted for matched filter bank validation are indicated as dotted white lines). [Figs. 5.10a-c], the peak response for the different range lines is concentrated around az =-0.095 m/s2, while for the along-track velocity based MFB [Figs. 5.10d-f] it is close to vx =1.8 m/s. From the similar MBF response of the vessel V4 as a function of range, it can be stated that V4 was not performing any maneuver (e.g. turning) during the formation of the synthetic aperture, which otherwise could have lead to much differentiated defocusing between the bow and stern. The implemented adaptive processor has been also validated for spaceborne data, using the TSX-DRA acquisition over the Strait of Dover as shown in Fig. 5.11. The processing has been applied over two vessels, V1 and V3, considering a SWMF [Figs. 5.11a and 5.11c] and an adaptation on vx[Figs. 5.11b and 5.11d]. For clarity in the representation, the images in Fig. 5.11 are the interpolated versions of the RD processor output, with an interpolation factor of 8 in range and azimuth. The improvement in the image quality comparing the MFB and the SWMF is not as important as in the airborne case. This is because for the spaceborne case the coherent processing interval is under 1 second. The azimuth sharpness gets better for an adaptive processing, especially evident in the brightest scatterers of vessels V1 and V3. 95 Chapter 5. Experimental MSAR-GMTI over maritime scenarios V1 MFB 604.203 Km -50 0 50 Azimuth w.r.t center scene [m] -20 -10 0 10 20 Along-track velocity [m/s] -60 -55 -50 -45 2 4 6 8 10 12 14 (a) V1 MFB 604.221 Km -50 0 50 Azimuth w.r.t center scene [m] -20 -10 0 10 20 -55 -50 -45 -40 -35 2 4 6 8 10 12 14 (b) V1 MFB 604.233 Km -50 0 50 Azimuth w.r.t center scene [m] -20 -10 0 10 20 -40.0 -30.0 -20.0 -10.0 0.0 [dB] 10 15 20 25 30 0 2 4 6 8 10 12 (c) V3 MFB 604.847 Km -200 -100 0 100 200 Azimuth w.r.t center scene [m] -20 -10 0 10 20 Along-track velocity [m/s] -80 -70 -60 -50 -5 0 5 10 15 (d) V3 MFB 604.857 Km -200 -100 0 100 200 Azimuth w.r.t center scene [m] -20 -10 0 10 20 -110-100 -90 -80 -70 -5 0 5 10 15 (e) V3 MFB 604.901 Km -200 -100 0 100 200 Azimuth w.r.t center scene [m] -20 -10 0 10 20 -40.0 -30.0 -20.0 -10.0 0.0 [dB] 30 40 50 60 70 -10 -5 0 5 10 15 (f) Figure 5.12: MFB maps (along-track velocity variation) on three extracted range lines (see Fig. 5.11) for vessel V1 and V3 over the Strait of Dover TSX-DRA acquisition: (a)-(c) V1 and (d)-(f) V3 (zoomed areas around the maximum are also included). Analogous to the analysis done with the F-SAR data, the MFB maps for three extracted range lines over both vessels are shown in Fig. 5.12. The vertical axis corresponds to the along-track velocity variation considered in the MFB operation, and the horizontal axis represents the azimuth position (w.r.t. scene center). For representation purposes, the results shown in Fig. 5.12 correspond to the interpolated (factor 8) results of a MFB sweeping vxfrom -20 m/s to 20 m/s with a 1 m/s step. The different images in Fig. 5.12 are normalized to the maximum response of the MFB along the corresponding vessels. As a general trend and unlike the airborne case, the sensitivity of the MFB as a function of vxis comparatively lower. For V1, vxof 8 m/s provides the highest peak response of the brightest point along the vessel (at a slant range of 604.221 Km), with an improvement of around 5 dB w.r.t the SWMF approach. The variation of the MFB along V1 is kept more or less constant, with a slightly better response at vxof 5 m/s for the scattering point with a slant range of 604.233 Km [Fig. 5.12c]. As far as V3 is concerned the best response is obtained when vxis 5 m/s, where the improvement factor (IF) is 2 dB over the SWMF case for the brightest scattering center (at a slant range of 604.847 Km). Target detection could be performed also using such MFB maps applying a certain amplitude thresholding. MFB is an attractive solution to resolve multi-target scenarios providing simultaneously target separation as well as parameter estimation (Doppler rate). 96 5.2 - SAR-GMTI processing schemes Nevertheless, the computational cost and subclutter conditions (reduced SCNR scenarios) are two issues that limit its operation. 5.2.2 GMTI at SAR image level In classical multichannel SAR-GMTI processing, moving target detection is performed in a pixel basis on the processed SAR images by means of either phase subtraction, ATI or both phase and magnitude difference, DPCA. These techniques were originally developed for dual-receive channel configurations. Then, a generalization of the DPCA for any number of receiving channels has been lately proposed by Cerutti et al. [29]. These techniques have been already introduced in chapter 2, and a detailed description of these algorithms can be found in [29,49]. Fig. 5.13 depicts the block diagram of the implemented SAR-GMTI processing chain operating at image level, which integrates EDPCA, DPCA and ATI algorithms. In the conception of this processing chain, the modularity and flexibility have been the main driven requirements in order to fit any possible input data from any possible sensor configuration. Three main modules can be differentiated: pre-processing,MFB adaptive SAR focusing and SAR-GMTI processing. The first one corresponds to the pre-processing stage, where five different sub-processing stages can be optionally activated: 1. Inverse azimuth SAR processing is carried out when the original experimental data is a set of focused SSC images, as in TSX-DRA products. Based on the RD processor presented in the previous section, an azimuth inverse SAR compression is performed and the RCMC is re-introduced, using the processing parameters specified in the SSC products. 2. Range compression of the raw data products based on the module in Fig. 5.6a. 3. Coregistration of the different channels with respect to a reference. The coregistration or spatial alignment of the different channels is performed in both the azimuth and the range dimension. In this sense, two different coregistration options have been included: (i) a 2D approach that performs linear phase ramps compensation in the 2D spectral domain, such that the ATI phase (azimuth baseline) and the range difference (across-track baseline) are estimated from the given input data in the range frequency Doppler domain; (ii) a two-step approach, where the coregistration in the two dimensions is performed sequentially by a phase ramp removal estimated in the corresponding 1D spectral domains, i.e., range Doppler and range frequency azimuth-time domains, or vice versa, depending on the selected option, azimuth-range or range-azimuth. 4. Aperture switching and baseline delays compensation is optionally performed, when no accurate data-based coregistration is possible. This is due to non-spatially homogeneous clutter conditions and/or reduced clutter-to-noise ratio (CNR). The accurate knowledge of the baselines and positions of the receiving antennas from on-board inertial system measurements and/or ground characterization is an attractive alternative solution. In any case, accurate (azimuth/along-track) coregistration via interpolation (phase ramp removal in frequency) is achieved whenever the Nyquist sample theorem is fulfilled, i.e., the PRF is high enough to avoid signal 97 Chapter 5. Experimental MSAR-GMTI over maritime scenarios EDPCA REF. PATCH COVARIANCE MATRIX EST. REF. PATCH BALANCING/ CALIBRATION PATCH INTEREST (AOI) INVERSE AZIMUTH SAR PROCESSING (Azimuth defocusing & RCMC re-introduction) PRE-PROCESSINGOUTPUTS SAR images SAR-GMTI images (SCNR) Detection maps Velocity maps (across-track) REF. PATCH COREGISTRATION RANGE COMPRESSION COREGISTRATION (2D & 2-step) APERTURE SWITCHING & BASELINE DELAYS COMPENSATION CHANNEL BALANCING/CALIBRATION (Digital balancing) ADAPTIVE SAR PROCESSING (SRC, RCMC, azimuth focusing) INPUTS DPCA: IMAGE SUBTRACTION (Diff. combination) ATI: INTERFEROMETRY (Diff. combination) SPATIAL BEAMFORMING CFAR DETECTION (1D magnitude DPCA & EDPCA, 2D-ATI) MFBSAR-GMTI PROCESSING INTERFERENCE COVARIANCE MATRIX EST. & CLUTTER CANCELLATION Figure 5.13: Block diagram of the integrated EDPCA, DPCA and ATI processing. aliasing in the Doppler domain. These ambiguities can cause additional decorrelation between channels due to coregistration errors, as they fold back in the Doppler band (±PRF/2) and the phase ramp removal leaves constant phase errors, [29,151]. Therefore a degradation on the GMTI performance capability is expected as already analyzed in Chapter 4. 