Optimal Baseline Design and Error Compensation for Bistatic Spaceborne InSAR

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1 Opial aseline Design and Eo Copensaion o isaic Spacebone InSAR Wenqin Wang (1,( (1 Naional Key Laboaoy o Micowave Iaging Tecnology, Insiue o Eleconics, Cinese Acadey o Sciences, eijing 18, P. R. Cina; ( Scool o Gaduae, Cinese Acadey o Sciences, eijing 18, P. R. Cina. Eail: dspwang@163.co Absacs: isaic SAR syses as opposed o onosaic SAR oe soe degees o eedo in coosing ansie and eceive sepaaely. In is pape, e spaial baseline in bisaic spacebone InSAR and e equieens o opial baseline ae analyzed in any aspecs. An equaion o deeine e opial spaial baseline is deived, and one eod o esiae and coec e baseline eo caused by e elaive oving beween e ansie and eceive is obained. Keywods: aseline design, isaic, InSAR, Spacebone, Eo copensaion 1 Inoducion isaic SAR syses as opposed o onosaic SAR oe soe degees o eedo in coosing ansie (illuinao and (passive eceive, ey use sepaaed ansie and eceive wic lying on dieen plaos [1]. So bisaic SAR aain oe and oe inees ove e las yeas as ey ae seen as a poenial eans o couneing vulneabiliy o eleconic couneeasue, especially in diecional esponsive jaing, and avoiding pysical aack o e ada plao [-4]. In addiion, e bisaic seup wi e age envionen opens up seveal ineesing possibiliies. Fo insance, using bisaic ineeoeic SAR wi lage bisaic angles i is likely o incease e signaue o seal ages. Oe ineesing aspecs o bisaic SAR ae e educed dynaic ange o callenging iaging envionens suc as uban ones. In is pape, e bisaic spacebone ineeoeic SAR (S-InSAR was discussed in deail. Te S-InSAR syses use sepaaed ansie and eceive lying on dieen plaos, can be eploed o ipleen ee possibiliies o e coeen cobinaion o SAR iages, wic ae Digial Elevaion Model (DEM, ocean cuen iaging and ipoving esoluion in ange and aziu. Fo a ig degee o auoaion a e pocessing o bisaic SAR iaging daa e baseline beween ansie and eceive o e plao owads eac oe us be known pecisely duing e ecoding. Tese paaees diecly aec e acievable geoeical esoluion and e geoey o e ada syse. We can ind a e baseline is an ipoan paaee and i is cucial in InSAR syse designing, daa pocessing and eo analysis. In addiion, o S-InSAR, e baseline design is oe coplicaed an a o geneal InSAR. So soe analysis o baseline o S-InSAR is necessay. In is pape, e spaial baseline in S-InSAR and e equieens o opial baseline o S-InSAR coeen pocessing ae analyzed in any aspecs. An equaion o deeine e opial spaial baseline is deived, and one eod o esiae and coec e baseline eo caused by e elaive oving beween e ansie and eceive is discussed. Te eaining secions o is pape ae oganized as e ollowing: In secion, e geoey and basic pinciple on e baseline o S-InSAR ae discussed. I is poined a, in secion 3, in e condiion o accepable DEM eo, ee us be an opial baseline, wic akes DEM pecision iges, so an equaion o deeine e opial spaial baseline is obained. Fo geneal InSAR, is baseline will no cange o cange less in e wole iaging ie. Howeve, in S-InSAR, due o e unsabiliy o e wo ada plaos, e paaees o baseline will cange duing e lying ie and i sould be esiaed dieenly. Te coon way o calculae e baseline is based on e DEM. Unounaely, e DEM is oen diicul o obain. So one eod o esiae and copensae e baseline eo caused by e elaive oving beween e ansie and eceive o S-InSAR is discussed in secion 4. Finally, in secion 5 soe diiculies and uue woks in S-InSAR ae discussed. aseline in S-InSAR In geneal, ee ae spaial baseline and epoal baseline in InSAR syse, spaial baseline is e spaial sepaaion o wo anennas and epoal baseline is e epoal sepaaion. As i is known, ineeoeic coeence in InSAR ainly depends on ee souces [5]: a, decoelaion o spaial sepaaion o wo passes o one anenna; b, decoelaion o pysical canges in e suace ove e ie peiod beween obsevaions; c, decoelaion due o suace oion o e individual scaeing cenes wiin eac esoluion eleens. Te is is spaial decoelaion and e las wo belongs o epoal decoelaion. Noe a only spaial baseline is consideed in is pape. Assue e signal odels in S-InSAR ae [6]

