Estimation of the Block Adjustment Error in UAV Photogrammetric Flights in Flat Areas

Citation: Arévalo-Verjel, A.N.; Lerma, J.L.; Prieto, J.F.; Carbonell-Rivera, J.P.; Fernández, J. Estimation of the Block Adjustment Error in UAV Photogrammetric Flights in Flat Areas. Remote Sens. 2022,14, 2877. https://doi.org/ 10.3390/rs14122877 Academic Editors: Kamil Krasuski and Damian Wierzbicki Received: 26 March 2022 Accepted: 11 June 2022 Published: 16 June 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). remote sensing Article Estimation of the Block Adjustment Error in UAV Photogrammetric Flights in Flat Areas Alba Nely Arévalo-Verjel 1,2, JoséLuis Lerma 1,* , Juan F. Prieto 3, Juan Pedro Carbonell-Rivera 4 and JoséFernández 5 1 Grupo de Investigación en FotogrametríayLáser Escáner (GIFLE), Departamento de Ingeniería Cartográfica, Geodesia y Fotogrametría, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain; [email protected] 2Grupo de Investigación en Hidrología y Recursos Hídricos (HYDROS), Departamento de Construcciones Civiles, Universidad Francisco de Paula Santander, Cúcuta 540003, Colombia 3ETSI Topografía, Geodesia y Cartografía, Universidad Politécnica de Madrid, Ctra. Valencia km 7, 28031 Madrid, Spain; [email protected] 4Geo-Environmental Cartography and Remote Sensing Group (CGAT), Universidad Politécnica de València, Camino de Vera s/n, 46022 Valencia, Spain; [email protected] 5Institute of Geosciences (IGEO), CSIC-UCM, Calle del Doctor Severo Ochoa, 7, Ciudad Universitaria, 28040 Madrid, Spain; [email protected] *Correspondence: [email protected].es Abstract: UAV-DAP (unmanned aerial vehicle-digital aerial photogrammetry) has become one of the most widely used geomatics techniques in the last decade due to its low cost and capacity to generate high-density point clouds, thus demonstrating its great potential for delivering highprecision products with a spatial resolution of centimetres. The questions is, how should it be applied to obtain the best results? This research explores different flat scenarios to analyse the accuracy of this type of survey based on photogrammetric SfM (structure from motion) technology, flight planning with ground control points (GCPs), and the combination of forward and cross strips, up to the point of processing. The RMSE (root mean square error) is analysed for each scenario to verify the quality of the results. An equation is adjusted to estimate the a priori accuracy of the photogrammetric survey with digital sensors, identifying the best option for µxyz (weight coefficients depending on the layout of both the GCP and the image network) for the four scenarios studied. The UAV flights were made in Lorca (Murcia, Spain). The study area has an extension of 80 ha, which was divided into four blocks. The GCPs and checkpoints (ChPs) were measured using dual-frequency GNSS (global navigation satellite system), with a tripod and centring system on the mark at the indicated point. The photographs were post-processed using the Agisoft Metashape Professional software (64 bits). The flights were made with two multirotor UAVs, a Phantom 3 Professional and an Inspire 2, with a Zenmuse X5S camera. We verify the influence by including additional forward and/or cross strips combined with four GCPs in the corners, plus one additional GCP in the centre, in order to obtain better photogrammetric adjustments based on the preliminary flight planning. Keywords: UAV; UAV-DAP; aerial close-range photogrammetry; GCP; flight planning 1. Introduction UAVs have become a valuable platform for obtaining digital images, and are deployed as a measuring instrument for numerous geomatic and geospatial applications [ 1 ]. UAV-DAP, classified as close-range aerial photogrammetry, is a versatile, accessible, and economical topographical method that can be rapidly developed to reconstruct the surface geometry of 3D objects [ 2 ]. Although the equipment was initially used only for military purposes, this method is now more widely used in the world of geomatics [ 3 ]. This technique offers excellent potential for mapping and remote sensing (RS) and satisfies the market’s needs for remote observation data. Remote Sens. 2022,14, 2877. https://doi.org/10.3390/rs14122877 https://www.mdpi.com/journal/remotesensing Remote