Scan matching by cross-correlation and differential evolution

elec onics A icle Scan Ma ching by C oss-Co ela ion and Di e en ial E olu ion Ja omi Konecny 1,* , Pa el K ome 1, Michal P auzek1and Pe Musilek2 1Facul y o Elec ical Enginee ing and Compu e Science, VSB—Technical Uni e si y o Os a a, 708 00 Os a a, Czech Republic 2Depa men o Elec ical and Compu e Enginee ing, Uni e si y o Albe a, Edmon on, AB T6G 1H9, Canada *Co espondence: ja omi [email p o ec ed]; Tel.: +420-59-732-5996 Recei ed: 28 May 2019; Accep ed: 30 July 2019; Published: 1 Augus 2019   Abs ac : Scan ma ching is an impo an ask, sol ed in he con ex o many high-le el p oblems including pose es ima ion, indoo localiza ion, simul aneous localiza ion and mapping and o he s. Me hods ha a e accu a e and adap i e and a he same ime compu a ionally e icien a e equi ed o enable loca ion-based se ices in au onomous mobile de ices. Such de ices usually ha e a wide ange o high- esolu ion senso s bu only a limi ed p ocessing powe and cons ained ene gy supply. This wo k in oduces a no el high-le el scan ma ching s a egy ha uses a combina ion o wo ad anced algo i hms ecen ly used in his ield: c oss-co ela ion and di e en ial e olu ion. The c oss-co ela ion be ween wo lase ange scans is used as an e icien measu e o scan alignmen and he di e en ial e olu ion algo i hm is used o sea ch o he pa ame e s o a ans o ma ion ha aligns he scans. The p oposed me hod was expe imen ally alida ed and showed good abili y o ma ch lase ange scans aken sho ly a e each o he and an excellen abili y o ma ch lase ange scans aken wi h longe ime in e als be ween hem. Keywo ds: scan ma ching; indoo localiza ion; di e en ial e olu ion; c oss-co ela ion; obo ics 1. In oduc ion The de e mina ion o he posi ion o a mo ing objec is an essen ial pa o many complex applica ions. While ou doo localiza ion can be achie ed wi h he help o global sa elli e ne wo ks including he Global Posi ioning Sys em (GPS) and he Global Na iga ion Sa elli e Sys em (GLONASS), an e icien indoo localiza ion is s ill an open p oblem [ 1 , 2 ]. I can be de ined as he p ocess o ob aining he loca ion o a mo ing objec in an indoo en i onmen [ 2 ]. Indoo localiza ion is an enabling echnology o a a ie y o loca ion-based se ices ha can be used in he con ex o ad anced manu ac u ing (Indus y 4.0) [ 3 ], In e ne o hings [ 2 ], sma buildings [ 1 ], indoo (unde g ound) escue ope a ions [4,5] and many o he applica ions. Sel -localiza ion o an au onomous mobile obo o an unmanned ae ial ehicle (UAV) [ 6 ], a special ype o indoo localiza ion, is one o he g ea challenges o mode n obo ics [ 7 , 8 ]. I elies on an independen measu emen and analysis o senso da a ha pe o med by he obo o es ima e i s own posi ion and mo ion ajec o y in an unknown indoo en i onmen . In con as o o he ypes o indoo localiza ion, i does no use any ex e nal signals, beacons o o he in o ma ion han is no sensed by he obo i sel [ 8 ]. Sel -localiza ion is associa ed wi h he p oblem o simul aneous localiza ion and mapping (SLAM). As SLAM, i equi es app oaches ha a e accu a e, obus and compu a ionally e icien a he same ime [8]. The e a e many me hods o mobile obo indoo sel -localiza ion [ 2 , 7 , 9 – 11 ]. In gene al, hey a e based on ideo signals analysis and compu e ision, in a ed and ul asound senso s, lase ange Elec onics 2019,8, 856; doi:10.3390/elec onics8080856 www.mdpi.com/jou nal/elec onics Elec onics 2019,8, 856 2 o 20 inde s, sona sys ems [ 7 , 12 ], adio- equency iden i ica ion (RFID), wi eless ne wo k echnologies such as Wi-Fi, Blue oo h [ 10 , 11 ] and Zigbee [ 2 ], ul a-wideband (UWB), magne ic senso s and acous ic signal analysis [ 2 , 10 ]. Indoo sel -localiza ion by ligh de ec ion and anging (LiDAR) elies on analysis o a sequence o lase ange scans. The scans cap u e he su oundings o he obo as a se ies o poin s ep esen ing he in e sec ions o he lase beam wi h nea by objec s [ 7 ]. They gene a e sequences o 2- o 3-dimensional poin clouds ha a e mu ually compa ed (ma ched) o