2 H A 1 α θ A Δ P wee (, o Fig. 1 Typical coniguaion o S-InSAR syse 4π 1 s1(, y = (, y ep j W(, y y ddy n1 (1 y epesens e cople scaeing eleens o e scene, (, W y epesens e ipulse esponse o e SAR, 1 is e disance o e scaees, is e ada waveleng, and y ae e aziu and gound ange coodinaes, and n 1 epesens a cople noise apliude added o e SAR signal. Te coesponding piel apliude o e second eceive is given by 4 π ( 1Δ1 s(, y = (, y ep j W(, y y ddy n ( wee we ave assued a ee is isegisaion only in e ange diension bu no e aziu diension. Te coelaion o signals o wo eceives in S-InSAR can be epessed as 4π y sinπ ( sinπ ( y y y E{ s1s 1} ep j = ddy π ( (3 π ( y y y wee is siply e aveage scaeing coss secion, is e spaial baseline, and y ae e esoluion in and y coodinaes especively. In ac, Eq. (3 can be sipliied as [5] y 4π y E{ s1s 1} = y 1 ep j (4 Le { * } E s s =, ee is 1 1 y 4π y y 1 ep j = (5 en we can obain e ciical spaial baseline ciical = (6 y As ee is [6] c = y W sinθ (7 So Eq. (6 can be canged as sinθ ciical = W (8 c Tus, wen InSAR ecnique is applied o opogapic apping, spaial baseline causes wo acs, e is is e eain eig easueen accuacy inceases wi spaial baseline because eig easueen sensiiviy inceases wi i, e second is coelaion o SAR iages deceases and eig easueen accuacy deceases wen spaial baseline inceases. So ee us be an opial spaial baseline a balances ese wo opposing acos. 3 Opial S-InSAR aseline In Fig.1, e equaion elaing e piel eig o pase dieence in an InSAR iage is given by

3 ( cos( α 9 θ Δ = (9 π φ = ( cosαsinθ sinαcosθ (1 = H cosθ (11 Unceainies in eac o e paaees,, α, H and θ will lead o unceainies in e eig ineed. Dieeniaing Eq. (11 wi espec o eac individual paaee, we obain e eig unceainies associaed wi eac paaee. Tey ae given by [7] = a H θ (1 a H θ Reeence [6] as illusaed e ypical unceainies, H, a and, associaed wi a spacebone InSAR can be ignoed. Ten ee is [8] pin = (13 1 wee p IN can be epessed as py pin = (14 1 wee p is ange esoluion. In an analogous way, ee is y ϕ.6w θ = (15 S N wee W is one ange cell wid in land and ϕ is e 3d pase wid in ineeoeic pase, wic can be epessed as ciical ϕ = cos( θ α Fo Eq. (11 we can obain a = cosθ = sinθ θ Subsiue Eq. (13 -Eq. (18 ino Eq. (1, we ave p y cos θ sin θ =.36W sin θ 1 1 p cos θ / 4 S/ N Le We ge Wee op op is e opial spaial baseline. ( y = 1 = py cos( θ a S 3 cos 3 1 N 16 an θ cos ( θ β ( θ a (16 (17 (18 (19 ( (1 4 Eo Copensaion Fo geneal InSAR, is baseline will no cange o cange less in e wole iaging ie. Howeve, e saellie s aiude, e ea oaion and e bisaic SAR oaion will aec e baseline in S-InSAR. Unounaely, up o now, e baseline o bi-/ulisaic SAR syse is deeined using independen Global Navigaion Saellie Syse (GNSS

4 like e GPS and dieenial GNSS syses (DGPS eceives on eac plao. Te acievable accuacy o a DGPS in eal-ie is abou 1 c and seveal illiees ae pos-pocessing. Howeve, e ypical.3 accuacy is needed o ineeoeic X-band SAR syses. So one eod o deeine e baseline and oienaion o plaos o aibone bisaic adas is poposed in [9], a piy is a i is oo cople o be used in acually S-InSAR syses. Fig. Pinciple o SLFMCW Rada Fequency ea equency Dopple si T (1 Tansied signal Wee, up dn up Delay ie Δ Tie ea signal Tie : up-peiod bea equency Received signal dn : down-peiod bea equency Fig.3 Waveo o SLFMCW Rada In is pape, we adop a illiee-wave syeical linea equency odulaed coninuous waveo (SLFMCW ada o anse is signal o e TX plao o e RX plao, oug wic ig accuacy o e baseline easueen ay be possible. Te pinciple o LFMCW ada is sown in Fig. and Fig. 3 [1], wee up is Up-peiod bea equency, dn is Down-peiod bea equency. Assue e cenoid o caie equency is and is bandwid is ansied equency is T ( Δ, en e = Δ ( Te signals eleced o e deeced age accopany a ie delay τ deeined by e disance o e age, and a Dopple si d caused by e elaive speed, wic is = ± d ( τ ( Δ T (3 Ten we ge Δ up = = d R v T τ = τ (4 Δ Δ dn = = τ d = R v T ct (5 Wee c is velociy o lig. Fo Eq. (4 and Eq. (5, we can obain e ange and appoacing speed o e age wic ay be epessed as [11] ct = ( up dn 4Δ (6 v = ( up dn 4 (7 Noe a ee is e easued baseline. Te equency esoluion Δ can be deeined as epessed below, using e odulaion equency o odulaion peiod T, since e sapling peiod o e FFT is liied o e up-peiod o e down-peiod o e wave odulaion [1]. Δ = = T (8 Accoding o Eq. (6 and Eq. (7, e disance esoluion Δ and e appoacing speed esoluion Δ v can be