5. Channel calibration/balancing is performed to equalize the response of the different channels. To obtain precise detection performance, the response of the different 98 5.2 - SAR-GMTI processing schemes channels should be well calibrated and balanced; otherwise, phase and magnitude channel and/or antenna imbalances could impair the GMTI operation. Section 5.2.4 briefly describes the different channel balancing methodologies that have been considered in the processing chain. Once the pre-processing operations have been performed, the next stage corresponds to the adaptive SAR processing, already presented in section 5.2.1, synthesizing several filters, each one matched to a different set of kinematic parameters (MFB). For each filter an adaptive SRC (for F-SAR data), RCMC and azimuth focusing are performed trying to maximize the SCNR of the targets prior to GMTI processing. The next stage carries out the SAR-GMTI processing of the data per filter iteration: 1. In the EDPCA case, the interference covariance matrix is estimated and inverted for clutter cancellation prior to spatial beamforming, which is adapted to the same target parameters of the bank of filters: •The covariance matrix estimation and clutter cancellation can be performed using two different approaches. In the first one, a specific portion of the image or the whole image is used for estimation purposes. The inverse of this matrix is applied over the whole image (for clutter cancellation), reducing the computational cost, but at the expense of possible GMTI degradation in case of non-homogeneous clutter background4. The second approach, which requires a higher computational effort, is based on a sliding window with a pixel basis displacement. The clutter cancellation is performed pixel by pixel, using the area that surrounds a given guard zone around the pixel under test. •The SAR-GMTI processed image (for each filter) is fed to a parametric CFAR detector based on the magnitude of the data. Similar to the covariance matrix estimation and clutter cancellation, two operative options are integrated for the estimation of the residual interference statistical parameters, either a specific portion of the image is selected or instead a sliding window approach is used. 2. For DPCA and ATI algorithms, complex image subtraction and complex conjugate multiplication are performed, respectively, for the selected pair of channel combinations and for each filter of the MFB. Then, the different SAR-GMTI images are passed through parametric CFAR detectors, 1D (magnitude) and 2D (magnitude and phase) for DPCA and ATI, accordingly. From the analysis and processing of the multichannel experimental data, it has been observed that channel calibration/balancing, coregistration and covariance matrix estimation steps play a main role in the proper GMTI operation, when using the data of interest for that aim. In this sense and as depicted in Fig. 5.13, the possibility of using patches or regions different from the one to be processed has been integrated in the processing chain. Therefore, dedicated reference patches can be optionally used for interference covariance matrix estimation, channel balancing and coregistration, such that the processing stages over the different patches can be interconnected as shown in Fig. 5.13. 4The impact of non-homogeneity can be solved dividing the whole image scene in several homogeneous invariant regions, applying the specific estimated covariance matrix. 99 Chapter 5. Experimental MSAR-GMTI over maritime scenarios REF. PATCH COVARIANCE MATRIX EST. REF. PATCH BALANCING/ CALIBRATION PATCH INTEREST (AOI) INVERSE AZIMUTH SAR PROCESSING (Azimuth defocusing & RCMC re-introduction) PRE-PROCESSINGOUTPUTS SAR-GMTI images (SCNR) Detection maps REF. PATCH COREGISTRATION RANGE COMPRESSION COREGISTRATION (2D & 2-step) APERTURE SWITCHING & BASELINE DELAYS COMPENSATION CHANNEL BALANCING/CALIBRATION (Digital balancing) INPUTSMFB GMTI PROCESSING REF. PATCH ANTENNA PATTERN EST. RE-INTRODUCING BASELINE DELAYS INTERFERENCE COVARIANCE MATRIX EST. & CLUTTER CANCELLATION ANTENNA PATTERN ESTIMATION/LOADING BEAMFORMING & ADAPTIVE SAR PROCESSING (SRC, RCMC, azimuth focusing) CFAR DETECTION (1D magnitude) Figure 5.14: Block diagram of the ISTAP processor. 5.2.3 GMTI at range-compressed image level It is well known that sufficient detection performance is only achieved, when using configurations with more than two receiving antennas in junction with full STAP [21]. DPCA, ATI and EDPCA methods, which exploit the SCNR enhancement after coherent integration (SAR focusing), operate in the SAR image domain; whereas conventional STAP methods, such as the suboptimal post-Doppler STAP are applied in the range-compressed data domain [14,44]. 100 5.2 - SAR-GMTI processing schemes In [28], Cerutti et al. propose the so called imaging STAP (ISTAP), which is a combination of post-Doppler STAP and SAR focusing. A similar approach has been also investigated by Cristallini in [41], where a post-Doppler STAP approach is integrated in a MFB based on a chirp scaling algorithm (CSA), known as mutlichannel-bank of CSA (MC-BCSA). In both cases, clutter cancellation is performed in the rangecompressed Doppler domain using only the spatial DoF. It is assumed that the time base (SAR acquisition time) is sufficiently long to allow asymptotic decoupling of the different Doppler frequency bins [44,45]. Unlike conventional post-Doppler STAP, there is no segmentation of the time basis into small coherent processing intervals (CPIs) and hence the whole data is coherently integrated. This provides an increase in the SCNR at the final SAR-GMTI image, making ISTAP well suited for spaceborne configurations. Fig. 5.14 shows the flowchart for the implemented ISTAP processing chain. Three main modules can be differentiated: the first corresponds to the pre-processing stage, which includes all the processing steps indicated in Fig. 5.13. A new submodule has been included after channel balancing, which re-introduces baseline delays (decoregistration process in the along-track dimension) since the post-Doppler STAP processor requires this inherent systematic phase. The second module carries out the interference covariance matrix estimation and clutter cancellation (via covariance matrix inversion) in the range-compressed Doppler domain. For these combined operations two options have been considered: (i) for each Doppler bin a set of range lines are used to estimate a single covariance matrix applied over the whole set of ranges; (ii) a range sliding window approach (with higher computational burden), where for each range of interest a guard zone is used to exclude the presence of moving targets. From the computational cost point of view ISTAP is more efficient compared to EDPCA as the clutter covariance estimation and clutter cancellation is performed only once and not for every filter of the MFB as EDPCA does. The last stage in Fig. 5.14 is devoted to perform the spatial beamforming and azimuth SAR focusing, both adapted to moving target parameters via a MFB. The spatial beamforming operation, using the beamformer d(ut, fd,ϑt), coherently combines the clutter canceled range-compressed data to maximize the SCNR for the specific matched filter. This step is performed in the range-Doppler domain and it requires the knowledge of the antenna pattern. This information can be a priori known, by means of on ground measurements or from calibration campaigns, as it is the case of TSX. However, for the processed F-SAR data sets, the quality of the available antenna pattern measurements was not good and so it should be estimated from the data itself. A magnitude-based CFAR detector is applied over the final ISTAP image, where it is possible to select an isolated region for statistical parameters estimation or, alternatively, using a sliding window. Analogous to the processing concept presented in section 5.2.2, dedicated reference patches (different from the one of interest) can be optionally used for interference covariance matrix estimation, channel balancing/calibration, coregistration and also antenna pattern estimation. This flexibility in the processing chain is mandatory for a correct operation of the ISTAP processor over the available real data. Fig. 5.15 illustrates schematically the input block of data5per channel, feeding the 5This input portion is either range-compressed data for F-SAR operation or SSC images in the TSX case. 101 Chapter 5. Experimental MSAR-GMTI over maritime scenarios ADDITIONAL RANGE GUARD RCM GUARD SYNTHETIC APERTURE GUARD (LSA/2) SYNTHETIC APERTURE GUARD (LSA/2) AREA OF INTEREST (AOI) RANGE (POWER OF 2 LENGTH) ADDITIONAL AZIMUTH GUARD ADDITIONAL AZIMUTH GUARD ADDITIONAL RANGE GUARD AZIMUTH (POWER OF 2 LENGTH) Figure 5.15: Schematic representation of the input data block’s conditioning. different processing chains. For an area of interest (AOI) to be processed, guards accounting for half of the synthetic aperture LSA (symmetric at both sides in azimuth dimension) should be considered. To ensure a power of two azimuth length of the data block, additional data is included symmetrically at both sides for efficient fast Fourier transform (FFT) based processing. Analogously, additional samples are considered in the range dimension for proper inclusion of the RCM in the far range region and also to ensure the total number of range samples is a power of two. IMAGE-1 (ref. channel) RANGE POWER ADAPTATION (mean over az.) IMAGE-2 (to balance) 2D-FFT 2D-FFT IMAGE-1 IMAGE-2 INTERFEROGRAM RANGE FREQ. ADAPTATION (mean over Dopp.) IMAGE-2' INTERFEROGRAM DOPP. FREQ. ADAPTATION (mean over range) ITERATIVE SPECTRAL EQUALIZATION Figure 5.16: Flow chart of the 2D digital balancing (DB) method. 