app oxima e he ajec o y o he obo in he en i onmen . In gene al, scan ma ching algo i hms can be spli in o wo majo g oups. Poin -based app oaches p ocess he en i e poin clouds, while ea u e-based echniques ocus on ea u es ex ac ed om he poin clouds by a ious ea u e ex ac ion algo i hms. The ea u es a e seen as landma ks and he changes in hei ( ela i e) loca ions a e used o es ima e he mo es o he obo [7]. Ad anced me hods ha u ilize a i icial in elligence, machine lea ning and so compu ing can be used o di e en ypes o sel -localiza ion applica ions. Fo example, a i icial neu al ne wo ks and suppo ec o machines ha e been used o build indoo localiza ion models based on he ecei ed signal s eng h indica o (RSSI) [ 2 ]. In his wo k, a no el scan ma ching algo i hm based on di e en ial e olu ion and modi ied c oss-co ela ion is in oduced. C oss-co ela ion is used o e alua e he alignmen o lase ange scans, while di e en ial e olu ion se es as an op imiza ion me hod o he app oxima ion o he scan ma ching pa ame e s. The con ibu ions o his wo k a e wo old: (1) I shows ha he di e en ial e olu ion can be used as an op imiza ion mechanism in a poin -based scan ma ching s a egy; and (2) I demons a es ha c oss-co ela ion is a compu a ionally e icien and a he same ime obus poin cloud alignmen measu e. The ex ensi e expe imen al e alua ion o hese no el concep s also demons a es ha he scan ma ching p ocedu e based on di e en ial e olu ion and c oss-co ela ion can be used o accu a e indoo localiza ion o au onomous mobile de ices. The emainde o his a icle is s uc u ed in he ollowing way. The p oblem o localiza ion is summa ized and ela ed wo k is e iewed in Sec ion 2. The algo i hms used in his wo k (scan ma ching, c oss-co ela ion and di e en ial e olu ion) a e desc ibed in Sec ion 3. The p oposed app oach is de ailed in Sec ion 4and expe imen ally e alua ed in Sec ion 5. The esul s o conduc ed expe imen s a e discussed in Sec ion 6and he a icle is concluded in Sec ion 7which also ou lines u u e esea ch di ec ions. 2. Rela ed Wo k Al hough indoo localiza ion has been add essed by a ple ho a o me hods and algo i hms wi h a ious p ope ies, i s ill emains an open p oblem. Tigh ly linked o mapping o (unknown) indoo en i onmen s, i is an essen ial elemen o he compound p oblem o simul aneous localiza ion and mapping (SLAM) [ 13 , 14 ]. Di e en ypes o localiza ion and SLAM algo i hms ha e been de eloped o a ious ypes o en i onmen s [ 15 ]. Accu a e SLAM algo i hms ha e been p oposed o la ge ou doo a eas [ 16 ] and limi ed indoo spaces [ 17 ]. Mon e Ca lo localiza ion (MCL) is a popula amily o localiza ion me hods [ 9 , 18 , 19 ] ha use, among o he s, pa icle and Kalman il e s [ 20 ]. A he s a ing poin o he MCL p ocess, a pool o andom posi ions and angles is c ea ed. When he obo mo es h ough an en i onmen , he algo i hm upda es all posi ions in he pool acco ding o a obo mo ion model. The expec ed obo su ounding is compa ed o da a om a senso (e.g., he LiDAR) su eying he ac ual en i onmen and he posi ions ha co espond o he eal da a mos a e ewa ded. The disad an age o he MCL me hod is he necessi y o obo mo emen and he need o addi ional senso s (e.g., odome e s) ha a e equi ed by he mo ion model [21]. Ano he amily o p omising SLAM app oaches is based on he use o e en came as [ 22 ]. E en came as p oduce sequences o ideo ames and, addi ionally, in o ma ion abou b igh ness changes on he pixel le el. The ad an ages o e en came as include e y high dynamic ange, absence o mo ion blu and only a small la ency (in he o de o mic oseconds [ 23 ]). An o e iew o SLAM algo i hms ha use e en came as is p o ided, o example, in [24]. Elec onics 2019,8, 856 3 o 20 Localiza ion is also one o he majo challenges o UAVs. They equi e in o ma ion abou p ecise loca ion in o o de o a oid obs acles [ 25 ] and o ajec o y planning [ 26 ]. UAVs can, in gene al, implemen simila localiza ion app oaches as mobile obo s. Howe e , he localiza ion me hods need o be adjus ed o add ess he speci ics o ae ial