5 epessed as ollows. Δ = ( c 4Δ Δ = c Δ (9 Δ v= ( c Δ = c = c T (3 Assue Δ = 1GHz, T = 4S, en 7 T Δ = 4 1 (31 So e easued ange esoluion is 8 c δ = = 1 Δ 1 =.15 (3 I is noed a, in ac, e acually easued ange esoluion ay decease in soe degee due o e syse clock iing, jies in e daa sapling clock, popagaion delay due o passage oug e aospee and ionospee, ec. 5 Conclusion Te baseline is an ipoan paaee and i is cucial in bisaic spacebone InSAR syse design, daa pocessing and eo analysis. Fo S-InSAR, e baseline design is oe coplicaed an a o geneal InSAR. So in is pape, e spaial baseline in S-InSAR and e equieens o opial baseline o S-InSAR coeen pocessing ae analyzed. An equaion o deeine e opial spaial baseline is deived, and one eod o esiae and coec e baseline eo caused by e elaive oving beween e ansie and eceive is discussed. I is us be poined ou a ee ae jus peliinay esuls and ee is sill oe wok o o coninuaion and ipoveens, suc as, e inluence o e ea oaion on e baseline o S-InSAR syse, ow o copensae e baseline eo caused by e elaive oving beween e wo ada plao and peo oe copue siulaions. Reeences 1. Gead Kiege, Hauke Fiedle, Albeo Moeia. i- and Muli-Saic SAR: Poenials and Callenges. Euopean coneence on syneic apeue ada, Vol. 1, pp , May, 4.. Souek, M. isaic Syneic Apeue Rada Invesion wi Applicaion in Dynaic Objec Iaging. IEEE Tansacions on Signal Pocessing, Vol. 39, No. 9, pp , W. Kelle, K. Kubik. isaic SAR using GPS signals eleced a e sea-suace. Euopean coneence on syneic apeue ada, Vol., pp , May, Gead Kiege, Albeo Moeia. Mulisaic SAR Saellie Foaions: Poenials and Callenges. IEEE Geoscience and Reoe Sensing Syposiu, Vol. 4, pp , July, Xu Huaping, Zou Yingqing, Li Cunseng. Analysis and siulaion o spacebone SAR ineeoeic baseline. CIE ada coneence, pp , Fuk K. Li, R.M. Goldsin. Sudies o ulibaseline spacebone ineeoeic syneic apeue adas. IEEE Tansacion on Geoscience and Reoe Sensing, Vol. 38, No. 1, pp , Zeng Fang, Ma Debao, Pei Huaining. Analysis o e eleens o baseline esiaion o ineeoeic SAR. Reoe Sensing Inoaion, No. 3, pp. 7-9, Vincen Msik, Glenn Vanlaicu, J., Gead Cadillo ec. Teain eig easueen accuacy o ineeoeic syneic apeue adas. IEEE Tans on Geoscience and Reoe Sensing, Vol. 3, No. 1, pp , Maias Weib. Deeinaion o baseline and oienaion o plaos o aibone bisaic adas. IEEE Geoscience and Reoe Sensing Syposiu, Vol. 3, pp , July, Wenqin Wang, Jingye Cai, Yuanwang Yang. A novel eod o ideniy uli-age by ansoable peiods and syeical LFM waveo, Inenaional Coneence on Counicaions, Cicuis and Syses, Vol., pp , May, Wang Wenqin, Cai Jingye. Reseac on e Applicaions o Auooive Collision Waning Tecnologies. AET 4 Poceedings, eijing, pp , May Yukinoi Yaada, Sesuo Tokoo, Yasuio Fujia. Developen o a 6 GHz ada o ea-end collision avoidance. Poceedings o e Inelligen Veicles Syposiu, pp.7-1, Oc

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission