CALIBRATION OF CONSTANT ANGULAR ERROR FOR CBERS-2 IMAGERY WITH FEW GROUND CONTROL POINTS

Size: px

Start display at page:

Download "CALIBRATION OF CONSTANT ANGULAR ERROR FOR CBERS-2 IMAGERY WITH FEW GROUND CONTROL POINTS"

Eleanore Freeman
6 years ago
Views:

1 CALIBRATION OF CONTANT ANGULAR ERROR FOR CBER- IAGER WITH FEW GROUND CONTROL OINT Jupeg U a, * uxao UAN a hel WU a a hool of Reoe esg ad Iforao Egeerg, Wuha Uversy, Wuha, Cha 4379 sregh71@16.o Cosso I, WG I/5 KE WORD: paebore reoe sesg, Hgh-resoluo age, pae phoograery, Calbrao, roess odellg, Auray ABTRACT: The rgorous geoer odel whh depeds o physal properes of he age aquso s he bas odel for obje posog of hgh resoluo saelle agery (HRI. Usg he lear ad agular elees provded by epheers ad aude easurg syse arred o he saelle, he obje oordaes a be deered by he rgorous geoer odel whe he age oordaes are gve. Alhough aude daa easurg srues have bee proved ree years, he preso of orgal aude daa aqured a hardly sasfy he requree of dre georefereg. For dre georefereg applao of CBER- saelles developed depedely Cha, he epheers daa are provded by (sso plag ad supporg syse ad G. The aude daa are provded by sar sesor. Afer pos-pass daa proessg, he error of epheers a be orolled wh eers, whle he errors of aude agles all hree axes (ph, roll, ad yaw exeed 5 ar seods.i hs paper, he rgorous geoer odel sued for CBER- saelles oag a seres of referee oordae rasforao s frs rodued. The dre georefereg resuls show ha loao roo ea square error s ore ha 1 eers for plaery, he a par of whh s sysea error aused by osa agular error (CAE. O he bass of he expere aalyss, a albrao odel for elag osa agular error for CBER- agery s esablshed. The albrao odel a be easly realzed ad requres oly few groud orol pos (GCs.The albrao odel has bee esed o wo sees of CBER- agery. I eah es, varous ubers of GCs have bee used o alulae he CAE ad he dso of he resuls s suble. Due o he suffe NR of CBER- aude daa, he albrao odel s able o redue he loao error o 5~65 eers for plaery by sgle GC, early 95 pere provee o orgal resul. I s sgfaly effe espeally uder he suao of la of GCs. Furher ore, afer albrag he al aude, he odel a provde refed al agular elees for he followg phoograery sso suh as spae reseo ad budle adjuse of he agery whe eough GCs are avalable. 1. INTRODUCTION Wh he fas develope of spaeraf aufaurg ad spaebore ops, spae sesors have provded ew ad effe daa soures for observg he surfae of he earh. Copared wh aeral phoograery, hgh resoluo saelle agery (HRI s faser, heaper, ore effe ad wh a larger swah wdh. I he defee applaos, HRI plays a pora role ellgee gaherg, hage deeo, prese appg ad arge avgao ad so o. Whereas vla area, HRI aes also orbuos o appg, osruo, g, urba plag, lad use vesgao, resoure aagee, agrulural survey, evroe oorg ad GI serve. Therefore ay oures, hgh resoluo reoely sesed saelles are posvely developed ad lauhed. Aog he, IKONO, QuBrd ad OT seres are he ypal exaples of oeral hgh resoluo reoely sesed saelles (hag, 4. The bes groud saplg dsae (GD has aheved sub-eer. I Cha, CBER- seres of saelles, whh are developed depedely, have bee suessfully rug se. CBER-- ad CBER--3 are equpped wh hgh resoluo pushbroo sesors, whh he lear array s fabraed by 4 pees of CCD seges alged wh he foal plae. The bes GD a adr po aheves 3 eers. I order o esablsh he geoer relaoshp bewee age oordaes ad he orrespodg groud oordaes, he aurae lear ad agular oreao elees us be rereved a frs. I aeral phoograery, we a alulae he oreao elees wh spae reseo ehod usg a leas 3 GCs. I spae phoograery, however, he slar proess s uh ore dfful due o he oplaed agg geoery. Furherore, o esure he auray ad relably of he oreao resul, eough quay ad suable dsrbuo of GCs are srly requred. For suh reasos, a prese os of he hgh resoluo reoely sesed saelles arry hgh-preso orb posog ad aude easurg syse oboard o provde dre easuree of he sesor oreao elees. O CBER- saelles, (sso plag ad supporg syse ad G (global posog syse a provde he sesor poso whle sar sesors provde he sesor aude a era sas of e. Ths forao, ogeher wh suable erpolao ehques, ay be used o alulae he sesor poso ad aude for ay parular sas of aquso ad apply dre georefereg. Ths ehod does o requre ay GCs, exep for fal heg, bu he effeveess ad relably of hs ehod deped o he auray of he avalable oreao * Correspodg auhor. 769