mo emen such as 3D SLAM. A comp ehensi e e iew o localiza ion s a egies o UAVs can be ound in [6]. Scan ma ching [ 27 , 28 ] is a g oup o popula high-le el localiza ion/SLAM me hods ha p ocess lase ange scans o an en i onmen [ 29 ]. They align wo lase ange scans o he (usually unknown) en i onmen in o de o de ec he change o he loca ion and o ien a ion o a mo ing objec [ 30 ]. Scan ma ching algo i hms can be classi ied as poin -based and ea u e-based. Poin -based me hods p ocess lase ange scans poin -by-poin whe eas ea u e-base me hods ex ac highe -le el ea u es such as lines, co ne s and so o h, and align hese ea u es. Fea u e-based me hods ex ac dis inc i e ea u es be o e ma ching i sel and hus dec ease he amoun o da a ha needs o be p ocessed. As a esul , hei scan ma ching phase has lowe compu a ional cos s bu hey su e om lowe obus ness and wo se accu acy in ich and well-s uc u ed en i onmen s. I e a i e closes poin (ICP) is a ypical ep esen a i e o poin -based scan ma ching algo i hms [ 31 ]. ICP is a seminal me hod ha has a numbe o modi ica ions [ 32 , 33 ]. A ep esen a i e o ea u e-based scan ma ching s a egies is he comple e line segmen (CLS) me hod [ 34 ]. I looks o la a eas in poin clouds, ex ac s lines and de ec s comple e and incomple e line segmen s. I expec s ha a comple e line segmen in an en i onmen has a speci ic cons an leng h om any poin o iew. O he ea u e-based scan ma ching s a egies include he ancho poin ela ionships (APR) algo i hm [ 35 ] ha de ec s speci ic ancho s, plane ex ac ion app oaches [36] and keypoin and keyline ex ac ion [37]. Na u e-inspi ed me hods, such as e olu iona y compu a ion, ha e been used in he a ea o mobile obo localiza ion as well. In [ 38 ], he di e en ial e olu ion algo i hm was used in conjunc ion wi h he adi ional no mal dis ibu ion ans o m (NDT) algo i hm [ 39 ]. Ano he wo k used di e en ial e olu ion as pa o a ea u e-based scan ma ching algo i hm ha ex ac ed lines, planes and sphe es om lase ange scans [ 40 ]. O he na u e-inspi ed me hods such as he ha monic sea ch algo i hm we e used o di e en ial scan ma ching as well [41]. This wo k p oposes a no el scan ma ching algo i hm based on a combina ion o wo ecen ly in oduced app oaches. The c oss-co ela ion app oach [ 42 , 43 ] is adop ed o he assessmen o lase ange scans’ simila i y and he di e en ial e olu ion is used o he sea ch o accu a e lase ange scan ans o ma ion pa ame e s [ 44 ]. The e alua ion o he p oposed scan ma ching s a egy is pe o med in a se ies o simula ion expe imen s wi h he help o a so wa e amewo k in oduced in [45]. 3. Backg ound This sec ion p o ides he backg ound o he p esen ed wo k. I ou lines he simula ion-based design s a egy i adop s, ele an scan ma ching me hods such as he i e a i e closes poin algo i hm, he undamen als o he c oss-co ela ion p inciple and he op imiza ion p ocess implemen ed by he di e en ial e olu ion. 3.1. Expe imen al Se up and Embedded Da a P ocessing The aim o his wo k is he design o a localiza ion algo i hm sui able o an au onomous mobile ehicle, o example a wheeled mini obo o explo a ion, su eillance and escue ope a ions. Ha dwa e a chi ec u e o such ehicle was desc ibed, o example, in [ 46 ]. The mechanical cons uc ion o he ehicle was based on he RC Baja 5B SS chassis and i was equipped wi h all necessa y elec onic de ices ha allowed he con ol o i s mo emen . The ehicle was also equipped wi h he SICK LMS 100 LiDAR and a se o odome y senso s. A no el algo i hm o a speci ic sys em o de ice ough o be alida ed in e ms o co ec ness, accu acy, eliabili y and obus ness. In o de o allow apid p o o yping and e alua ion o a ious app oaches, a model-based de elopmen using a so wa e simula ion o pa icula sys em componen s (i.e., So wa e in he Loop) was adop ed o alida e he scan ma ching algo i hm. The simula ion Elec onics 2019,8, 856 4 o 20 amewo k p o ides in o ma ion abou he ue posi ion and o ien a ion o he de ice, simula es i s mo emen in a p e-de ined indoo en i onmen and p oduces simula ed LiDAR