An Adaptive Approach of Satellite Baseline Estimation in InSAR
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1 Intenational Jounal of Geoience, 2015, 6, Pulied Online Deceme 2015 in SciRe. ttp:// ttp://dx.doi.og/ /ijg An Adaptive Appoac of Satellite Baeline Etimation in InSAR Xiangua Wang 1,2 1 Scool of Infomation Engineeing, Cina Univeit of Geoience (Beijing), Beijing, Cina 2 Academic Affai Office, Minzu Univeit of Cina, Beijing, Cina Received 24 Septeme 2015; accepted 13 Deceme 2015; pulied 16 Deceme 2015 Copigt 2015 auto and Scientific Reeac Puliing Inc. Ti wo i licened unde te Ceative Common Attiution Intenational Licene (CC BY). ttp://ceativecommon.og/licene//4.0/ Atact Baeline i an impotant paamete of ada intefeomet. Geneall, it can e etimated atellite oital data o gound contol point. In ti pape, an adaptive metod i popoed to etimate it wit comination atellite oital data, and te accuac of aeline etimated can e impoved witout gound contol point; actual data of ERS and ENVISAT ASAR ave een ued in algoitm development and te final otained elevation ow tat te pecie oit data i moe accuate tan oiginal oit data in etimating aeline. Kewod Baeline Etimation, Optimal Baeline, Adaptive Metod, InSAR 1. Intoduction Intefeometic Sntetic Apetue Rada (InSAR) tecnolog a een ued fequentl to monitoing tin land uface defomation in ecent ea. Land taget elevation can e otained fom pae infomation caied ada ignal. Couple of ingle loo complex view of te ame aea otained fom two antenna imultaneoul o two paallel oevation fom one antenna ae ued to poduce te intefeometic image; te geometic elation of two antenna and te oeved taget mae intefeomet tuning into te tut. Comination wit te oit and eno paamete, moe accuate and ige eolution elevation can e otained. A an impotant facto in InSAR, aeline i ued to deie te patial o tempoal geometic elation etween te two antenna and te lant ange; te ig-accuac aeline can enance intefeomet of eceiving ignal, ut poo-qualit aeline will caue intefeence lo and lead to te low pecie elevation evaluation. In ti tud, te optimal aeline i alo ued, and te eult i veified te ERS and ENVISAT ASAR data and ow good conitenc wit te oevation. ow to cite ti pape: Wang, X.. (2015) An Adaptive Appoac of Satellite Baeline Etimation in InSAR. Intenational Jounal of Geoience, 6, ttp://dx.doi.og/ /ijg
2 2. InSAR Imaging Teo In geneal, te patial location of antenna wa diffeent in twice epetition wile eceiving ignal fom te ame land taget, ee A 1 and A 2 epeented te fit poition and econd poition, epectivel. Te diffeence etween te two location poduce te intefeence aeline vecto, and ee epeented it lengt, te angle wit te oizon diection wa epeented, te oizontal and vetical component of wa epeented and z, epectivel. Te eigt diffeence etween A 1 and efeence plane wa epeented, te eigt of land taget T Wa epeented () and it lant ange wa epeented, δ epeented te lant ange etween A 2 and land taget T, all mol ae deied in Figue 1. Two complex image S 1 and S 2 wee geneated afte poceing eco ignal of A 1 and A 2 uing SAR tool, epectivel. Te intefeence image wit da and igt tip can e otained afte te opeation S1 S 2, ee S 2 mean te conjugation of S 2. te pae of eac pixel in intefeence image i in popotion to te ditance diffeence δ and a contant atio 2π λ owing to te emiion antenna i alo eco eceive. in common, cuvatue of te eat can not e ignoed in atellite-aed poceing. So te expeion concluded fom Figue 1 ae lited a follow [1]: λφ δ = (1) 2π in ( ) ( ) 2 δ = (2) 2 ( ) ( ) ( ), = a co in R E wee R E indicated te eat adiu and a indicated te alf of te majo axi of atellite oit, mean te lant ange and i ound up wit eco dela, λ,,, and ae nown paamete,, and δ can e calculated expeion (1), (2) and (3) if given φ value. 