Sens. 2022,14, 2877 2 of 17 UAV-DAP is one of the most widely used RS techniques in small extension studies, due to its flexibility in data acquisition, low operating costs, and high spatial and temporal resolution [ 3 , 4 ]. UAV-DAP is based on structure from motion (SfM) algorithms, and uses the high spatial resolution of photographs to recognise textures [ 5 ] and orient the photographs by identifying common points, without the need to know the camera parameters or the grid geometry [ 6 ]. It produces results such as digital surface models (DSM), contour lines and orthomosaics, which are used in a range of studies, such as the inspection and surveillance of natural risks [ 7 ], infrastructures or civil engineering works [ 8 ], calculating earth movements in open mines or quarries, levelling beaches [9], coastal monitoring [10], landslides monitoring [ 11 ], subsidence analysis [ 12 ], fire surveillance [ 13 ], precision agriculture [ 14 ], forest inventories [15], and vegetation monitoring [16]. Among the main advantages of UAV-DAP is its lower application cost compared to lidar (light detection and ranging) technology [ 17 ], while its results are similar in terms of precision and spatial resolution [ 18 ]. Compared to classic topography (GNSS, total station, tachymetry), one of the most important benefits is the generation of a dense cloud with less fieldwork. The UAV-DAP technique has a higher spatial resolution [ 19 ] than the satellite segment and allows data to be obtained under cloud cover. There are currently a range of applications for planning and automating flights with UAV and photo processing programmes. During the flight planning phase, it is necessary to know the legal aspects governing the flight, and to verify whether the study zone is within an urban or rural area and whether it is affected by any restrictions from the civil aviation authority. The regulations in each country (Ref. [ 20 ], for the case of Spain) and the general specifications of the equipment, contained in the manufacturer’s manual, must be followed to operate the UAV. There is usually an obligation to obtain an operating licence in order to avoid accidents and prevent causing harm to third parties. In regard to technical aspects, the correct location of the ground control points (GCPs), flight time, maximum sensor speed, and the orientation and position of the photographs to be captured must be established, and the programmed flight must be uploaded to the application to be used. It is important to consider the solar height and the GNSS satellite constellation, and to review any meteorological phenomena that directly impact the flight (Regulation (EU) 2019/947). There are also some general recommendations, such as determining the topography of the area using a digital elevation model (DEM), in the case of steep terrain, as this produces a better image cover and a more homogeneous ground sampling distance (GSD) [ 21 ]. On this type of terrain, or when there are occlusions, it is recommended to take oblique photographs to improve the orientation process and obtain more orthogonal shots of the subject. The aspects that affect the accuracy of the camera orientation, and hence the photogrammetric outputs, include the loss of the GNSS signal and the transformations in the system of coordinates (image-terrain). The GCPs allow the absolute orientation, transforming the solution to its position on the ground. In absolute orientation, the cartographic product is oriented, levelled, and scaled. In photogrammetric flights, the GCPs must therefore be taken strategically, preferably on the periphery or on the corners of the block for the planimetric component, so that the transmission error is minimal inside the block, in the case of regular surveys. Chains of GCPs located across the block should be used for altimetric control to reduce altimetric error; another option is to make cross strips at the ends of the block or every certain number of models, to minimise altimetric error, or in the case of surveys with several flights. Therefore, the strips are stabilised in the direction of the flight, producing a more stable solution [22]. The number of GCPs directly influences the model’s accuracy [ 23 – 28 ]. In this sense, to increase the accuracy of