5.2.4 Channel balancing techniques The 2D adaptive balancing method, from now on referred as digital balancing (DB), represents the core of the different calibration algorithms integrated in the pre-processing step. Originally proposed by Ender [152] and further developed by Gierull [74], it performs a phase and magnitude balancing between the channel transfer functions. This is an iteratively adaptive method that operates in the 2D frequency domain (range frequency/Doppler), trying to equalize the spectral responses of the different channels even if they are not coregistarted, since it removes any phase ramp in the frequency domain [74]. A schematic representation of the 2D digital balancing operation is presented in Fig. 5.16. This sort of method does not modify the reference channel and so it is useful to calibrate the responses of the different channels for configurations with more than two receivers. Ideally, this 2D adaptive channel balancing algorithm adjusts the second channel spec- 102 5.2 - SAR-GMTI processing schemes tral response X2(fr, fd) to reference channel one X1(fr, fd) by a least square minimization min H(r) 1,2(fr),H(a) 1,2(fd)ZX1(fr, fd)−X2(fr, fd)H(r) 1,2(fr)H(a) 1,2(fd) 2dfrdfd(5.9) where an approximation of the calibration weights H(r) 1,2(fr) and H(a) 1,2(fd) can be iteratively solved via X(n+1) 2(fr, fd) =X(n) 2(fr, fd)H(n,r) 1,2(fr) = X(n) 2(fr, fd)RX1(fr, fd)X(n)∗ 2(fr, fd)dfd RX(n) 2(fr, fd) 2dfd , X(n+2) 2(fr, fd) =X(n+1) 2(fr, fd)H(n+1,a) 1,2(fd) = X(n) 2(fr, fd)RX1(fr, fd)X(n+1) ∗ 2(fr, fd)dfr RX(n+1) 2(fr, fd) 2dfr (5.10) In (5.10), X(n) 2(fr, fd) for n=0,1,2,... refers to the iteratively improved calibration of the second channel spectral data. The iterative range frequency and Doppler dependent calibration weights, H(n,r) 1,2(fr) and H(n+1,a) 1,2(fd) defined in (5.10), can be understood as a measure of complex coherence between the channels to be calibrated. This digital channel equalization can be performed over a specific spectral extension fd=fDC −Ba,c 2, fDC +Ba,c 2, fr=−Br,c 2,Br,c 2(5.11) to avoid considering spectral regions with reduced CNR conditions and/or high ambiguities’ impact. In (5.11), Ba,c and Br,c correspond to the azimuth (Doppler) and range calibration bandwidths, respectively. In practice, and following the implementation proposed by Gierull in [74], the iterative balancing process in (5.10) stops if one of two conditions is met: 1. The number of iterations nis greater than a specified maximum. 2. The difference between the mean values of the range frequency and Doppler dependent calibration weights is smaller than a threshold, i.e., ZH(n,r) 1,2(fr)dfr−ZH(n+1,a) 1,2(fd)dfd≤ηthres (5.12) When applying DB over real data, it has been observed that there is an important degradation of the second channel response in terms of magnitude due to channel decorrelation. Spectral components away from the so called mainlobe response have degraded CNR conditions and/or higher impact of the ambiguities. This would require to drastically reduce the calibration bandwidths, especially for the case of TSX in the DRA 103 Chapter 5. Experimental MSAR-GMTI over maritime scenarios configuration, where the reduced CNR and the azimuth ambiguities are issues of major concern. In this regard, a first alternative has been considered, where only the phase component of the calibration weights H(n,r) 1,2(fr) and H(n+1,a) 1,2(fd) is included. Based on the iterative channel balancing principle, a different and simplistic approach, referred from now on as modified digital balancing (MDB), has been implemented to avoid magnitude degradation of second channel response for those spectral components away from the mainlobe response. For this methodology the complex iterative calibration weights are computed as H(n,r) 1,2(fr) = R|X1(fr, fd)|dfd RX(n) 2(fr, fd)dfd exp     ∠  RX1(fr, fd)X(n)∗ 2(fr, fd)dfd RX(n) 2(fr, fd) 2dfd       , H(n+1,a) 1,2(fd) = R|X1(fr, fd)|dfr RX(n+1) 2(fr, fd)dfr exp     ∠  RX1(fr, fd)X(n+1) ∗ 2(fr, fd)dfd RX(n+1) 2(fr, fd) 2dfd        (5.13) For the different calibration methodologies, a range power (profile) adaptation of the second channel to the first is performed at (range-compressed) image level before the iterative two-dimensional spectral balancing, as suggested in [153]. This correction calibrates only the amplitude of the channel to be equalized using an averaging along azimuth for each range bin of the range-compressed image. Differences between each channel and the reference one, named channel imbalances, can be computed in the two-dimensional spectral domain as [148] I(fr,k, fd,l) = PLr i=−LrPLa j=−LaX1(fr,k+i, fd,l+j)X∗ 2(fr,k+i, fd,l+j) PLr i=−LrPLa j=−La|X1(fr,k+i, fd,l+j)|2(5.14) where a moving average filter (boxcar) is applied, using 2Lr+ 1 range frequency and 2La+ 1 Doppler neighboring bins. 5.3 F-SAR data 5.3.1 Data analysis In this section a preliminary analysis of the multichannel data to be processed has been carried out. This study has been useful to provide some insights in the required channel balancing/calibration strategies to be considered in the SAR-GMTI processing as well as to identify possible anomalies in the available data. In a first iteration of the data processing, a range (elevation) dependent antenna pattern compensation was performed on the available range-compressed data and analogously an azimuth pattern compensation during the azimuth focusing. The processing of this data showed that the azimuth pattern considered in the correction was not the real one, as it introduced artificially ambiguous vessel responses. Taking into account these considerations, no antenna pattern correction, either in range or in azimuth, has been 104 5.3 - F-SAR data (a) (b) (c) (d) (e) (f) (g) (h) Figure 5.24: SCNR images for DPCA over sea patch AOIFSAR, longest X31VH-X31VV (2nd column) and shortest X31VH-X32VV (3rd column) baseline combinations: (a) SAR image of channel X31VH with a SWMF and (b) with adaptive focusing (vz=-5 m/s and vx =1.8 m/s); (c)-(d) DPCA images with no channel balancing; (e)-(f) with DB using reference land patch CALFSAR for calibration; and (g)-(h) with DB using AOIFSAR itself for calibration (adaptive SAR imaging, vz=-5 m/s and vx=1.8 m/s, used for (c)-(h) images). DPCA detection maps are displayed in Fig. 5.25 when considering DB (on phase and magnitude) for the longest [Fig. 5.25a] and shortest [Fig. 5.25b] baseline configurations. As expected from the SCNR performance, a much higher number of detected pixels over 111 Chapter 5. Experimental MSAR-GMTI over maritime scenarios (a) (b) Data distribution 0 10 20 30 40 Magnitude 0.00 0.02 0.04 0.06 0.08 0.10 PDF Filtered data Rayleigh dist. Filtered data Rayleigh dist. Filtered data Rayleigh dist. (c) Figure 5.25: Detection maps for DPCA technique over sea patch AOIFSAR acquired with F-SAR platform (DB has been applied using the reference CALFSAR region): (a) longest baseline; (b) shortest baseline; and (c) residual interference (clutter + noise) data distribution for DPCA X31VH-X32VV using a portion of image as indicated by the white box in Fig. 5.24b (Rayleigh PDF fitting and CFAR threshold level are included). the different vessels is obtained for the shortest configuration due to the lower impact of clutter decorrelation. In order to set up the threshold of the magnitude CFAR detector, a portion of the image (indicated by the solid white box in Fig. 5.24b), free of moving targets, has been selected to estimate the related statistical parameters under the assumption of a Rayleigh distributed amplitude. Data distribution and the corresponding fitting of a Rayleigh statistics are in good agreement as sketched in Fig. 5.25c, where the estimated CFAR threshold level is also (as vertical dashed blue line). 