2 The Ieraoal Arhves of he hoograery, Reoe esg ad paal Iforao ees. Vol. VII. ar B1. Bejg 8 elees. A grea uber of dre georefereg experes wh CBER- agery have show ha loao auray of CBER- agery s abou 8 eers or eve worse. Coparg o he Freh saelle OT-5 whh has a slar GD of.5 eers ad he loao auray of 5 eers, he perforae of CBER- agery s far fro expeao. Whe o osderg erra udulao, roo ea square error (RE loag he obje po wh CBER- agery vary bewee 6 eers o 11 eers for plaery. Aordg o offal publ forao, afer pos-pass daa proessg he dre easurg error of orb posog a be orolled wh eers, whh has relavely lle effe o he resul of dre georefereg. Obvously, he ajor loao error s aused by sysea errors of he orgal aude daa. Relave researhes have show ha he a par of sysea error s osa error, whh should be separaed a frs (Wag,. Therefore, s of grea porae o effevely elae he osa agular error (CAE.I hs paper, he rgorous geoer odel sued for CBER- saelles ludg a seres of oordae rasforao s rodued frsly. The dre georefereg ess o CBER- agery wh rgorous odel ofr he exsee of he CAE. The a ew ehod for albrag he CAE wh few GC s esablshed. Afer opesag he CAE, he RE of dre georefereg has bee proved suffely..1. RIGOROU GEOETRIC ODEL Colleary equao Colleary equao s he rgorous geoer odel for dre georefereg of HRI ad he bas odel for HRI geoer proessg (ol,. I order o elae he oplaed dsoro effe aused by earh urvaure ad selfroao, earh ered roag oordae syse (ECR suh as WG-84 s always adoped as he obje spae oordae syse rgorous er odel. For oveee of oordae rasforao fro a age po o s orrespodg groud po, he spae auxlary oordae syse s defed wh he perspeve ere as he org ad hree axes parallel o hose of he ECR. The rgorous geoer odel s frs o alulae he spae auxlary oordae hrough a seres of oordae rasforao (ua, 3. The proess a be expressed as: x λrt f T [ f ] Where, RT are he auxlary x oordae of age po, (1 are he oralzed oordaes of ; are spae oordaes of he (,, groud po ECR.,, are spae oordaes of ( he perspeve ere for age po ; λ s he sale elee; s he rasforao arx for overg he saelle orb oordaes o ECR oordaes; T s he rasforao arx for overg he sesor oordaes o he saelle body oordaes; R s he rasforao arx for overg he saelle body oordaes o he orb oordaes, ad a be aaozed as : where, R ω R R R R R R ( ω 1, os ω s ω s ω os ω os s, 1 s os os s. s os 1 Where, ω,, are respevely he ph, roll, yaw agle of he sa le. I s pora o oe ha ad R are boh depede o sa e whle T s deered by he poso of he age po he lear sesor. All of he are orhogoal rasforao arxes. CBER- saelles use CCD lear array sesors, whh geerae D agery he pushbroo ode. Due o he sably of he saelle rajeory, he oo of he perspeve po ad he hage of he aude a be expressed by ulorder polyoal fuos as (ol, 4: a + a + a + + a 1 LL b + b + b + + b 1 LL LL ω d + d 1 + d + LL + d e + e1 + e + LL + e f + f 1 + f + LL + f Where, a are he oreao elees of he, b,, d, e, f ere sa le; a are he oeffes of he 1, LL, f polyoals ad hey a be opued by he dsree epheers ad aude observao values provded eadaa fle. The referee (og, 3 daes ha he fg error s o ore ha.5 eers for lear elees ad.1 ar seod for agular elees whe he order s 4 or above.. The prple of age georefereg Georefereg of he reoe-sesg agery s aually o oba he erseo po of he agg ray wh he earh surfae. Fg (1 shows he erseo po graphally. (3 77