the bundle block adjustment, it is recommended to understand the behaviour of the planimetric and altimetric errors based on the number of GCPs. For altimetry, the GCPs should be distributed across the flight lines along chains or cross strips Remote Sens. 2022,14, 2877 3 of 17 on the edges of the block [ 2 , 23 ]. However, currently, there is usually no distinction between planimetric control and altimetric control, and surveyors measure full XYZ coordinates. Besides, the absence of GCPs makes it challenging to detect coarse global errors [23,29]. The influence of the number of GCPs has been recently studied for UAVs based on the area studied. Table 1summarises the error reported in different contributions, showing how a greater density of GCPs per hectare (ha) may not directly increase the accuracy of the photogrammetric bundle block adjustment. Table 1. Studies on the number of GCP and their relation with the study area. Reference GCP AREA (ha) Ratio GCP/ha RMSE (cm) [2] 3 0.02 150 52 [29] 45 1 45 0.23 [27] 5 0.83 6 6.2 [25] 27 5.0 5.4 6.6 [23] 7 1.5 4.6 51 [30] 5 2.73 1.83 3 [31] 15 12 1.25 14.3 [32] 20 17.6 1.13 3.6 [24] 15 17.6 0.85 5.8 [26] 11 37.4 0.29 5.9 [33] 6 38 0.15 1.3 [28] 102 1200 0.1 1 [34] 9 270 0.03 3.2 The main aim of this study is to demonstrate how the flight plan influences the results obtained with UAV-DAP by applying aerial triangulation with bundle block adjustment. 2. Materials and Methods The study was conducted in Lorca (Murcia, Spain). The study zone has been continually monitored for ten years. It presents important subduction of the terrain due to the intensive overexploitation of the local aquifers, which has led to deformations in the vertical and horizontal components of up to 10 cm/year [ 35 – 38 ]. Prior to the flights, NOTAM information for the area to be flown was reviewed. The information was consulted on the geoportal dedicated to drone flights of the Spanish Aviation Safety and Security Agency (https://drones.enaire.es/ accessed on 15 May 2021). A UAV photogrammetric survey was carried out during the field campaign (May 2021), dividing the area of interest into four blocks to cover a total area of 80 ha (Figure 1); the areas of each block are shown in Table 2, with the type of UAV used. Table 2. Area in hectares for each block studied; h f refers to the forward flight height, and h c refers to cross flight height. Block Strips Type Area (ha) UAV Flight Height Block 1 Forward strips 19.11 Phantom 3 Pro hf= 120 m Block 1 Cross strip 1 0.8 Inspire 2 hc= 110 m Block 1 and 2 Cross strip 2 0.8 Inspire 2 hc= 110 m Block 2 Forward strips 19.11 Phantom 3 Pro hf= 120 m Block 2 and 3 Cross strip 3 0.8 Inspire 2 hc= 110 m Block 3 Forward strips 22.95 Inspire 2 hf= 120 m Block 3 and 4 Cross strip 4 0.8 Inspire 2 hc= 110 m Block 4 Forward strips 18.86 Phantom 3 Pro hf= 120 m Block 4 Cross strip 5 0.8 Inspire 2 hc= 110 m Total 84.03 Remote Sens. 2022,14, 2877 4 of 17 Remote Sens. 2022, 14, x FOR PEER REVIEW 4 of 18 Figure 1. Location of the study area in Lorca, Vía Camino de Puente Alto; the coordinates for the reference system are UTM 30N ETRS89. Points 7,8,9,10,33 have the maximum deformation in the study of [35]. Table 2. Area in hectares for each block studied; h f refers to the forward flight height, and h c refers to cross flight height. Block Strips Type Area (ha) UAV Flight Height Block 1 Forward strips 19.11 Phantom 3 Pro h f = 120 m Block 1 Cross strip 1 0.8 Inspire 2 h c = 110 m Block 1 and 2 Cross strip 2 0.8 Inspire 2 h c = 110 m Block 2 Forward strips 19.11 Phantom 3 Pro h f = 120 m Block 2 and 3 Cross strip 3 0.8 Inspire 2 h c = 110 m Block 3 Forward strips 22.95 Inspire 2 h f = 120 m Block 3 and 4 Cross strip 4 0.8 Inspire 2 h c = 110 m Block 4 Forward strips 18.86 Phantom 3 Pro h f = 120 m Block 4 Cross strip 5 0.8 Inspire 2 h c = 110 m Total 84.03 During the flights, there was a NOTAM in force in the area affecting Flight Level 100/Flight Level 220, issued by the General Air Academy based in San Javier (Murcia), so we had to coordinate operations with the control tower. Two multirotor UAVs were used to acquire photogrammetric data: a DJI Phantom 3 Pro (Figure 2a) and a DJI Inspire 2, equipped with a Zenmuse X5S camera (Figure 2b). The camera specifications are shown in Table 3. The