and odome y da a. The s uc u e o he en i onmen is de ined by a loo plan. The a ge p ocesso is an Ad anced RISC Machine (ARM) Co ex-M mic ocon olle expec ed o un he scan ma ching algo i hm and o compu e he es ima ed posi ion and o ien a ion o he de ice in he eal de ice. This op–le el design s a egy is isually illus a ed in Figu e 1. Figu e 1. An ou line o he simula ion-based design. An ARM Co ex-M p ocesso suppo s di e en unc ionali y depending on i s e sion. Table 1 desc ibes he basic ea u es o se e al ecen ARM Co ex-M e sions (M0+, M3, M4 and M7) [ 47 ]. In gene al, he p oposed app oach makes use o summa ion, mul iplica ion and di ision ope a ions ha can be implemen ed as in ege o loa ing-poin ope a ions. Elec onics 2019,8, 856 5 o 20 Table 1. O e iew o a ious ARM Co ex-M ea u es use ul o compu a ional localiza ion. ARM Co ex-M Ve sion M0+ M3 M4 M7 A chi ec u e CPU a chi ec u e Von Neumann Ha a d Ha a d Ha a d Pipeline s ages 2 3 3 6 In ege ope a ions MULT 32 bi Fas /Slow Fas Fas Fas DIV 32 bi No Yes Yes Yes DSP No No Yes Yes Floa ing-poin ope a ions FPU single p ecision No No Op ional Op ional FPU double p ecision No No No Op ional The pe o mance o a p ocesso can be assessed om h ee di e en pe spec i es. An ARM Co ex-M p ocesso can implemen he on Neumann o he Ha a d a chi ec u e. The Ha a d a chi ec u e has a sepa a e ins uc ion bus connec ed o an in e nal c oss-ba bus. I suppo s ha dwa e pa allelism by allowing simul aneous access o ins uc ions and da a. The second impo an p ope y o he implemen ed a chi ec u e is he numbe o s ages in he ins uc ion pipeline. A highe numbe o pipeline s ages can accele a e ins uc ion execu ion and inc ease he compu a ional powe o a p ocesso . Fo in ege ope a ions, he p ocesso implemen s an add ins uc ion as a s anda d unc ionali y o an a i hme ic logic uni (ALU). Howe e , mul iply, di ide and digi al signal p ocessing (DSP) ins uc ions a e op ional. ARM Co ex-M amily p ocesso s can be equipped wi h slow (32 cycles) o as (1 cycle) mul iply ins uc ions, 32-bi di ide ins uc ions and digi al signal p ocessing ins uc ions (e.g., a mul iply–accumula e ope a ion) use ul o inpu signal il e ing. I he execu ed algo i hm uses loa ing-poin da a ypes, hen he p esence o a loa ing-poin uni (FPU) is highly ecommended due o he long p ocessing imes wi hou his ma hema ical co-p ocesso . An FPU can be ealized in he p ocesso co e as a single (32-bi ) o a double (64-bi ) p ecision e sion o a ma hema ical co-p ocesso . The selec ion o a sui able p ocesso co e e sion depends no only on da a- ype implemen a ion bu he e a e se e al impo an algo i hm pa ame e s including he esolu ion o inpu da a, g id map cell size and he ype and con igu a ion o he op imiza ion p ocedu e. 3.2. Scan Ma ching Scan ma ching is a high-le el sel -localiza ion s a egy based on he assump ion ha wo spa io- empo ally colloca ed lase ange scans o an en i onmen a e alike and can be ( o a la ge ex en ) aligned [ 48 ]. Scan ma ching me hods seek ans o ma ions ha align wo lase ange scans aken by a obo in he same en i onmen bu a di e en loca ions and om a di e en angle. The i s lase ange scan, aken a he i s loca ion, is usually called he e e ence scan and he second lase ange scan, aken a he second loca ion, is called he cu en scan. The ans o ma ion ha aligns he scans is de ined by pa ame e s ha desc ibe he ela i e posi ion and o a ion o he scan (see Figu e 2). Figu e 2a shows wo lase ange scans be o e he ans o ma ion (alignmen ) and Figu e 2b shows he same scans a e a success ul alignmen . Scan ma ching is mos o en based on 2 o 3-dimensional poin clouds cap u ed by LiDAR lase ange inde s. The LiDAR pe iodically measu es he dis ance o he nea es objec in he di ec ion o a lase beam i emi s [ 48 ]. In a 2-dimensional LiDAR, he measu ing lase beam is o a ed on he ho izon al plane and c ea es a lase ange scan ha co esponds o he su ounding o he scanne [ 49 ]. 3-dimensional LiDARs also il he measu ing senso in he e ical di ec ion and ob ain 3-dimensional poin clouds [ 50 ]. A ypical 2-dimensional LiDAR lase ange inde , also used in his s udy, is Sick LMS 100 by SICK AG. This ype o ange scanne p oduces coun e clockwise o ien ed ec o s o dis ances o he nea es obs acle. The ou pu o he scanne is a ange ec o , ~ a=h|a1|,|a2|, . . . , |asmax |i, (1) Elec onics 2019,8, 856 6 o 20 composed o a sequence o dis ances o he nea es objec s, |a1| , |a2| , . . . , |asmax | and smax is he numbe o measu emen s eps wi hin he ape u e ange o he scanne . Each measu ed dis ance, |aφi| , co esponds o a pa icula angle, φiand each ange ec o ,~ a, co esponds o a ec o o angles, ~ φ=hφ1,φ2, . . . , φsmax i, (2) whe e he index o he angle co esponds o he o ien a ion o he lase beam. The ange ec o , ~ a , oge he wi h he angle ec o , ~ φ , desc ibe he su ounding o he scanne in he pola coo dina e sys em. The lase ange scan, (~ a,~ φ), can be ans o med o he Ca esian coo dina es by A= h|a1| · cos(φ1),|a2| · cos(φ2), . . . , |asmax | · cos(φsmax )i h|a1| · sin(φ1),|a2| · sin(φ2), . . . , |asmax | · sin(φsmax )i!, (3) whe e A∈R2×smax is a eal ma ix wi h he i s ow ep esen ing he x coo dina es and he second ow o he y coo dina es o he poin s in he scan exp essed in Ca esian coo dina es. Each column o A,~ as∈A, co esponds o a single poin o he scan in Ca esian coo dina es: ~ as= ax ay!= |as| · cos(φs) |as| · sin(φs)!,s∈ {1, smax}(4) The scan ma ching p oblem can be o mula ed as he sea ch o a ec o o pa ame e s, ~ =h x, y,Φi, o an a ine ans o ma ion, T(~ as, x, y,Φ) = cos Φ−sin Φ sin Φcos Φ!·~ as+ x y!,∀s∈ {1, smax}, (5) ha leads o he bes alignmen o he e e ence scan o he ans o med cu en scan. (a) (b) Figu e 2. Scan ma ching: p oblem de ini ion. (a) Scans be o e alignmen (b) Scans a e alignmen . Elec onics 2019,8, 856 7 o 20 3.3. I e a i e Closes Poin The I e a i e closes poin algo i hm is he de- ac o s anda d poin -based scan ma ching algo i hm. I is based on he sea ch o he pai s o he closes poin s in he ma ched lase ange scans [ 51 ]. Fo each poin in he aligned scan, i inds he nea es poin in he e e ence scan and seeks ans o ma ion pa ame e s ha minimize he Euclidean dis ance be ween hese wo poin s [ 31 ]. The ICP consis s o he ollowing s eps [51]: 1. P ep ocessing 2. Ma ching 3. Rejec ion 4. Cos unc ion e alua ion 5. Minimiza ion o he cos unc ion (go o s ep 1. when e mina ion c i e ia a e no me ) In he p ep ocessing s ep, he poin s ha a e no use ul o ma ching o he wo poin clouds (e.g., ou lie s) a e il e ed ou o educe he olume o he da a. The pai s o he closes poin s in he ma ched scans a e ound in he ma ching phase. The ejec ion phase disca ds he poin pai s wi h oo la ge dis ance in-be ween. The cos unc ion, cos , ha e alua es he le el o alignmen be ween he e e ence scan, A and he cu en scan, B, is de ined as [52] cos A,B, x, y,Φ= smax ∑ s=1  T(~ as, x, y,Φ)−~ bϑ(s)   2, (6) whe e T is an a ine ans o ma ion de ined in Equa ion (5), ϑ ep esen s he unc ion ha inds o each poin ~ as∈A he nea es poin ~ bϑ(s)∈B . The pa ame e s o T in ICP a e ound by an a bi a y eal-pa ame e op imiza ion me hod, o example he New on-Raphson me hod [53]. 3.4. C oss-Co ela ion C oss-co ela ion is a concep known in he a ea o signal p ocessing. I is a measu e ha e alua es he simila i y be ween wo signals, x and y , shi ed in ime by a speci ic alue, τ [ 54 ]. The c oss-co ela ion o wo a bi a y signals, exp essed by Ndisc e e samples, Rxy(τ) = N−1 ∑ i=0 xi( )·yi( −τ), (7) eaches maximum o a alue o τ o which a e he signals mos simila . In his s udy, he c oss-co ela ion p inciple is used o ma ch wo lase ange scans o indoo obo localiza ion. C oss-co ela ion o a lase ange scan, A , wi h a ansla ed and o a ed e sion o ano he scan, B , is maximized when he pa ame e s o he ans o ma ion ha co espond o he cumula i e ansi ion and o a ion o he obo (scanne ) be ween he scans we e aken a e ound [ 42 ]. The e alua ion o he c oss-co ela ion be ween wo 2-dimensional lase ange scans unde a ine ans o ma ion T wi h pa ame e ec o ~ = ( x, y,Φ)can be exp essed by RAB( x, y,Φ) = A(T(B, x, y,Φ)), (8) whe e  is an ope a o ha compa es wo 2-dimensional lase ange scans and quan i ies he deg ee o hei alignmen (i.e., an implemen a ion o Equa ion (7) sui able o he compa ison o 2-dimensional signals). The de ini ion o  is essen ial o he p ope ies o he p ocess. A simple measu e such as he oo mean squa e e o (RMSE) can p o ide a easonable es ima e o he deg ee o scan alignmen and i can be used as a pa o an op imiza ion-based scan ma ching p ocedu e [ 44 ]. Howe e , i s compu a ional complexi y is oo high o p ac ical use. In his wo k, an e icien nume ical algo i hm, Elec onics 2019,8, 856 8 o 20 implemen ing he c oss-co ela ion p inciple o 2-dimensional signals, is used ins ead o RMSE o e alua e he le el o alignmen o wo lase ange scans in he scan ma ching p ocedu e. In he p oposed app oach, he lase ange scan is con e ed o Ca esian coo dina es in he same manne as in [ 44 ]. Nex , a g id map simpli ying he scene is c ea ed om he poin cloud da a. The g id map can be build using an a bi a y compu a ionally easible p ocedu e. Figu e 3illus a es wo me hods o g id map c ea ion. The app oach, shown in Figu e 3a, is based on a ea compa ison. I assumes ha he bes scan ma ch is achie ed when he o al olume o he o e lapping egions is maximized. Fo each cell in he g id, he algo i hm decides whe he i is inside o he i s o he second scan and hen compu es he numbe o o e lapping cells. The second me hod, shown in Figu e 3b, is based on bounda y line analysis. I assumes ha he bes scan ma ch is ob ained when he in e sec ion o he bounda y lines is maximized. This app oach does no equi e any ope a ions o e emp y g id cells and lase scans can be ep esen ed by lis s o non-emp y g id cells ha con ain he poin s o he scans. (a) (b) Scan B Scan A In e sec ion Figu e 3. Deg ee o alignmen app oaches: (a) A ea compa ison (b) Bounda y line compa ison. Du ing he g id map c ea ion, mo e han one poin can be loca ed in a single g id cell. This ac can be used by he scan ma ching p ocedu e. Fo example, each cell can ha e a weigh co esponding o he numbe o poin s i con ains [ 42 ]. The cell weigh can hen a ec he emainde o he scan ma ching p ocedu e. Howe e , ini ial expe imen s ca ied ou in he scope o his s udy showed ha he use o cell weigh s leads o he p ema u e con e gence o he op imiza ion p ocess and, in many cases, i p e en s he algo i hm om eaching he global op ima. The scan ma ching algo i hm is mo e obus when he cell weigh s a e no aken in o accoun and he g id cells a e simply ma ked as occupied o emp y. The numbe o occupied cells is usually no g ea e han 10% o all g id cells and he c ea ion o g id maps as well as hei compa ison is as . 3.5. Di e en ial E olu ion Di e en ial e olu ion (DE) is a success ul s ochas ic e olu iona y op imiza ion me hod o con inuous pa ame e op imiza ion [ 55 , 56 ]. I is an e olu iona y op imiza ion p ocess based on he concep o scaled ec o di e en ials. The DE ep esen s a con inuous al e na i e o he widesp ead gene ic algo i hms ha wo k wi h a disc e e encoding o he candida e solu ions. Bo h algo i hms a e na u e-inspi ed p oblem-sol ing s a egies ha e ol e a popula ion o candida e solu ions. On he o he hand, hey use di e en solu ion encodings ( eal– alued s. disc e e one), apply di e en ope a ions o e ol e he popula ion and as a esul implemen di e en sea ch s a egies. Elec onics 2019,8, 856 9 o 20 The DE algo i hm has a his o y o success ul applica ions in many indus ial and enginee ing domains. I was designed as a gene ic global op imiza ion me aheu is ic bu wi h p ac ical enginee ing applica ions in mind [ 56 ]. I was used, among o he s, o p edic he g ound s a e s uc u es o hyd ogena ed amo phous silicon (Si-H) clus e s in ma e ial science, o s eamline non-imaging op ical design in op ics and ligh ning de elopmen , o achie e 3D image egis a ion in heal hca e imaging, o design ans e sal digi al il e s in elec onics and in pa icula signal p ocessing, o use senso da a in obo ics , o op imize indus ial comp esso supply sys ems, o ealize sys em