3 The Ieraoal Arhves of he hoograery, Reoe esg ad paal Iforao ees. Vol. VII. ar B1. Bejg 8 3. CALIBRATION OF CONTANT ANGULAR ERROR FOR CBER 3.1 Error of he observed audes Fgure.1 Ierseo of loo dreo wh he Earh ellpsod Afer deerg he loo dreo of he agg ray ECR syse, we have: + λ( + λ( + λ( Aoher avalable odo s he ellpsod equao of he earh: ( (5 A B whh A a + h; B b + h ad a, b are he seaxle leghs of he Earh ellpsod. h s he ellpsod hegh ha a be assued as rough value whe o erra daa avalable. If DE s avalable, he ellpsod hegh a be rereved fro DE hrough a erave proess. Cobg equaos (4 ad (5, we a exra he quadra equao as below: ( + ( ( ( + λ + A B ( + ( ( + A ( + I I I λ + ( + B A B 1 I s obvous ha wo heore soluos of λ a be obaed fro equaos (6 bu jus oe of he s he aual soluo. A sple ehod s o pu boh wo soluos o equao (4 ad he oe whh aes he orrespodg ( ore,, lose o,, s he aual soluo. ( (6 Though he aude easurg srues suh as sar sesor has bee proved for ree years, s preso a o sasfy he requree of dre georefereg for HRI. Aually, he preso of sar sesor s deered by vsual agle foal legh he uber ad dsrbuo of he dsgushed sars easurg e. I ay ases he uber of sars s suffe or hey do' evely dsrbue he vew feld, whh leads o he dfferee bewee real preso ad heory preso. Cosequely, he ueray of he values of observed audes beoes he ajor ause of loao error. The radoal ehod o refe he al observaos s leassquares adjuse bu requres a era uber of GCs he arge area. For uh area shor of GCs suh as he wes rego of Cha, we have o searh alerave ehod o prove he georefereg auray. Due o he ajor par of he aude error s osa, a sple way o redue he loao error s elag he osa aude error (CAE by few GCs. For here exs obvous CAE he orgal aude observaos, hs ehod s very effe ad praable. 3. aheaal odel for albrag CAE Gve he sesor oordaes ( x, y of ay sgle age po ad s orrespodg groud po (, we a,, alulae he poso of he orrespodg perspeve ere ( ad he orgal aude value,, ( ω by equao (3. Whe he auray of,, ( ad s hgh eough,,, (,, equao (7 a be regarded as he exa loo dreo of he agg ray, whh osues he prerequse odo for deeg CAE: where, (7 Aordg o equao (4 we have: (8 For ay sgle orol po, hree observao equaos a be osrued by learzg Eq. (8. 771

4 The Ieraoal Arhves of he hoograery, Reoe esg ad paal Iforao ees. Vol. VII. ar B1. Bejg 8 V V V V Δω ( ( ( (9 Δ L ω Δ rgorous geoer odel. The age qualy of boh wo aes was good. No ssg les exs. Tab1 gves he resuls of dre georefereg whou usg ay GCs. Where, ( L ( ( ad. ( ( ( s he resduals veor bewee I equao (9, ( ω,, are used as al values ad he orreo veor ( Δ ω, Δ, Δ a be obaed by leassquares esao. The albraed aude are assued o be ( ω,,.by 3~4 es of erao + Δω + Δ + Δ alulag, he values of ( Δ ω, Δ, Δ beoe gorable ad he erao sopped. 3.3 Copug CAE wh few GCs Whe orgal observed audes oag osa agular error, he error a be esaed wh few GCs. For here exss he sae osa error for eah sa le oe age see, orreo veor ( Δω, Δ, Δ obaed by he way rodued 3. a be ae as he CAE f oly oe GC avalable; Whe GCs sa les have bee easured, for eah sa le we a oba her orrespodg orreo audes ad a ore relable CAE a be obaed by opug her ea value, suh as equao (1 expressed:. 1 Δω 1 Δ 1 Δ Δω Δ Δ (1 Afer opesag CAE for he orgal observed audes, he preso of he aude s suffely proved. However, here us be rado errors reaed he albraed audes, whh a be reoved by furher adjuse way suh as spae reseo ehod whe a leas 6 GCs are avalable. 4. TET AND REULT ANALI I order o prove he exsee of he CAE ad he effey of above albrao ehod, wo sees of CBER agery have bee esed. ee1 s aqured o Nov17 of 4. ee s aqured o De7 of 4.The szes of boh ages are 1pxels 1pxels ad he proessg level are level1,.e." shed raw" age daa whou orreos exep for he radoer provee. Level1 daa a be proessed wh CENE RE ( Table 1. Resuls of dre loao for CBER- agery Afer opug he aude orreos by he way preseed 3., s oable ha he aude orreos all hree axs dsrbue aroud era values, whh a be osdered as he osa errors. The resuls of usg dffere uber of GCs radoly seleed o esae he CAE for wo sees are lsed a Tab ad Tab3. I s pora o oe ha he CAEs for dffere CBER ages are dffere so hey should be proessed depedely. GCs CAE (ar seods Δ ω Δ Δ Table. Cosa agular error of agery ee1 GCs CAE (ar seods Δ ω Δ Δ Table 3. Cosa agular error of agery ee For here are ay oplaed faors effeg loao auray durg age olleg proess, he rado errors do exs. If osderg he CAE as sgal whle oher rado errors as ose, he esao effay of CAE s deered by he NR. Whe NR s sall whh eas ha CAE s o sgfa opared o he rado error, wll be relua o separae CAE. Whe NR s suffe, he CAE a be reoved effely by eve sgle GC.I s very useful he suao shor of GCs. Tab 4 are he dre georefereg resuls afer opesag he CAE, Copared o Tab1, he loao auray of CENE1 has bee proved by 95% ad he loao auray of CENE has bee proved by 94%. Aordg o he orrespodg resoluo of he groud, he loao auray s beer ha pxels. I fa, he auray wll be furher proved afer reovg he age easurg error. The resuls fully show he effey of he albrao odel o CBER agery. 77