flights were made under a VLOS (Visual Line of Sight) operational scenario with the visual scope of the UAV, using the Dronedeploy application for the flight plan [39]. The meteorological conditions for the flights were optimal: a sunny day with calm winds. Figure 1. Location of the study area in Lorca, Vía Camino de Puente Alto; the coordinates for the reference system are UTM 30N ETRS89. Points 7,8,9,10,33 have the maximum deformation in the study of [35]. During the flights, there was a NOTAM in force in the area affecting Flight Level 100/Flight Level 220, issued by the General Air Academy based in San Javier (Murcia), so we had to coordinate operations with the control tower. Two multirotor UAVs were used to acquire photogrammetric data: a DJI Phantom 3 Pro (Figure 2a) and a DJI Inspire 2, equipped with a Zenmuse X5S camera (Figure 2b). The camera specifications are shown in Table 3. The flights were made under a VLOS (Visual Line of Sight) operational scenario with the visual scope of the UAV, using the Dronedeploy application for the flight plan [ 39 ]. The meteorological conditions for the flights were optimal: a sunny day with calm winds. Remote Sens. 2022, 14, x FOR PEER REVIEW 5 of 18 (a) (b) Figure 2. UAVs used in the study: (a) Phantom 3 Pro; (b) Inspire 2 with a Zenmuse X5S camera. Table 3. Camera and image specifications for the Phantom 3 Pro and Inspire 2 UAV used in the study. Drone Phantom 3 Pro Inspire 2 Resolution 4000 × 3000 pixels 5280 × 3956 pixels DJI FC300X Zenmuse X5S F-stop f/2.8 f/1.7 Focal distance 4 mm 15 mm Equivalent 35 mm focal length 20 30 2.1. GNSS Campaign The GCPs and ChPs (check points), also known as ground evaluation points (GEP), were marked before the flight. This was done by creating a cardboard template of a target of 60 cm × 60 cm comprising three blades, each separated by 120°, and a central circle. Each point was marked using reflective white paint, and a survey nail was placed in the centre (Figure 3a). (a) (b) Figure 3. GCP: (a) target with three blades and a central circle with a nail in the centre; (b) dual-frequency GNSS receiver positioned on a tripod and centred on the point mark. All the points (GCPs and ChPs) were measured with dual-frequency GNSS receivers (GPS + GLONASS) on a tripod and centred on the point mark (Figure 3b) for at least 15 Figure 2. UAVs used in the study: (a) Phantom 3 Pro; (b) Inspire 2 with a Zenmuse X5S camera. Remote Sens. 2022,14, 2877 5 of 17 Table 3. Camera and image specifications for the Phantom 3 Pro and Inspire 2 UAV used in the study. Drone Phantom 3 Pro Inspire 2 Resolution 4000 ×3000 pixels 5280 ×3956 pixels DJI FC300X Zenmuse X5S F-stop f/2.8 f/1.7 Focal distance 4 mm 15 mm Equivalent 35 mm focal length 20 30 2.1. GNSS Campaign The GCPs and ChPs (check points), also known as ground evaluation points (GEP), were marked before the flight. This was done by creating a cardboard template of a target of 60 cm × 60 cm comprising three blades, each separated by 120 ◦ , and a central circle. Each point was marked using reflective white paint, and a survey nail was placed in the centre (Figure 3a). Remote Sens. 2022, 14, x FOR PEER REVIEW 5 of 18 (a) (b) Figure 2. UAVs used in the study: (a) Phantom 3 Pro; (b) Inspire 2 with a Zenmuse X5S camera. Table 3. Camera and image specifications for the Phantom 3 Pro and Inspire 2 UAV used in the study. Drone Phantom 3 Pro Inspire 2 Resolution 4000 × 3000 pixels 5280 × 3956 pixels DJI FC300X Zenmuse X5S F-stop f/2.8 f/1.7 Focal distance 4 mm 15 mm Equivalent 35 mm focal length 20 30 2.1. GNSS Campaign The GCPs and ChPs (check points), also known as ground evaluation points (GEP), were marked before the flight. This was done by creating a cardboard template of a target of 60 cm × 60 cm comprising three blades, each separated by 120°, and a central circle. Each point was marked using reflective white paint, and a survey nail was placed in the centre (Figure 3a). (a) (b) Figure 3. GCP: (a) target with three blades and a central circle with a nail in the centre; (b) dual-frequency GNSS receiver positioned on a tripod and centred on the point mark. All the points (GCPs and ChPs) were measured with dual-frequency GNSS receivers (GPS + GLONASS) on a tripod and centred on the point mark (Figure 3b) for at least 15 Figure 3. GCP: ( a ) target with three blades and a central circle with a nail in the centre; ( b ) dualfrequency GNSS receiver positioned on a tripod and centred on the point mark. All the points (GCPs and ChPs) were measured with dual-frequency GNSS receivers (GPS + GLONASS) on a tripod and centred on the point mark (Figure 3b) for at least 15 min. All the points were measured twice with a different constellation and different receivers, which were configured for a static survey. A total of ten GCPs were measured, distributed at the four corners of each block, and nine ChPs were arranged randomly so that there were at least two ChPs in each block. The distribution of the points is shown in Figure 4. When designing this distribution, priority was given to ensuring that the points were located on the firm ground, such as roadways, and that no nearby elements would impede the satellite signal. The GCPs were positioned in the common areas between the blocks. Short cross flights were made in these same areas to optimise the UAV batteries and reduce the number of GCPs. The precise geodetic ionospheric correction models of the CODE (Centre for Orbit Determination in Europe [ 40 ]) and the precise ephemerides of the IGS (International GNSS Service) [ 41 ] were used to calculate the GCPs and ChPs coordinates for both constellations. Data from 22 continuous stations were processed to improve the general network configuration and link the local measurements to a regional geodetic reference framework. These stations are located in the southeast of the Iberian Peninsula and are part of the regional networks of the Region of Murcia (REGAM and MERISTEMUM) and the Spanish National ERGNSS-IGN Network (National Geographic Institute), with 24 h and 30 s of observation over ten days. The GNSS vectors in the network were processed using Leica Infinity software, with absolute antenna calibration models and Vienna Mapping Functions Remote Sens. 2022,14, 2877 6 of 17 (VMF) [42] for the tropospheric modelling. Subsequently, the vectors previously obtained in the network were combined with their complete variance-covariance matrices using Microsearch GeoLab software. This allows the estimation of the whole set of coordinates of the network points on the ETRS89 system, with an independent weighting strategy based on the quality of the vectors following the methodology used in high-precision networks [43,44]. Remote Sens. 2022, 14, x FOR PEER REVIEW 6 of 18 min. All the points were measured twice with a different constellation and different receivers, which were configured for a static survey. A total of ten GCPs were measured, distributed at the four corners of each block, and nine ChPs were arranged randomly so that there were at least two ChPs in each block. The distribution of the points is shown in Figure 4. When designing this distribution, priority was given to ensuring that the points were located on the firm ground, such as roadways, and that no nearby elements would impede the satellite signal. The GCPs were positioned in the common areas between the blocks. Short cross flights were made in these same areas to optimise the UAV batteries and reduce the number of GCPs. Figure 4. Location of the ten GCPs at the corners of each block and nine ChPs distributed within the blocks; the reference system is UTM 30N ETRS89. The precise geodetic ionospheric correction models of the CODE (Centre for Orbit Determination in Europe [40]) and the precise ephemerides of the IGS (International GNSS Service) [41] were used to calculate the GCPs and ChPs coordinates for both constellations. Data from 22 continuous stations were processed to improve the general network configuration and link the local measurements to a regional geodetic reference framework. These stations are located in the southeast of the Iberian Peninsula and are part of the regional networks of the Region of Murcia (REGAM and MERISTEMUM) and the Spanish National ERGNSS-IGN Network (National Geographic Institute), with 24 h and 30 s of observation over ten days. The GNSS vectors in the network were processed using Leica Infinity software, with absolute antenna calibration models and Vienna Mapping Functions (VMF) [42] for the tropospheric modelling. Subsequently, the vectors previously obtained in the network were combined with their complete variance-covariance matrices using Microsearch GeoLab software. This allows the estimation of the whole set of coordinates of the network points on the ETRS89 system, with an independent weighting strategy based on the quality of the vectors following the methodology used in high-precision networks [43,44]. Figure 4. Location of the ten GCPs at the corners of each block and nine ChPs distributed within the blocks; the reference system is UTM 30N ETRS89. 