5.3.2.2 ATI processing In the implemented processor, the ATI algorithm has been used as a moving target detector and as an across-track ground velocity estimator over the detected pixels, exploiting the interferometric phase information. A 2D-CFAR parametric detector, based on the joint PDF of ATI magnitude and phase, has been used under the assumption of a complex Gaussian distributed sea clutter. Two approaches have been considered to estimate the across-track ground velocity. The first one, polynomial method, estimates the acrosstrack ground velocity vzinverting the complete expansion of the ATI phase in (2.5), which includes the impact of motion parameters such as vxand az. This inversion requires the solution of a third order polynomial, where complex root solutions are excluded as po- 112 5.3 - F-SAR data (a) (b) Figure 5.26: ATI detection maps over the sea patch AOIFSAR for the shortest baseline configuration X31VH-X32VV, DB on phase and magnitude has been applied: (a) using the AOIFSAR region itself for calibration and (b) with CALFSAR as reference. (a) (b) Figure 5.27: (a) Two-dimensional distribution of the ATI (X31VH-X32VV) phase and magnitude of the interference data (clutter+noise) for the rectangular delimited region in Fig. 5.24b (DB using CALFSAR as reference); (b) fitted theoretical PDF for Gaussian distributed clutter. tential velocities. To complement this across-track velocity estimator, the linear method exploits the widely used approximate relationship ψij (ϑt)=2πdxi−dxjvzsin γ0/veλ. Two detection maps obtained from the 2D-CFAR ATI detector, are presented in Fig. 5.26 for the shortest baseline configuration (X31VH-X32VV), once digital channel balancing has been applied. No multilook processing has been considered in the processor. If the reference region CALFSAR is used for inter-channel calibration [Fig. 5.26b] better results are obtained compared to the case of considering the region of interest itself [Fig. 5.26a], as demonstrated by the higher density of detected pixels. For the case analyzed in Fig. 5.26b, the two-dimensional data distribution (histogram) and its fitted theoretical PDF, (2.20), under Gaussian distributed clutter hypothesis, are compared in Fig. 5.27, showing good agreement. Note that the 2D-PDF is not centered at zero phase due to the shift induced by the clutter motion (sea/river current), since the reference (non-moving) land patch CALFSAR has been used for calibration; otherwise, 113 Chapter 5. Experimental MSAR-GMTI over maritime scenarios 44 45 46 47 48 49 50 51 52 Incidence angle [deg] 0 5 10 15 20 25 vz [m/s] Figure 5.28: ATI related ambiguous velocities (ground) for the different baselines (color coded, X31VH-X31VV in red, X31VH-X32VH in blue and X31VH-X32VV in green): directional ambiguity in solid lines, first blind velocities as dotted lines and first Doppler ambiguous velocities as long dashed lines. this motion-related phase would have been compensated. The thresholding function used in the 2D-CFAR detector is plotted on top of Fig. 5.27b and it is obtained as a constantdensity contour line of the joint PDF, such that the integration of the PDF outside this region gives the desired probability of false alarm. The ATI phase is subject to several ambiguities that can impair the estimation of vz, [68,154]. The directional ambiguities occur when the difference in the two-way propagation distance to the target (from the two receive channels) exceeds λ/2, i.e., the ATI phase is greater than π.Blind velocities appear when the target two-way slant range variation over the time between receiver channels6is nλ/2, such that the ATI phase is a multiple of 2π, appearing as a zero phase. Doppler ambiguities occur due to the finite azimuth bandwidth sampling, i.e., when the Doppler frequency of the moving target exceeds ±PRF/2, these components are wrapped to the opposite side of the spectrum. Fig. 5.28 shows these ambiguous velocities for the different baseline configurations as a function of the incidence angle corresponding to the region CALFSAR7. The X31VH-X31VV combination, with the largest separation, has a directional ambiguous ground velocity (solid red line) around 3 m/s; the Doppler ambiguous ground velocities (long dashed lines), which depend only on the operated PRF and incidence angle, have the same variation from 23 m/s to 20 m/s for the different baselines. The information of the detected pixels is used to generate the estimated across-track ground velocity maps of the vessels accordingly, as illustrated in Fig. 5.29 for the shortest baseline formation X31VH-X32VV. Figs. 5.29a and 5.29b correspond, respectively, to the first and third roots of the polynomial used to estimated the vz, including the impact of azand vx. The first root indicates the negative values of vz, showing an estimated value between -2.5 m/s and -5 m/s; whereas the third root refers to the positive, mostly related to the sidelobes of the vessels, where the phase behavior could be ambiguous producing velocity wrapping. For the linear relationship between ATI phase and vz[Fig. 5.29c] good agreement is observed when compared to the polynomial approach [Fig. 5.29a]. The velocity distributions for the different baselines and the two estimation methods 6It corresponds to the time it takes the two apertures or receiving antennas to spatially coincide. 7Only the positive value has been represented since the negative ones are symmetrical. 114 5.3 - F-SAR data (a) (b) (c) Figure 5.29: Vessels’ estimated across-track ground velocity maps from the shortest baseline configuration X31VH-X32VV over sea patch AOIFSAR, DB on phase and magnitude has been applied (using CALFSAR as reference): (a) first and (b) third roots of the polynomial vzinversion method; and (c) estimation based on the approximately linear relationship between ATI phase and vz. (a) (b) (c) Figure 5.30: Sea clutter’s estimated across-track ground velocity maps from the shortest baseline configuration X31VH-X32VV over sea patch AOIFSAR, DB on phase and magnitude has been applied (using CALFSAR as reference): (a) first and (b) third roots of the polynomial vzinversion method; and (c) estimation based on the approximately linear relationship between ATI phase and vz. 115 Chapter 5. Experimental MSAR-GMTI over maritime scenarios Polynomial root 1 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Across-track ground velocity [m/s] 0.0 0.5 1.0 1.5 Histogram X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV (a) Polynomial root 3 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Across-track ground velocity [m/s] 0.0 0.5 1.0 1.5 Histogram X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV (b) Linear -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Across-track ground velocity [m/s] 0.0 0.5 1.0 1.5 Histogram X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV (c) Figure 5.31: Vessels’ estimated across-track ground velocity distributions over sea patch AOIFSAR, DB on phase and magnitude has been applied (using CALFSAR as reference) for the different baseline configurations: (a) first and (b) third roots of the polynomial vzinversion method; and (c) estimation based on the approximately linear relationship between ATI phase and vzrelationship. Polynomial root 1 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Across-track ground velocity [m/s] 0.0 0.5 1.0 1.5 Histogram X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV (a) Polynomial root 3 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Across-track ground velocity [m/s] 0.0 0.5 1.0 1.5 Histogram X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV (b) Linear -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Across-track ground velocity [m/s] 0.0 0.5 1.0 1.5 Histogram X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV X31VH-X31VV X31VH-X32VH X31VH-X32VV (c) Figure 5.32: Sea clutter’s estimated across-track ground velocity distributions over sea patch AOIFSAR, DB on phase and magnitude has been applied (using CALFSAR as reference) for the different baseline configurations: (a) first and (b) third roots of the polynomial vzinversion method; and (c) estimation based on the approximately linear relationship between ATI phase and vzrelationship. 