5 The Ieraoal Arhves of he hoograery, Reoe esg ad paal Iforao ees. Vol. VII. ar B1. Bejg 8 CENE RE ( Table 4. Resuls of dre loao afer aude albrao 5. CONCLUION Usg he CAE albrao odel preseed hs paper, CAE of he CBER agery a be effely opesaed usg oly oe GC. Wholly speag, he auray of dre georefereg a be proved o pxels afer CAE opesao. Cosderg ha he geoer odo of sgle age s weaer ha ha of sereo ages, hs resul s aepable he preso less-deadg ases. Copared o usg affe rasforao oeffes o odel he sysea errors, he albrao ehod requres uh less GCs ad he effe ay be eve beer. Alhough he advaages of he albrao odel are obvous, he odel gores soe oher auses leadg o loao error. For exaple, he lear elees easured by orb posog syse also oprse sysea error. I addo, here exs a spae offse bewee he observed po of he posog syse ad he real perspeve ere. Ths offse s also a uow value. Furherore, he er oreao elees are presued o be prese ad aosphere refrao effe s gored. All hese faors are boud o geerae loao error. To beer solve hs proble, he ore oplaed adjuse odels are o be vesgaed. REFERENCE ol, D.,. Geeral odel for Arbore ad paebore Lear Array esors. Ieraoal Arhves of hoograery ad Reoe esg, ar B1, pp ol, D., 4. Oreao of aelle ad Arbore Iagery fro ul-le ushbroo esors wh a Rgorous esor odel. Ieraoal Arhves of hoograery ad Reoe esg,ar B1, pp og Wedog, Wag Wex, Hu ghua, 3. rese Aquso of OT-5 Exeror Oreao Elees Usg eadaa Daa Fle. Bulle of urveyg ad appg, 3(1, pp.9-31 OT aelle Geoery Hadboo. hp:// Wag Rexag,. EF Aeral Tragulao of aelle Bore Three-le Array CCD Iage (II. ee of urveyg ad appg, (1, pp.1-7 ua uxao, hag Guo, 3. Obje Loao of aelle uder Lag Groud Corol os. Geoas ad Iforao ee of Wuha Uversy, 8(5, pp hag ogsheg, Gog Dahao, e al, 4. Applao of Hgh-resoluo Reoe esg aelles. ee ress, Bejg. ACKNOWLEDGEENT Thas for he supporg fro he 973 rogra of he eople s Republ of Cha uder Gra 6CB713 ad he Naoal Naural ee of Cha uder Gra

6 The Ieraoal Arhves of he hoograery, Reoe esg ad paal Iforao ees. Vol. VII. ar B1. Bejg 8 774

Solution. The straightforward approach is surprisingly difficult because one has to be careful about the limits.

Solution. The straightforward approach is surprisingly difficult because one has to be careful about the limits. ose ad Varably Homewor # (8), aswers Q: Power spera of some smple oses A Posso ose A Posso ose () s a sequee of dela-fuo pulses, eah ourrg depedely, a some rae r (More formally, s a sum of pulses of wdh