2.2. Image Acquisition Flights were planned with the DroneDeploy application for PC, which allows the importation of KML (Keyhole Markup Language) or KMZ (Keyhole Markup Language compressed). These formats are based on XML to store geographic data and related content, and are an official standard of the Open Geospatial Consortium (OGC) [ 45 ]. The flights were programmed prior to the data campaign, taking into account the autonomy of the equipment batteries and the study area; the blocks were imported to the DroneDeploy application in the KMZ format. Three flight missions were carried out with the Phantom 3 Pro following the scheme in Figure 5a, and one with the Inspire 2 (Figure 5b) to cover the four blocks. Another five flight missions were completed with the Inspire 2 (Figure 5c) for the cross strip at the height of 110 m (h c , cross flight height). The images were acquired orthogonally and with a forward and side overlap of over 60% [46]. The flight configurations were the following: - Phantom 3 Pro: For Blocks 1,2, and 4, flight height (h f ) 120 m (the maximum allowed by Spanish regulation), forward overlap 80%, side overlap 60%, and speed 9 m/s for an area of 19 ha, with a GSD of 5.1 cm. The flight duration was 14 0 8 0 0 , taking 326 images for Block 1, 296 for Block 2, and 310 for Block 4. - Inspire 2: Flight height 120 m (h f ), forward overlap 80%, side overlap 60%, speed 10 m/s for an area of 23 ha, with a GSD of 2.1 cm. The flight duration was 14 0 38 0 0 , taking a total of 327 images in Block 3. Remote Sens. 2022,14, 2877 7 of 17 - Inspire 2: Strip flight height 110 m (h f ), forward overlap 80%, side overlap 60%, speed 10 m/s for an area of 0.8 ha, with a GSD of 2.4 cm. The flight duration was 4 0 39 0 0 , taking a total of 74 images for each block. Remote Sens. 2022, 14, x FOR PEER REVIEW 7 of 18 2.2. Image Acquisition Flights were planned with the DroneDeploy application for PC, which allows the importation of KML (Keyhole Markup Language) or KMZ (Keyhole Markup Language compressed). These formats are based on XML to store geographic data and related content, and are an official standard of the Open Geospatial Consortium (OGC) [45]. The flights were programmed prior to the data campaign, taking into account the autonomy of the equipment batteries and the study area; the blocks were imported to the DroneDeploy application in the KMZ format. Three flight missions were carried out with the Phantom 3 Pro following the scheme in Figure 5a, and one with the Inspire 2 (Figure 5b) to cover the four blocks. Another five flight missions were completed with the Inspire 2 (Figure 5c) for the cross strip at the height of 110 m (h c , cross flight height). The images were acquired orthogonally and with a forward and side overlap of over 60% [46]. The flight configurations were the following: - Phantom 3 Pro: For Blocks 1,2, and 4, flight height (h f ) 120 m (the maximum allowed by Spanish regulation), forward overlap 80%, side overlap 60%, and speed 9 m/s for an area of 19 ha, with a GSD of 5.1 cm. The flight duration was 14′8″, taking 326 images for Block 1, 296 for Block 2, and 310 for Block 4. - Inspire 2: Flight height 120 m (h f ), forward overlap 80%, side overlap 60%, speed 10 m/s for an area of 23 ha, with a GSD of 2.1 cm. The flight duration was 14′38″, taking a total of 327 images in Block 3. - Inspire 2: Strip flight height 110 m (h f ), forward overlap 80%, side overlap 60%, speed 10 m/s for an area of 0.8 ha, with a GSD of 2.4 cm. The flight duration was 4′39″, taking a total of 74 images for each block. (a) (b) (c) Figure 5. The flight programming was initially carried out with the DroneDeploy application: (a) Phantom 3 Pro, Block 1; (b) Inspire 2, Block 3; (c) cross strip Inspire2, Block 1. For measuring 