116 5.3 - F-SAR data are represented in Fig. 5.31. In the polynomial case [Figs. 5.31a-b], the first root provides the negative valued velocities, while the third root gives the positive velocities. A good match between these two methods is obtained. For the shortest baseline configuration (X31VH-X32VV), where the directional ambiguity is between 8.5 m/s and 10 m/s (depending on the incidence angle), the velocity distribution over the detected pixels of the different vessels is between -2.5 m/s and -5 m/s, which is coherent with the results of the EDPCA and ISTAP processing, where the maximization of the output SCNR is obtained close to -4.5 m/s and -5 m/s for vessel V1 and V4, respectively (see Table 5.4). For the X31VH-X32VH, having an absolute directional ambiguity 4-5 m/s, the effect of phase/velocity wrapping can be recognized (−4.5m/s≤ˆvz≤4.5m/s). In a similar way, the estimated vzfor the longest baseline formation (with the lowest directional ambiguity 3 m/s) lies between -2.5 m/s and 2.5 m/s. Analogously, sea current velocity maps can be obtained for the non-detected pixels at the output of the 2D CFAR detector, as shown in Fig. 5.30. As in the vessel’s case, the two approaches for across-track velocity estimation have been applied showing similar results. These can be better interpreted from the velocity distribution obtained over the sea clutter pixels as depicted in Fig. 5.32. A (ground) current velocity close to 0.7 m/s is obtained for both estimation techniques (linear and polynomial approximations) and the different configurations. Such figures are consistent with the measured current velocities over the same area exploiting ATI TSX (in AS mode) as done in [92]. In this case values of ground current velocities between -3.3 m/s and 2.47 m/s (-1.74 m/s and 1.30 m/s line- of-sight for incidence angle around 32 degrees) have been obtained from TSX, matching quite good the available numerical models. 5.3.2.3 EDPCA processing The impact of channel balancing on the EDPCA processing over the region of interest AOIFSAR is presented in Fig. 5.33, where a portion of the image (delimited by the solid white box in Fig. 5.24b) free of moving vessels, has been used for covariance matrix estimation. If DB (on phase and magnitude) is applied considering the (rangecompressed) calibration weights extracted from the reference land region CALFSAR [see Fig. 5.33b], there is an improvement in terms of SCNR all over the vessel’s structure for V1 (down-right corner) and V4 (upper-left corner), compared to the case of no calibration in Fig. 5.33a. When DB is applied considering the region itself for calibration (including the different vessels) there is a degradation on the SCNR comparable to or even below the non-calibrated case in Fig. 5.33c. The related detection maps are presented in Figs. 5.34a-b. The increased SCNR conditions when applying EDPCA over the calibrated channels using the reference land patch CALFSAR provides a much higher number of detected pixels around the vessels, which are precisely related to the higher contribution of the sidelobes. A good fitting is obtained with the Rayleigh distribution on the (normalized) amplitude of the residual interference, as shown in Fig. 5.34d. The estimation region delimited by the solid white box in Fig. 5.24b has been used to extract statistical parameters required by the parametric CFAR detector. The corresponding threshold level has also been included as a vertical dotted blue line in Fig. 5.34d. The effect of target self-whitening can be clearly appreciated in Fig. 5.35, where all 117 Chapter 5. Experimental MSAR-GMTI over maritime scenarios (a) (b) (c) Figure 5.33: SCNR images for EDPCA over sea patch AOIFSAR with adaptation (SAR processing and steering vector) to motion parameters vz=-5 m/s and vx=1.8 m/s, using the portion of image indicated in Fig. 5.24b for estimation of the covariance matrix: (a) no calibration has been applied; (b) DB considering the reference patch CALFSAR; and (c) DB using the region AOIFSAR itself (including the vessels). (a) (b) (c) Data distribution 0 1 2 3 4 Magnitude 0.0 0.2 0.4 0.6 0.8 Histogram Filtered data Rayleigh dist. Filtered data Rayleigh dist. Filtered data Rayleigh dist. (d) Figure 5.34: EDPCA detection maps over sea patch AOIFSAR with adaptation (SAR processing and steering vector) to motion parameters vz=-5 m/s and vx=1.8 m/s, using the portion of image indicated in Fig. 5.24b for estimation of the covariance matrix: (a) no calibration; (b) DB considering the reference patch CALFSAR (c) DB using the region AOIFSAR itself (including the vessels); and (d) depicts the distribution of the residual interference after EDPCA processing for the processing considered in (b). 118 5.3 - F-SAR data (a) (b) Figure 5.35: SCNR images for EDPCA over sea patch AOIFSAR with adaptation (SAR processing and steering vector) to motion parameters vz=-5 m/s and vx=1.8 m/s, using the whole image itself for estimation of the interference covariance matrix: (a) SCNR image and (b) detection map (DB using reference land patch CALFSAR has been applied). image pixels have been considered for the estimation of the interference covariance matrix. In this case the degradation in terms of SCNR is notorious and below the single-channel SCNR image in Fig. 5.24b, leading to a reduction in the number of detected pixels associated to the different vessels. This case study is an extreme situation, but it points out how crucial is the proper estimation of the covariance matrix in the EDPCA operation. In the results here presented the estimation of this matrix has been based on using an isolated portion of the image free of moving targets to reduce the computational load of a sliding window approach. Nevertheless, in other scenarios, where this region is not so easily defined and/or with high heterogeneous background, the boxcar-based approach could provide better performance. In this sense, and to avoid target self-whitening, proper definition of the guard zones around the pixel under test are required taking into account the expected vessels’ size. For the best case situation, with adapted focusing and DB using a land reference calibration, the EDPCA technique provides the best SCNR when compared to DPCA; which, even for such large and bright vessels, proves and validates the EDPCA processing concept. The EDPCA processor, based on a MFB SAR focusing and the adaptation of the steering or beamformer vector, provides an estimation of the vessels motion parameters as summarized in Table 5.4. A velocity of -5 m/s and -4.5 m/s on the adaptive EDPCA processor maximizes the response of the output SCNR for vessel V1 and V4, respectively. These values are coherent with the across-track velocity estimation obtained exploiting the ATI phase as described in the previous section. 5.3.2.4 ISTAP processing ISTAP technique integrates a suboptimal post-Doppler STAP in the SAR formation process to provide high-resolution SAR images of the moving targets. Fig. 5.36 depicts the range-Doppler amplitude images before and after post-Doppler STAP operation over the region of interest AOIFSAR for different calibration conditions. The images have been accordingly normalized to the noise floor. The post-Doppler beamformer is tunned to vz 119 Chapter 5. Experimental MSAR-GMTI over maritime scenarios (a) (b) (c) (d) Figure 5.36: F-SAR range-Doppler images (normalized to the average noise floor) before and after post-Doppler operation over region AOIFSAR: (a) X31VH image before clutter cancellation (BCC); (b) after clutter cancellation and beamforming (ACCB) with no channel balancing; (c) ACCB with DB; and (d) ACCB with modified DB (post-Doppler beamformer for vz=-5 m/s and vx=1.8 m/s, CALFSAR patch used for calibration). =-5 m/s and vx=1.8 m/s. Before clutter cancellation (BCC) the clutter contribution weighted by the antenna pattern can be clearly recognized within the spectral Doppler range of 300 HZ to 1300 Hz. The different range-compressed vessels’ signatures can be also identified close to the right edge of the clutter bandwidth. After clutter cancellation and beamforming (ACCB) operations, clutter contribution has been reduced down to the noise level for the different calibration situations [see Figs. 5.36b-d]. In this case, the upper region of the image (within the white box in Fig. 5.36a) has been used for interference covariance matrix estimation. A degradation in the SNR over the vessels’ signature can be appreciated when no channel balancing has been applied compared to the DB and MDB cases and, even before the post-Doppler STAP operation. Therefore, a loss in SCNR is expected in the final ISTAP images as indicated by the different processing results, comparing the SCNR images with no channel balancing [Fig. 5.37a] and once the original DB has been applied [Fig. 5.37b]. Analogous to the study made for EDPCA processing, the fact of using the region of interest itself (including moving vessels) for calibration purposes, produces a degradation in the ISTAP performance, as shown in Fig. 5.37c. In the different ISTAP images there is an odd pattern along-azimuth and at both sides of the vessels, which is not present in the EDPCA images. It is not related to secondary lobes responses, but rather it seems to be a kind of constant level replicas or ghosts of the vessel. Additional processing of the data, considering only the