3. Optimal Baeline A an impotant paamete in InSAR poceing, aeline i defined a te line etween te diffeent location of twice atellite epetition. It accuac can detemine te accuac of land taget elevation. accoding to te teo of InSAR, te pae diffeence, wave lengt and aeline ae te deteminant of computing land taget elevation, tat i to a, te oit paamete ae necea wen calculating te elevation, and te infomation include te poition of atellite, aeline and it azimut wen atellite anning te taget. A it i nown, te moe longe te patial aeline i, te moe weae te intefeence of two image i, inceaing te patial aeline can inceae te accuac of elevation, ut te incement of aeline a it limitation, and te limitation can e epeented B in te Equation (4). C 12 (3) A 2 z A 1 δ T () Figue 1. Geomet of InSAR. 1262
3 B C λ0 = 2ρ co β ( ) wee β epeented te uface gadient and 0 epeented te ditance etween te antenna and te land taget. Aumed tat all te paamete ae independent eac ote, te oveall oot mean quae eo σ can e epeented te following equation [2]. 2 2 = σ σ σ σ σ σ wee σ and σ ae oot mean quae eo of,,, and, epectivel. Accoding to te eo teo ae conideed a tem eo a te ae vaied wit diffeent eno tem and ave caacte of common eo, o te ae ignoed in te following computation. σ i decided amiguit of timing tem, viation of ampling tem and latenc wile electomagnetic wave paing toug ai and comic pace. It can e expeed te following equation: ρin σ = (6) 12 ρ ρ IN = (7) 1 BB C wee ρ IN indicate te eolution of lant ange in intefeometic image and it can e computed te following equation: Wee ρ indicate te ange eolution and B C indicate te limitation of aeline. Te meauement eo σ can e computed te following equation [3]: 2 ϕ 0.6W σ = S N λ ϕ = 2 co( ) wee W indicate te land taget effective extenion in one unit ange loe wic i pependicula to te diection of electomagnetic wave. ϕ indicate te alf powe widt of eac loe poduced pae intefeomet and can e expeed te following equation: Sutitution Equation (6), (7), (8) and (9) to Equation (5), te etimated vaiance of land taget eigt can e appoximatel otained wile aeline i pependicula to te ange diection [4] [5]: σ ρ co λ ( ρ λ) in = 0.36W in co 4 2 S N wee S N i ignal to noie atio of te eceive. Taing deivative to in Equation (10) and maing te deivation i equal to zeo, ten te optimal aeline can e computed te following equation: opt λ = 2ρ co ( ) S 2 3 co ( β) N 16 tan co ( ) Te Equation (11) ow tat te optimal aeline will inceae wile wave fequenc deceae. (4) (5) (8) (9) σ (10) (11) 4. Algoitm Development 4.1. Oiginal Satellite Data Te atellite oit can e expeed poition vecto R and velocit vecto V at given time in ECR coo- 1263
4 dinate tem. Seveal vecto R and V at pecific time can e found in te meta data of ada poduct, uc a ERS-1, ERS-2 and ENVISAT ASAR, te all povide five couple of R and V at given time. Te patten of ecoding R and V i neal ame in meta data: fitl, te oit tate vecto nume N i ecoded and te time t 0 wic i coeponding to te fit tac, te time peiod t etween te adjacent tac; econdl, eve tac vecto couple lie ( X,, ) T Y Z and ( X,, ) T v Yv Z v i ecoded at pecific time in incement ode. To eolving te poition model, te amount N, te oveall diete pai of R ( t i ) and V ( t i ), i ued to calculate te pai of R ( t) and V ( t ) at an given time in inteval [ t0, t0 N t]. Te poition vecto of atellite can e expeed te following polnomial [6]: N at X N Y = t Z N ct (12) N 1 at X N 1 Y = t Z N 1 ct Te velocit vecto can e otained taing diffeential to time t in polnomial (12), and velocit will eep conitenc wit poition at given time. Te velocit can e expeed a polnomial (13). Wee N i te degee of polnomial and it value mut e le tan o equal to ( N 1). Te vecto eie N can e ued to evaluating paamete of velocit uing te leat quae metod. In geneal, onl te diffeential poition to time polnomial i fitted Pecie Oit Data Te pecie oit data ae povided DEOS (Delft Intitute fo Eat-oiented Space Reeac), in wic ERS-1, ERS-2 and ENVISAT ASAR ae include. Running te pogam (geto, veion 2.2.0) povided DEOS at given tat time, tep ize and peiod, te geodetic o geocentic coodinate will e intepolated automaticall afte eading oital data ecod, te pogam alo can intepolate oital pofile eve epoc and can pint te UTC time, eo, longitude, latitude, eigt of oit (GRS80) and XYZ poition value [7]. Inputting te oiginal oit pofile and pecie oit pofile to pogam(geto), ten uing polnomial fitting o linea intepolation to calculating te coefficient of oit, tanfoming te oiginal image coodinate to oit coodinate accoding to te Dopple equation, ten computing te aeline and compaing it wit te optimal aeline, if te iae of aeline computed pecie oit ae le tan te iae computed oiginal oit data, te elevation will e computed te aeline poduced pecie oit, otewie, te oiginal oit data will e ued. 5. Reult and Diuion In ti pape, ERS-1 and ERS-2 ae ued to calculating te oit equation fitl, ten oiginal oit and pecie oit ae ued to compute te elevation. Tale 1 and Tale 2 ow te oit data and te pecie atellite data, epectivel. Tale 3 ow te elevation computed te oit data. Fom Tale 3, we can ee tat te accuac of elevation otained pecie oit i ette tan tat otained oiginal data, and te elative eo computed pecie data i malle tan te oiginal. Meanwile, te compaion i conitent wit te eult otained te optimal aeline; te eult ave een veified ERS and ENVISAT and ow te conitenc; (13) 1264
5 Tale 1. Oiginal atellite data. Tpe T () X (m) Y (m) Z (m) 11, ,484, ,618, ,677, Pincipal Oiginal data 11, ,483, ,635, ,651, , ,483, ,653, ,625, , ,483, ,670, ,598, , ,482, ,687, ,572, , ,484, ,618, ,677, Auxilia Oiginal data 11, ,483, ,635, ,651, , ,483, ,653, ,625, , ,483, ,670, ,598, , ,482, ,687, ,572, Tale 2. Pecie atellite data. Tpe T () X (m) Y (m) Z (m) 11, ,484, ,598, ,708, Pincipal Pecie data 11, ,484, ,615, ,683, , ,483, ,631, ,658, , ,483, ,648, ,632, , ,483, ,664, ,607, , ,484, ,599, ,707, Auxilia Pecie data 11, ,484, ,615, ,682, , ,483, ,632, ,656, , ,483, ,648, ,631, , ,483, ,665, ,606, Tale 3. Computed elevation. Ode Teo (m) Oiginal (m) Pecie (m) Relative eo (oiginal) Relative eo (pecie) 1 11, , , , , , , , , , , , , , , , , , , , , , , , , , ,
6 it ow tat te metodolog ued in te pape povide moe accuate aeline etimation and can e an impotant efeence fo etimating aeline paamete. Refeence [1] Yuan, X.K. (2003) Intoduction to Spaceone Sntetic Apetue Rada. National Defene Indut Pe, Beijing. [2] Li, Z.., Liu, N.J. and Xu, C.J. (2004) Eo Anali in InSAR Data Poceing. Jounal of Wuan Univeit Infomation Science Edition, 29, [3] Ruan, C.J., Xiang, J.B. and Wang, F. (2004) Te Bet Baeline Etimation of Spaceone InSAR. Jounal of Ai Foce Rada Academ, 18, 4-6. [4] de Rooi, J.J. and Eile, P..C. (2012) Mixtue Model fo Baeline Etimation. Cemometic and Intelligent Laoato Stem, 117, ttp://dx.doi.og/ /j.cemola [5] Beaulne, P.D. and Sianeta, I.C. (2005) A Simple and Pecie Appoac to Poition and Velocit Etimation of Low Eat Oit Satellite. Defence R&D Canada Tecnical Memoandum. [6] ioi, K. and Maaio, T. (1997) Baeline Etimation Uing Gound Point fo Intefeometic SAR IGARSS'97, Poceeding. Vol. 1, Piatawa, NJ, Intitute of Electical and Electonic Enginee, Inc., [7] Delft Intitute of Eat Oevation and Space Stem, Delft Univeit of Tecnolog, DORIS Ue Manual and Tecnical Documentation, Deceme
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