80 ha of the overall study area, it was divided into four areas (Figure 4) with its corresponding blocks (Figure 6), in a way such that a single set of UAV batteries was used for each block. Figure 6 displays the setup for the overall study area, Scenario C (next section). Figure 5. The flight programming was initially carried out with the DroneDeploy application: (a) Phantom 3 Pro, Block 1; (b) Inspire 2, Block 3; (c) cross strip Inspire2, Block 1. For measuring 80 ha of the overall study area, it was divided into four areas (Figure 4) with its corresponding blocks (Figure 6), in a way such that a single set of UAV batteries was used for each block. Figure 6displays the setup for the overall study area, Scenario C (next section). Remote Sens. 2022, 14, x FOR PEER REVIEW 8 of 18 Figure 6. (Upper row) Study area distributed in four blocks. (Bottom row) Distribution of the flight lines for Scenario C. 2.3. Photogrammetric Processing The data was processed using a laptop equipped with an ASUS processor Intel (R) Core (TM) i7 -4210U CPU 1.70 GHz 2.40 GHz, RAM 16 GB and an NVIDIA GEFORCE 820 M graphics card, running under Windows 10 (64 bits). The program used for processing the images was Agisoft Metashape Professional (64 bits), analysing several scenarios to generate the dense point cloud to compare and verify which of the four scenarios obtained the best results: • Scenario A: Flight mission with flight strips, (example Block 1, Figure 7A). • Scenario B: Flight mission with flight strips, in addition to a flight strip covering the whole perimeter of each block (example Block 1, Figure 7B). • Scenario C: Flight mission with flight strips; in addition, one cross strip at both ends of each block (example Block 1, Figure 7C). • Scenario D: Flight mission with flight strips; an additional strip covering the whole perimeter and two cross strips at both ends of each block (example Block 1, Figure 7D). Scenarios A, B, and C are image subsets of Scenario D. Figure 6. ( Upper row ) Study area distributed in four blocks. ( Bottom row ) Distribution of the flight lines for Scenario C. 2.3. Photogrammetric Processing The data was processed using a laptop equipped with an ASUS processor Intel (R) Core (TM) i7 -4210U CPU 1.70 GHz 2.40 GHz, RAM 16 GB and an NVIDIA GEFORCE 820 M graphics card, running under Windows 10 (64 bits). The program used for processing the images was Agisoft Metashape Professional (64 bits), analysing several scenarios to generate the dense point cloud to compare and verify which of the four scenarios obtained the best results: •Scenario A: Flight mission with flight strips, (example Block 1, Figure 7A). • Scenario B: Flight mission with flight strips, in addition to a flight strip covering the whole perimeter of each block (example Block 1, Figure 7B). • Scenario C: Flight mission with flight strips; in addition, one cross strip at both ends of each block (example Block 1, Figure 7C). • Scenario D: Flight mission with flight strips; an additional strip covering the whole perimeter and two cross strips at both ends of each block (example Block 1, Figure 7D). Remote Sens. 2022,14, 2877 8 of 17 Remote Sens. 2022, 14, x FOR PEER REVIEW 9 of 18 Figure 7. Processing of each scenario: (A) Scenario A, processing of photographs with conventional flight planning; (B) Scenario B, Scenario A plus the block perimeter; (C) Scenario C, Scenario A plus one cross strip at each edge; (D) Scenario D, Scenario B plus three cross strips at each edge. 2.4. Accuracy of the Results For the evaluation of the results, two statistics were used: the a priori accuracy of the block and RMSE. 2.4.1. A Priori Accuracy of the Block The estimation of the a priori planimetric error of the blocks with four GPSs at the edges (Scenario A) uses the next equation: σ B,L = (0.47 + 0.25n s )σ M,L , (1) where: σ B,L = estimated planimetric accuracy of the block (L = XY); σ o = sigma naught of the bundle block adjustment; n s = number of strips; σ M,L = estimated planimetric accuracy of a single model. Equation (1) was conceived for aerial photographs measured with analytical stereoplotters [47]. For digital photogrammetry with digital sensors, we can rewrite Equation (1) as the following: σ B,XYZ = μ xyz * σ o * GSD (2) where: σ o = sigma naught of the bundle block adjustment can be taken as the mean reprojection error of the adjustment. Figure 7. Processing of each scenario: ( A ) Scenario A, processing of photographs with conventional flight planning; ( B ) Scenario B, Scenario A plus the block perimeter; ( C ) Scenario C, Scenario A plus one cross strip at each edge; (D) Scenario D, Scenario B plus three cross strips at each edge. Scenarios A, B, and C are image subsets of Scenario D. 2.4. Accuracy of the Results For the evaluation of the results, two statistics were used: the a priori accuracy of the block and RMSE. 2.4.1. A Priori Accuracy of the Block The estimation of the a priori planimetric error of the blocks with four GPSs at the edges (Scenario A) uses the next equation: σB,L = (0.47 + 0.25ns)σM,L, (1) where: σB,L = estimated planimetric accuracy of the block (L = XY); σo= sigma naught of the bundle block adjustment; ns= number of strips; σM,L = estimated planimetric accuracy of a single model. Equation (1) was conceived for aerial photographs measured with analytical stereoplotters [ 47 ]. For digital photogrammetry with digital sensors, we can rewrite Equation (1) as the following: σB,XYZ =µxyz ∗σo∗GSD (2) Remote Sens. 2022,14, 2877 9 of 17 where: σo = sigma naught of the bundle block adjustment can be taken as the mean reprojection error of the adjustment. µxyz = weight coefficients depending on the layout of both the GCP and the image network. This paper seeks to identify the weight coefficients ( µxyz ) in Equation (2) for the four scenarios acquired by UAV, A, B, C, and D, in order to determine the best equation for the a priori accuracy estimation valid for the UAV-DAP with absolute GNSS on flat areas. To the authors’ knowledge, no similar equation exists in the literature. 2.4.2. RMSE The RMSE is calculated to determine the accuracy of the photogrammetric results. The square of the RMSE is equal to the arithmetic mean of the squares of the true errors [ 48 ], defined by the next equation: RMSE =s∑n i=1(XYZ −Control)2 n(3) where: XYZ = photogrammetric coordinates; Control = reference data (GCP and ChP) taken in the field with GNSS; n = number of verification points. 3. Results 3.1. Results of the Global Navigation Satellite System (GNSS) Table 4shows the coordinates and uncertainties of the GCP and ChP, in addition to the four continuous stations located in the area near the study zone. The grid was finally adjusted with a loose restriction, taking into account the regional velocity field developed in [35,44]. The values of the uncertainties were calculated with a 95% confidence level. Table 4. Coordinates of the GCP and the four continuous stations (ALHA, LORC, LRCA, and MAZA) for the observation period used for the adjustment; Microsearch GeoLab software, reference system UTM 30N ETRS89. Coordinates (m) Std (m) Point East North Altitude East North Altitude 1 GCP 619,066.137 4,167,121.713 290.788 0.007 0.005 0.012 2 GCP 619,228.593 4,167,279.381 291.107 0.006 0.004 0.010 3 GCP 618,657.880 4,167,476.026 293.247 0.006 0.005 0.011 4 GCP 618,807.284 4,167,654.158 293.218 0.006 0.005 0.010 5 GCP 618,439.352 4,168,023.346 295.627 0.006 0.005 0.012 6 GCP 618,252.834 4,167,885.737 296.434 0.005 0.004 0.011 7 GCP 617,869.899 4,168,444.438 301.216 0.008 0.007 0.012 8 GCP 617,725.688 4,168,267.210 301.212 0.005 0.004 0.008 9 GCP 617,556.991 4,168,820.869 306.724 0.008 0.007 0.012 10 GCP 617,373.720 4,168,634.016 305.914 0.007 0.006 0.011 11 ChP 617,949.400 4,168,139.298 299.812 0.013 0.010 0.025 12 ChP 618,565.778 4,167,644.981 294.215 0.009 0.007 0.017 13 ChP 617,639.593 4,168,465.141 303.490 0.012 0.010 0.020 14 ChP 617,775.094 4,168,586.984 301.914 0.010 0.008 0.018 15 ChP 617,496.083 4,168,564.809 305.395 0.011 0.011 0.018 16 ChP 618,259.189 4,168,060.380 296.895 0.005 0.004 0.009 17 ChP 618,525.229 4,167,874.276 294.169 0.006 0.005 0.012 18 ChP 618,839.705 4,167,325.172 292.311 0.009 0.007 0.016 19 ChP 618,805.372 4,167,568.696 293.171 0.006 0.005 0.012 ALHA 636,738.931 4,185,231.011 201.790 0.003 0.003 0.004 LORC 615,840.139 4,168,225.450 313.952 0.003 0.002 0.003 LRCA 614,704.897 4,168,655.120 332.211 0.003 0.002 0.004 MAZA 649,154.772 4,162,049.757 55.060 0.002 0.002 0.003 Remote Sens. 2022,14, 2877 16 of 17 18. 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