post-Doppler STAP combination of the different channels (beamforming) with no application of the interference covariance matrix inverse to the data (no clutter cancellation), doesn’t show up these ghost patterns. Therefore, filtering the multichannel data with the Doppler-dependent interference covariance matrix inverse modifies the spectrum of the vessel producing this odd effect. Comparing the different calibration situations considered in Fig. 5.37, for non-proper channel balancing strategies or not equalization at all, the level of these ghosts w.r.t the real vessels is smaller compared to the case of an adequate calibration. This ratio is around 40-50 dB when applying DB with the land patch CALFSAR as reference calibration. The different detection maps obtained once the magnitude of the ISTAP output 120 5.4 - TerraSAR-X data (a) (b) (c) Figure 5.44: Estimated ˆvzfor TSX-DRA mode on top of the ATI detected pixels over region AOITSX considering an adaptive SAR processing to vx=5 m/s: (a) linear method; and (b) first and (c) third roots of the polynomial vzinversion method (DB calibration has been applied considering CALTSX region as reference). Table 5.5: Estimated ˆvzin m/s for brightest scatterer at each of the six vessels in region AOITSX, using the ATI phase linear relationship with the motion parameters (results for different calibration approaches are presented). Vessel ˆvz[m/s] No cal. DB ph. DB MDB V1 2.560 1.817 1.777 1.776 V2 2.638 2.127 1.979 1.955 V3 1.980 1.034 1.039 1.032 V4 3.077 2.317 2.321 2.316 V5 3.457 2.553 2.583 2.582 V6 2.466 1.667 1.612 1.591 estimate the required statistical parameters. This patch is also used for the estimation of the interference covariance matrix when operating the EDPCA technique. The estimated across-track velocity map over the ATI detected pixels is shown in Fig. 5.44 for the linear as well as polynomial ATI phase-vzrelationships, considering a channel balancing based on the original DB technique. Both approaches, linear and polynomial, provide similar results, with values of ˆvzbetween 1 m/s and 2.5 m/s for the different vessels moving away from the satellite’s track. The polynomial first root solution provides an estimation of the negative valued across-track velocities, in a way that only the left-sided ambiguities are present in the corresponding velocity map as noticed in Fig. 5.44b; whereas, the third root solution gives positive valued vzestimations, as shown in Fig. 5.44c. The influence of channel balancing on the ATI estimated vzis summarized in Table 5.5 for each of the calibration strategies. This table provides ˆvzfor the brightest scattering point of each vessel using the classical linear ATI phase-vzrelationship, considering an 127 Chapter 5. Experimental MSAR-GMTI over maritime scenarios Vessel V3 -0.4 -0.2 0.0 0.2 0.4 Azimuth w.r.t center scene [Km] -0.66 -0.64 -0.62 -0.60 -0.58 -0.56 Slant range w.r.t center scene [Km] -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 Across-track ground velocity [m/s] -5 -4 -3 -2 -1 0 1 2 3 4 5 [m/s] (a) Left-ambiguity vessel V3 -5.0 -4.8 -4.6 -4.4 -4.2 Azimuth w.r.t center scene [Km] -0.66 -0.64 -0.62 -0.60 -0.58 -0.56 Slant range w.r.t center scene [Km] -50.0 -46.0 -42.0 -38.0 -34.0 -30.0 -26.0 -22.0 -18.0 -14.0 -10.0 Across-track ground velocity [m/s] -50 -46 -42 -38 -34 -30 -26 -22 -18 -14 -10 [m/s] (b) Right-ambiguity vessel V3 4.2 4.4 4.6 4.8 5.0 Azimuth w.r.t center scene [Km] -0.66 -0.64 -0.62 -0.60 -0.58 -0.56 Slant range w.r.t center scene [Km] 10.0 14.0 18.0 22.0 26.0 30.0 34.0 38.0 42.0 46.0 50.0 Across-track ground velocity [m/s] 10 14 18 22 26 30 34 38 42 46 50 [m/s] (c) Vessel V3 -0.4 -0.2 0.0 0.2 0.4 Azimuth w.r.t center scene [Km] -0.66 -0.64 -0.62 -0.60 -0.58 -0.56 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 Across-track ground velocity [m/s] -5 -4 -3 -2 -1 0 1 2 3 4 5 [m/s] (d) Left-ambiguity vessel V3 -5.0 -4.8 -4.6 -4.4 -4.2 Azimuth w.r.t center scene [Km] -0.66 -0.64 -0.62 -0.60 -0.58 -0.56 -50.0 -46.0 -42.0 -38.0 -34.0 -30.0 -26.0 -22.0 -18.0 -14.0 -10.0 Across-track ground velocity [m/s] -50 -46 -42 -38 -34 -30 -26 -22 -18 -14 -10 [m/s] (e) Right-ambiguity vessel V3 4.2 4.4 4.6 4.8 5.0 Azimuth w.r.t center scene [Km] -0.66 -0.64 -0.62 -0.60 -0.58 -0.56 10.0 14.0 18.0 22.0 26.0 30.0 34.0 38.0 42.0 46.0 50.0 Across-track ground velocity [m/s] 10 14 18 22 26 30 34 38 42 46 50 [m/s] (f) Figure 5.45: Estimated ˆvzfor TSX-DRA mode, using the linear relationship with ATI phase over the ATI detected pixels of vessel V3 (first row) and its related left (second row) and right (third row) ambiguities; no channel balancing results are shown in the left column and for the DB approach, with CALTSX as reference, in the right column (histograms of the estimated velocities are also included on top of the images). 128 5.4 - TerraSAR-X data adaptive SAR processing to vxof 5 m/s. It can be recognized that after channel balancing the estimated velocity is reduced compared to the non-calibrated scenario. Little variations are observed among the different calibration strategies, even for the original DB approach. Similar values are obtained for the polynomial-based approach. In Fig. 5.45 a zoom of the estimated vzmaps over vessel V3 as well as its left/right ambiguities is sketched before and after channel balancing. A histogram of the velocity distribution over the vessel and its ambiguities is also included on top of each image. An over-estimation of the corresponding V3 velocity for the non-calibrated case when compared to the channel balanced one (original DB) can be noticed, i.e., from 2 m/s to 1 m/s. This behavior is not so clear in the case of ambiguities, where the ambiguous component phase is dominant, giving unrealistic velocities on maritime scenarios 34 m/s≤ |ˆvz| ≤ 38 m/s. It must be also noted that channel balancing has been restricted to a 2 KHz bandwidth around the Doppler centroid and so the phase impact on the ambiguities is almost unaffected. Unfortunately, there is no access to ground truth data for that region at the acquisition time, which could help support the validity of the presented results. Nevertheless, from the estimated across-track ground velocity and considering in a first approximation vx =5 m/s, the related velocity of the vessels is between 9-10 knots. These values are congruent with the available AIS information for vessels cruising in this geographical area (typically 7-13 Knots), obtained from on-line sources such as Maritime Traffic [155] or Vessel Finder [156]. 5.4.1.3 DPCA processing DPCA detection maps over region AOITSX are represented in Fig. 5.46 for different channel balancing conditions. Compared to the two-dimensional CFAR ATI detector, the number of detected pixels over the different vessels has been reduced. This behavior is expected from the complex subtraction of the two channels, which degrades the effective SCNR for the slowly moving vessels as observed from the theoretical analysis in Fig. 4.9 (comparing the operation of X-DPCA and single channel SCNR). This tendency is also ratified from the SCNR analysis over the brightest scattering point of each vessel summarized in Table 5.6 (at the end of the TSX results section). Regarding the ambiguous vessels, and specifically for the V3 case, the detection is somehow reinforced due to the phase induced error on the ambiguities, as observed from the analysis of the ATI technique. This is related to the fact that the DPCA condition for this TSX-DRA acquisition configuration is not fulfilled, which otherwise would reduce the impact of the ambiguous vessels in the same manner as the non-ambiguous. Comparing DPCA detection maps for the different channel balancing methodologies, no clear differentiation is observed, except for the vessel V3, for which the number of detected pixels is slightly lower in the MDB compared to the original DB. When analyzing the DPCA response in detail and comparing the effective SCNR at the output of the DPCA’s processor some discrepancy between the different methodologies can be found. From Table 5.6, similar results are obtained for the phase-only DB and the MDB, with SCNR values around 2 to 4 dB below the case of original DB, which has an SCNR close to the non-calibrated case. 129 Chapter 5. Experimental MSAR-GMTI over maritime scenarios (a) (b) (c) Figure 5.46: DPCA detection maps over region AOITSX, considering an adaptive SAR processing to vx=5 m/s: (a) no channel balancing; (b) original DB and (c) modified DB (MDB). (a) (b) (c) Figure 5.47: EDPCA merged detection maps over region AOITSX, considering an adaptive SAR processing to vx=5 m/s and a variation of −1 m/s≤vz≤10 m/s in steps of 0.5 m/s: (a) no channel balancing; (b) DB and (c) MDB. 5.4.1.4 EDPCA processing In case of EDPCA processing, and compared to DPCA, an improvement in the detection capabilities can be clearly appreciated over the different vessels in region AOITSX, as demonstrated by the corresponding detection maps in Fig. 5.47. These images correspond to the merged detections, where the different detection maps for each iteration of the EDPCA beamformer vz(from -1 m/s to 10 m/s in steps of 0.5 m/s) and vx=5 m/s adaptation have been combined through the logical OR operator. When comparing the results for the different channel balancing approaches, quite similar results are obtained. In terms of SCNR, there is an improvement of approximately 1.4 dB w.r.t the single channel case, even for the non-calibrated conditions. The reduced number of channels and the corresponding short baseline configuration in combination with the low CNR conditions over the ocean for TSX (around 3 dB for this acquisition) limits the EDPCA improvement compared to the single channel for the small velocity 130 5.4 - TerraSAR-X data (a) (b) (c) (d) Figure 5.48: TSX range-Doppler images before and after post-Doppler operation over region AOITSX: DRAFore image (a) before clutter cancellation (BCC); (b) after clutter cancellation and beamforming (ACCB) with no channel balancing; (c) ACCB with DB; and (d) ACCB with MDB (post-Doppler beamformer tunned to vz=1 m/s and vx=5 m/s). region (-10 m/s to 10 m/s). These metrics are consistent with the results predicted by the SAR-GMTI theoretical evaluation of TSX carried out in section 4.2.2. The values of vz, providing the corresponding maximum SCNR response, are different for each calibration strategy, as indicated in Table 5.7. In the non-calibrated case there is an over-estimation of the across-track velocity compared to the case of operating with balanced channels. Taking into account that a coarse step of 0.5 m/s has been considered in the MFB, the corresponding estimated ˆvzis, using the EDPCA-SCNR maximization, coherent with the results obtained for the ATI approach in Table 5.5. 5.4.1.5 ISTAP processing DRAFore and DRAAft SSC products are already co-registrated, the systematic phase ramp (in Doppler domain) due to the baseline time delay should be re-introduced (after any channel balancing) since it bears crucial information for array processing-based techniques such as ISTAP. In Fig. 5.48 the range-Doppler amplitude images normalized to the noise floor are shown, before and after operation of the post-Doppler STAP integrated in the ISTAP algorithm. Fig. 5.48a refers to DRAFore channel before clutter cancellation (BCC), where the clutter contribution can be recognized in the spectral Doppler range between -1 KHz and 1 KHz. After clutter cancellation and beamforming in the range-Doppler domain for different calibration conditions [Figs. 5.48b-5.48d], it can be observed that the clutter contribution has been reduced to the noise level. This effect is not as obvious as in the case of F-SAR acquisitions due to the comparatively reduced CNR conditions. No big differences can be appreciated after the post-Doppler STAP operation among the different calibration strategies. For ISTAP, similar detection performance to EDPCA is achieved, as indicated by the combined or merged detection maps presented in Fig. 5.49. Nevertheless, there is a different behavior on the ambiguous response for both techniques. The so called left-sided vessel ambiguities are reinforced when compared to EDPCA operation under the same calibration conditions and for the same beamformer variation (−1 m/s≤vz≤10 m/s in steps of 0.5 m/s); while, the impact of the right-sided is reduced. The interference 131 Chapter 5. Experimental MSAR-GMTI over maritime scenarios (a) (b) (c) Figure 5.49: ISTAP merged detection maps over region AOITSX acquired with TSX-DRA, considering an adaptive SAR processing to vx=5 m/s and a variation of −1 m/s≤vz≤ 10 m/s in steps of 0.5 m/s: (a) no channel balancing; (b) DB and (c) MDB. No calibration 0 2 4 6 8 10 Across-track ground velocity [m/s] 20 25 30 35 40 45 50 55 60 SCNR [dB] DRAFore DPCA EDPCA ISTAP DRAFore DPCA EDPCA ISTAP DRAFore DPCA EDPCA ISTAP (a) DB (Ba,c=2 KHz) 0 2 4 6 8 10 Across-track ground velocity [m/s] 20 25 30 35 40 45 50 55 60 DRAFore DPCA EDPCA ISTAP DRAFore DPCA EDPCA ISTAP DRAFore DPCA EDPCA ISTAP (b) MDB (Ba,c=2 KHz) 0 2 4 6 8 10 Across-track ground velocity [m/s] 20 25 30 35 40 45 50 55 60 DRAFore DPCA EDPCA ISTAP DRAFore DPCA EDPCA ISTAP DRAFore DPCA EDPCA ISTAP (c) Figure 5.50: SCNR as a function of vzfor brightest scatterer on vessel V3 over region AOITSX, considering an adaptive SAR processing to vx=5 m/s and a variation of −1 m/s≤ vz≤10 m/s in steps of 0.5 m/s (left and right ambiguities identified by the different line styles with circle and cross symbols, respectively): (a) no channel balancing; (b) DB and (c) MDB. covariance matrix is estimated for each Doppler bin using only the upper part portion of the range-compressed data (as denoted by the white rectangular region in Fig. 5.48a). The SCNR as a function of the across-track velocity for the brightest scatterer over vessel V3, as shown in Fig. 5.50, is a good and illustrative metric to understand the operation of the different clutter cancellation based techniques (DPCA, EDPCA and ISTAP) for different channel balancing conditions. The SCNR input conditions for the DRAFore channel are also included for comparative purposes as well as the SCNR related to the left and right ambiguities, identified by the circle and cross symbols, respectively. As expected DRAFore and DPCA response are independent on the vzvariation; while EDPCA and ISTAP SCNR vary slightly as function of the adapted beamformer velocity. This small sensitivity of EDPCA and ISTAP w.r.t the across-track ground velocity is due to the compact baseline configuration and to the reduced CNR when operating with TSX; which is consistent with the theoretical SAR-GMTI performance analysis of TSX done in section 4.2.2. The SCNR for DPCA is well below the single channel SCNR, around 17 dB for the 132 5.4 - TerraSAR-X data non-calibrated and the original DB cases; whereas the MDB SCNR is approximately 22 dB smaller than DRAFore response. Comparatively, for the ambiguities case, DPCA provides values of SCNR only 13 dB and 18 dB (right and left ambiguities) below the single channel case, being almost insensitive to channel calibration. This is because the balancing techniques are restricted to 2 KHz Doppler bandwidth around the Doppler centroid, excluding the regions where the azimuth ambiguities have higher impact. For the EDPCA case an improvement on the SCNR (≈1.4 dB) compared to the single channel case is obtained, with a quite flat response as a function of the across-track velocity. Such a behavior is in accordance with the theoretical analysis of the TerraSAR-X mission considered in section 4.2.2. Comparing the different calibration conditions (from left to right), the maximum of the EDPCA SCNR response moves towards smaller acrosstrack velocities as already observed from the ATI vzestimation. Contrary to the DPCA case the SCNR for the ambiguous vessels varies significantly with vzwhen processing with EDPCA. In any case, and for the set of considered across-track velocities, EDPCA provides lower response on the ambiguities compared to DPCA. In case of ISTAP similar performance to EDPCA is obtained. As already pointed out from the detection maps, the impact of the left-sided vessel ambiguity for ISTAP is comparatively higher, while the right-sided keeps below the EDPCA case for beamformer velocities above 0 m/s. Very small differences in terms of SCNR response for the different calibration strategies are obtained when using ISTAP as indicated in Table 5.6, phaseonly calibration giving the “best” performance. It can be also noticed that EDPCA provides slightly better SCNR in general. Since ISTAP is operating directly on the range-compressed Doppler domain, the Doppler-dependent covariance matrix estimation and inversion (for clutter cancellation) applied across the PRF band is affected by the azimuth ambiguities. Hence, this could justify the slight reduction in terms of SCNR when compared to the EDPCA technique. Differences between ISTAP and EDPCA can be also appreciated in the across-track velocity of the MFB that produces the maximum SCNR response of the brightest scatterer for the different vessels in region AOITSX, as summarized in Table 5.7. For the channel balanced scenarios, ISTAP provides smaller values of ˆvzwith an average variation of 0.5 m/s for vessels V3 to V6. Nonetheless, for the small vessels V1 and V2 the velocity is much lower and deviates from the expected velocity using the ATI technique. Further analysis on the operation of the ISTAP algorithm is required to properly understand the different issues here raised up. 133 Chapter 5. Experimental MSAR-GMTI over maritime scenarios Table 5.6: Estimated SCNR for the brightest scatterer at each of the six vessels in region AOITSX, considering an adaptive SAR processing with vx=5.0 m/s (results for different calibration approaches are presented). Vessel SCNR [dB] Input DPCA EDPCA ISTAP No cal. DB ph. DB MDB No cal. DB ph. DB MDB No cal. DB ph. DB MDB V1 46.108 30.851 30.977 26.992 27.019 47.601 47.447 47.578 47.598 47.051 47.064 47.079 47.099 V2 35.490 20.885 20.111 18.648 18.469 37.031 37.110 37.019 37.038 37.435 37.452 37.470 37.479 V3 54.724 37.472 37.273 32.506 32.280 56.292 56.203 56.332 56.336 55.936 55.906 55.971 55.961 V4 44.590 30.705 30.008 27.693 27.761 46.082 46.011 46.134 46.133 46.011 46.010 46.075 46.074 V5 40.088 27.088 26.347 24.150 24.199 41.598 41.392 41.609 41.590 40.796 40.731 40.820 40.813 V6 38.586 22.983 23.901 19.050 18.977 40.090 39.806 40.058 40.049 39.701 39.649 39.712 39.700 Table 5.7: Estimated ˆvzfrom the MFB integration in the EDPCA and ISTAP processing for the brightest scatterer at each of the six vessels in region AOITSX, considering an adaptive SAR processing with vx=5.0 m/s (results for different calibration approaches are presented). Vessel ˆvz[m/s] EDPCA ISTAP No cal. DB ph. DB MDB No cal. DB ph. DB MDB V1 2.5 2.0 1.5 1.5 1.5 -1.0 -1.0 -1.0 V2 2.5 2.0 2.0 2.0 0.0 0.0 0.0 0.0 V3 2.0 1.0 1.0 1.0 2.5 0.5 0.5 0.5 V4 3.0 2.0 2.0 2.0 1.5 1.5 1.5 1.5 V5 3.5 2.5 2.5 2.5 3.0 2.0 2.0 2.0 V6 2.5 1.5 1.0 1.0 1.5 1.5 1.5 1.5 134 5.5 - Concluding remarks 5.5 Concluding remarks This chapter has explored the SAR-GMTI capabilities of current state-of-the-art airborne (F-SAR) and spaceborne (TSX) sensors, when operating over maritime scenarios. The performance of both classical dual-channel GMTI techniques (DPCA and ATI) as well as promising adaptive techniques recently proposed (EDPCA and ISTAP) has been analyzed. The objective of the chapter was to raise up possible limitations and issues to be considered when processing multichannel real data from pioneering airborne and spaceborne SAR sensors. In this sense, one of the main focus of the chapter is the study of different calibration or channel balancing strategies and how they can impair the GMTI performance. Two complete SAR-GMTI processing chains have been implemented, providing flexibility in the different stages. Specific reference patches, different from the ones of interest, can be accordingly selected for calibration and estimation purposes (interference covariance matrix and antenna pattern). The first processor integrates jointly the SAR-GMTI image based techniques (ATI, DPCA and EDPCA); while, in the second one the adaptive ISTAP technique has been implemented. In both chains, an adaptive SAR processor has been build up on the basis of a range-Doppler (RD) algorithm, being able to process both airborne and spaceborne multichannel data. This processor has been integrated in the processing chain using a MFB approach, and it can be used to refocus and estimate target parameters. Its ability to compensate for motion related defocusing has been demonstrated for airborne and spaceborne acquisitions. The image quality improvement as well as the SCNR recovery are much more clear for the airborne case, where the longer aperture times produce an important image degradation compared to the spaceborne case. In the same manner, the MFB sensitivity with across-track accelerations or/and along-track velocities is, as expected, much higher for the aerial platforms. This refocusing capability could be crucial for the SAR-GMTI detection performance, when imaging small fast boats as analyzed in section 4.3.2, and it is of great interest for post-processing target classification, delivering high-resolution images of the moving vessels. As pointed out in the literature, accurate channel balancing is crucial for the GMTI operation and the corresponding moving target parameter extraction. Under this view, different calibration strategies have been applied, being the so called digital balancing (DB), a two-dimensional spectral iterative equalization technique, the basis of these methodologies. It has been observed that reduced CNR conditions and so channel coherence could produce an important channel degradation when using such balancing techniques. This has suggested first, to limit its applicability to a given spectral extent, i.e., to define calibration bandwidths; and second, to propose alternative strategies based on a phaseonly DB and a modified version of the original DB. When the TSX operates in the DRA mode, the impact of azimuth ambiguities is important, particularly at the edges of the Doppler spectrum. Thus, the calibration strategy should avoid these spectral regions when computing the balancing weights. The reduced CNR conditions over maritime scenarios, especially important for spaceborne acquisitions, has suggested the use of land patches as a reference for extraction of the iterative calibration/balancing weights. For F-SAR data, it has been observed that an important residual phase between the different channels exists even after application of MOCO, which also performs channel coregistration. Channel equalization, consider- 135 Chapter 5. Experimental MSAR-GMTI over maritime scenarios ing the different strategies, allows an improvement of 30 to 34 dB in terms of SCNR for DPCA technique over the shortest baseline configuration for two of the vessels in the region of interest; in case of EDPCA and ISTAP this figure is around 4-6 dB. For the spaceborne acquisitions using TSX data, no big differences are observed when considering or not channel balancing, taking into account that some type of phase calibration has been already applied on the TSX products [148]. Despite the fact that the available data sets contain only big vessels with high reflectivity, such that the potential subclutter detection capabilities of the sensors combined with the adaptive processing techniques has not been evidenced, a proof of the processing concept for the different GMTI algorithms has been achieved. For the four channel F-SAR configuration, the EDPCA and ISTAP techniques provide a considerable improvement in terms of SCNR around 16 dB compared to the single channel case and close to 6 dB w.r.t DPCA technique. For the TSX data set, with slow moving targets (1-2 m/s of acrosstrack velocity), both EDPCA and ISTAP provide similar detection capabilities with an SCNR slightly above the single channel case. In the same line, the DPCA technique provides a lower number of detected pixels over the different vessels compared to ATI, which shows similar detection capabilities to the new adaptive techniques EDPCA and ISTAP. A major concern in the evaluation of the SAR-GMTI operation of the TSX-DRA mode is the role of the vessel ambiguities, which could be falsely detected as moving targets. From the different processed results, it seems that EDPCA and ISTAP provide a much better signal-to-ambiguity-ratio. For these scenarios, with bright vessels and the related ghost or ambiguous artifacts, several proposals have been considered to discriminate the real vessels from their related ambiguities exploiting polarimetry: in [157,158] the use of crosspolarized channels HV and VH filters vessel ambiguities; and in [159] time-frequency (TF) analysis of polarimetric data allows discriminating the real ships from the ghosts. From the analysis carried out in this chapter some points remain open and need to be further analyzed: the fringe-like pattern along azimuth in the F-SAR ISTAP images; and the different behavior of EDPCA and ISTAP over the moving target ambiguities. Apart from these considerations, a much more interesting study to investigate the potential capabilities of both X-band sensors is required based on ad-hoc experimental campaigns, which consider worse-case scenario of moving vessels, i.e., small slow moving boats sailing on a rough sea. These experiments should be well-defined in order to make available ground-truth data of both vessels and sea conditions at the acquisition instants for validation purposes. Additionally, an accurate characterization of the instrument would be desirable, specifically regarding the measured antenna patterns. In summary, the different results presented in this chapter show the capability to exploit several SAR-GMTI algorithms for maritime surveillance using both airborne and spaceborne SAR sensors, providing (re-focused) high-resolution images of the moving vessels. The study performed points out also the key role of the channel balancing (calibration) strategies in the SAR-GMTI operation. 136