iden i ica ion o decision making and in gene al in he a ea o obo ics and expe sys ems [ 56 ]. The algo i hm has also been applied in elec ical enginee ing and elec omagne ics. Fo example, i was used o op imize design o an ennas o low signal- o-noise a io condi ions, o imp o e powe alloca ion o he in e lea e-di ision mul iple-access channel access me hod, o op imize an enna loca ions in a wi eless ne wo k o maximum space co e age and o op imize sou ce pulses and de ec ion empla e in ul a-wideband adio sys ems. In he a ea o elec omagne ics, he DE has been used o sol e elec omagne ic in e se sca e ing p oblems, he equency assignmen p oblem wi h eal-wo ld cons ain s and mul iple objec i es and o model la ge de ices wi h dis ibu ed dipoles [56]. The wide a ie y o indus ial applica ions shows ha he DE is a me aheu is ic op imiza ion algo i hm popula among p ac i ione s. In his a icle, i is used as an op imiza ion me hod o he egis a ion o wo 2-dimensional lase ange scans. F om an op imiza ion poin o iew, he DE e ol es a g oup (popula ion) o eal- alued ec o s by an i e a i e applica ion o he di e en ial mu a ion and c osso e ope a ions [ 55 ]. So-called ial ec o s a e in e e y i e a ion o he algo i hm c ea ed om he cu en popula ion by he di e en ial mu a ion and ecombined wi h co esponding a ge ec o s by he c osso e ope a o . The no el solu ions he ial ec o s ep esen a e e alua ed in he con ex o he p oblem and he ial ec o s compe e wi h he a ge ec o s o su i al in he popula ion. The DE p ocedu e s a s wi h a andomly cons uc ed popula ion o N eal– alued ec o s. In he cou se o he e olu ion, new ial ec o s a e c ea ed as scaled pe u ba ions o exis ing popula ion ec o s. The algo i hm c ea es ial ec o s as scaled di e ences o a minimum o wo dis inc popula ion ec o s added o a hi d one. I a ial ec o ep esen s a be e solu ion han he co esponding a ge ec o , i akes i s place in he popula ion. DE’s mos impo an con ol pa ame e s a e scaling ac o and mu a ion p obabili y [ 55 ]. The scaling ac o , F∈[ 0, ∞] , a ec s he a e a which he popula ion e ol es and he c osso e p obabili y, C∈[ 0, 1 ] , egula es he a io o elemen s ( ec o alues) ha a e ans e ed o he ial ec o om he a ge ec o . Popula ion size, N and he choice o pa icula di e en ial ope a o s a e impo an pa ame e s o he op–le el op imiza ion p ocess, oo. The elemen a y DE ope a ions can be de ined using he ollowing equa ions [ 55 ]: he andom ini ializa ion o he i h ec o o leng h Nis gi en by ~ xi[j] = and(bL j,bU j),j∈ {1, . . . , N}, (9) whe e bL j is he lowe bound o he j - h pa ame e , bU j is he uppe bound o he j - h pa ame e and and(a , b) e u ns a andom numbe om he ange [a , b] . The basic di e en ial mu a ion is de ined as ~ i=~ 1+F(~ 2−~ 3), (10) whe e F is he scaling ac o and ~ 1 , ~ 2 and ~ 3 a e h ee dis inc ec o s selec ed andomly om he popula ion. The ec o ~ 1 is he base ec o , ~ 2 and ~ 3 a e he di e ence ec o s and ~ i is he ial ec o . Elec onics 2019,8, 856 16 o 20 (a) (b) Figu e 8. An example o scan alignmen by he CORR me hod: ( a ) Inco ec alignmen due o a o a ion e o . (b) Co ec alignmen . Compa isons o ansla ion and o a ion e o s o scan ma ching expe imen s in ela ion o he leng h o he obo ajec o y be ween he scans a e shown, espec i ely, in Figu es 9and 10. I can be seen ha he ICP algo i hm p o ides he bes alignmen o scans aken a e he obo a eled be ween 75 mm o 450 mm. The e o o scan alignmen by ICP s a s o ise o scans aken a e he obo a eled 750 mm o mo e. I s accu acy de e io a es e en mo e when ma ching lase ange scans aken a e he obo a eled long dis ances, ha is, 1500 mm o 3000 mm. Based on he execu ed scan ma ching expe imen s, he p oposed scan ma ching me hod (CORR) has o scans spaced 75 mm o 450 mm only sligh ly wo se esul s han he ICP, s ill su icien o p ac ical indoo localiza ion. Howe e , he CORR algo i hm shows supe io esul s when ma ching lase ange scans aken a e he obo a eled long dis ances o 750 mm o mo e. In hese cases, i p o ides signi ican ly be e localiza ion han he s anda d ICP algo i hm. (a) (b) Figu e 9. Absolu e ( a ) and ela i e ( b ) ansla ion e o s o scan ma ching expe imen s o lase ange scans aken a e obo mo emen o 75–3000mm. Elec onics 2019,8, 856 17 o 20 (a) (b) Figu e 10. Absolu e ( a ) and ela i e ( b ) o a ion e o s o scan ma ching expe imen s o lase ange scans aken a e obo mo emen o 75–3000mm. Figu es 9and 10 also illus a e he con e gence o he p oposed app oach. In con as o he ICP, RMSE and CORR a e bo h s ochas ic me hods wi h andom ini ializa ion. They we e ou pe o med by he ICP o scans aken when he obo a eled be ween 75 and 750 mm in e ms o minimum and a e age absolu e and ansla ion and o a ion e o s. Howe e , he igu es also clea ly illus a e ha all independen CORR uns ha p ocessed lase ange scans aken a e he obo mo ed 1500 mm and mo e ob ained be e a e age esul s han he ICP me hod. This sugges s ha he p oposed app oach, al hough no de e minis ic, p oduced in hese cases, on a e age, scan alignmen s o be e quali y han he ICP me hod. 7. Conclusions A no el scan ma ching s a egy, based on he combina ion o c oss-co ela ion and di e en ial e olu ion, was in oduced in his wo k. I uses c oss-co ela ion as an accu a e, obus and compu a ionally e icien measu e o he simila i y o 2-dimensional lase ange scans and di e en ial e olu ion o he sea ch o scan ans o ma ion pa ame e s. The p oposed scan ma ching s a egy was implemen ed and ex ensi ely e alua ed. The e alua ion used a so wa e amewo k o he simula ion o he mo emen o an au onomous mobile obo in an in e io . The amewo k gene a ed a da a se composed o i ual lase ange scans, aken when he obo ollowed a p e-de ined ajec o y in a i ual oom. The p oposed me hod was used o ma ch lase ange scans aken by he obo a e i a eled di e en dis ances anging om 75 mm o 3000 mm. The accu acy o he es ima ed ansla ion and o a ion o he obo was compa ed o he accu acy o ansla ion and o a ion ob ained by a s anda d scan ma ching algo i hm, ICP and a p e ious me hod based on a combina ion o RMSE and di e en ial e olu ion. The expe imen s showed ha he p oposed me hod has only sligh ly lowe accu acy han he ICP algo i hm when ma ching lase ange scans aken a e he obo a eled be ween 75 mm and 750 mm bu i achie ed subs an ially be e esul s o scans aken a e i a eled 1500 mm o 3000 mm. The esul s o he compu a ional expe imen s sugges ha he p oposed app oach is an accu a e and obus scan ma ching s a egy sui able in pa icula o si ua ions when he mobile obo a els longe dis ances. The u u e wo k will include an e icien implemen a ion o he p oposed me hod o embedded de ices ( o example, NVIDIA Je son Nano) and ield es s wi h a physical mobile obo in a eal en i onmen . Au ho Con ibu ions: Concep ualiza ion, J.K., P.K., and P.M.; Me hodology and So wa e, J.K. and P.K.; Valida ion, J.K., P.K., and M.P.; Fo mal Analysis, J.K. and M.P; In es iga ion, J.K. and P.K.; W i ing—O iginal D a P epa a ion, J.K., P.K, and M.P.; W i ing—Re iew & Edi ing, P.K. and P.M.; Visualiza ion, J.K. Elec onics 2019,8, 856 18 o 20 Funding: This wo k was suppo ed by he Eu opean Regional De elopmen Fund in he Resea ch Cen e o Ad anced Mecha onic Sys ems p ojec , p ojec numbe CZ.02.1.01/0.0/0.0/16_019/0000867 wi hin he Ope a ional P og amme Resea ch, and also by he p ojec s SP2019/107, “De elopmen o algo i hms and sys ems o con ol, measu emen and sa e y applica ions V”, SP2019/135, and SP2019/141 o he S uden G an Sys em, VSB - Technical Uni e si y o Os a a. Con lic s o In e es : The au ho s decla e no con lic o in e es . Re e ences 1. Tu gu , Z.; Aydin, G.Z.G.; Se bas, A. Indoo Localiza ion Techniques o Sma Building En i onmen . P ocedia Compu . Sci. 2016,83, 1176–1181. [C ossRe ] 2. Za a i, F.; Gkelias, A.; Leung, K.K. A Su ey o Indoo Localiza ion Sys ems and Technologies. a Xi 2017 , a Xi :1709.01015. 3. Sybe eld , A.; Ayani, M.; Holm, M.; Wang, L.; Lindg en-B ews e , R. Localizing ope a o s in he sma ac o y: A e iew o exis ing echniques and sys ems. 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