SIMULATOR OF INTERFEROGRAM FOR SPACEBORNE SAR SYSTEM

Transcription

1 SIMULATOR OF INTERFEROGRAM FOR SPACEBORNE SAR SYSTEM K. Ren a, b, *, G. Wu b, *, X.Q.Sh a, and V. Prnet b a Dept. of Electronc Engneerng, Nanjng Unversty of Scences and Technology, Nanjng, Chna-kren@nlpr.a.ac.cn b Natonal Laboratory of Pattern Recognton, Insttute of Automaton, CAS -gwu@nlpr.a.ac.cn KEY WORDS: SAR, Interferometer, DEM, Remote Sensng, Satellte, Geometry ABSTRACT: In nterferometrc synthetc aperture radar (InSAR) processng, smulaton of nterferogram s a common practce. It s used as synthetc data to test and valdate the whole chan of InSAR processng from the nterferogram creaton to the DEM reconstructon. The objectve of ths paper s to develop a smulator for valdaton of geocodng processng and phase-to-heght converson processng algorthm. The smulator ncludes two parts: dgtal elevaton model (DEM) of terran smulaton and nterferogram smulaton wth DEM and satellte orbt parameters. DEM s realzed by the fractal Browan moton (fbm) model wth the mdpont dsplacement method and the terran roughness and average slope are determned by two descrbng parameters of the model. Smulators for nterferometry are generally developed n a smplfed magery geometry model. Here the geolocaton method s adopted and the geographc coordnates (lattude, longtude) of the synthetc DEM n the magery regon are assgned accordng to the real orbt. Smulaton experments on smulated and ERS-/ tandem real orbt data demonstrate the effcency of the proposed smulator. The developed smulator can also be used to test the accuracy of baslne estmaton.. INTRODUCTION Snce ncreasng spaceborne synthetc aperture radar (SAR) mages over the most part of world s nowadays wdely avalable, SAR Interferometry (InSAR) technology, as a new applcaton of SAR, has been an mportant observaton measurement of Earth n remote sensng communty n recent ten years. In applcaton research of SAR or InSAR, smulators are developed for selectng an optmum magery mode of SAR, understandng the effects of llumnaton angle and terran relef on SAR mages, testng and optmzng nterferometrc SAR (InSAR) processng algorthms, or gong nsght nto radar receved sgnal of gven the terran [Wary L. S., etc, 000]. These smulators can be generally dvded nto two groups. One s to smulate SAR raw data based on the backscatter model of land surface and SAR pulse transformaton functon [Franceschett G., 998]; and the other one s to smulate nterferogram based on a dgtal elevaton model (DEM)[Xu W.and Cummng B., 997]. Here we pay attenton on the nterferogram smulator. Wth a hgh qualty DEM as the smulator nput, the topographc phase contrbuton can be solated completely n a real nterferogram from other phase varables caused by object deformaton or temporal decorrelaton. When nput DEM s coarse, the synthetc nterferogram s useful for flat phase removal processng and mprovng the phase unwrappng processng. In ths paper a smulator of nterferogram for spaceborne SAR system, combned wth terran smulaton, s developed to valdate phase-to-heght converson and geocodng processng algorthm. DEM s realzed by the fractal Browan moton (fbm) model wth the mdpont dsplacement method and the terran roughness and average slope are determned by two descrbng parameters of the model. For the nterferogram smulaton, an mproved method s developed, whch works wth two real radar sensor parameters and ther warp relatonshp of coregstraton. The smulator mplementaton s descrbed n detal. Experment results on real senor and orbt parameters are gven to demonstrate the effcency of the presented method. Ths paper s organzed as follows: Sectons and 3 descrbe DEM smulaton and nterferogram smulaton respectvely. Secton shows the smulaton results and Secton 5 s concluson.. Prncple. DEM SIMULATION In ths paper, the terran data are smulated by fractal Browan moton (fbm). A fractal s the shape made of parts smlar to the whole n some ways; t can descrbe many complex objects too rregular to be dealt wth n tradtonal geometrcal language. It has been shown that terran surface possesses some fractal characterstcs under a wde range of scale, and fbm s regarded as a proper model for terran representaton [Petgen Henz-Otto etc., 988], [Jn Y.W. and Lu S.J., 998]. FBm s a random process, whose ncrement s statonary, and satsfes Gaussan dstrbuton as follows: or f X X f X ( + ) ( ) ~ (0, N σ H ) X () * Correspondng authors.

2 H E ( f ( X + X ) f ( X ) ) = σ X ( 0 < H < ) () Here H and σ are two mportant parameters to control the model, and the meanngs of them can be llustrated n D case [Zhu Q., 995]. (a) (b) (c) Let Y = f(0) f( X), Z = f( X) f(0) be the past and future ncrement of f, respectvely, thus the correlaton coeffcent of Y and Z s descrbed as E( YZ) H ρ ( Y, Z) = = (3) ( E( Y ) E( Z )) Fgure. (a) The th subdvson d (b) The (+)th subdvson d = + + = (c) The (+)th subdvson, d d In Fgure, the th subdvson s llustrated n (a) wth the grd nterval ; n (b), the (+)th subdvson s completed by d nterpolatng each four neghbors to get the red ponts and then form the red grd that rotate 5 degrees aganst the th one; (c) s the (+)th subdvson, wth the blue ponts nterpolated, the grd becomes denser wth the nterval of d as half as d. Durng the subdvson, the nterpolaton s formulated as follows, d + It ndcates that H s a measure of correlaton between ncrements of f. The smaller H s, the rougher f shows n h = hk + (5) shape. ~ N(0, v ) (6) In addton, let X =, then () yelds v k = H = d σ H (7) d = d (8) E( f( X + ) f( X) ) = σ () () ndcates that σ s an ndex of the average dfference of f at unt dstance, or s regarded as average slope. Generalzng ths to D case, the terran surface can be modeled as a D fbm. Then H reflects the roughness of the surface, and σ reflects the average slope of the surface. In general, the flat regon s wth bg H and small σ. The contrary case s wth the hgh mountan regon. And the mddle mountan or hll regon s between the former two cases. Therefore, the dfferent types of the terran can be generated by adjustng parameters H and σ, and used to valdate the nterferogram smulaton algorthm.. Algorthm Here we use the mdpont dsplacement algorthm [Zhu Q., 995] to smulate terran data. The man dea of ths algorthm s to form the fnal regular elevaton grd by recursve subdvson. In each subdvson, the elevaton of a pont h s obtaned by nterpolatng ts four neghbors hk ( k =,,3, ) and a random statonary dsplacement, where the dsplacement s determned by H, σ and the recursve number. So repeatng ths process can reach a small enough grd nterval d. 3. Prncple 3. INTERFEROGRAM SIMULATION It s well-known that the dstance between the satellte and the target on the ground can be determned accurately by the phase nformaton of the SAR mage. Based on the observaton, the phase dfference of two SAR mages s defned as nterferogram φ gven by π φ = ψ ψ = ( r r ) (9) λ where r, r = the dstances between a target pont P and satellte S, S, respectvely. λ = wavelength of radar. The smulaton of nterferogram reles therefore on the accurate determnaton of the range dfference between two magery dstances. 3. Target pont poston n Cartesan coordnates system The DEM data (lattude φ, longtudeψ, heght h) are generally defned n geodetc coordnates. For the smulaton, the data should be frstly converted to the correspondng (P x, P y, P z ) n the Earth Center Cartesan coordnates system. The

3 transformaton from geodetc coordnates to Cartesan coordnates s gven as The slant range of target pont P can be expressed by target column ndex col: Px = ( R + h)cos( φ )cos( ψ ) Py = ( R + h)cos( φ )sn( ψ ) Pz = [ R( e ) + h]sn( φ ) where P x, P y, P z = coordnates of target pont P n Earth center Cartesan coordnates system a = the sem-major axe of the Earth b = the sem-mnor axe of the Earth e = ( a + b ) a, the earth numerc eccentrcty r ( col ) r + col spc () = 0 (0) where r 0 = slant range of frst column, spc = range resoluton In order to acheve mage coordnates (row, col) of the target pont P, the followng equatons system must be solved: S( row) P = r( col) range equaton Vs( row) ( S( row ) P) = f Doppler equaton λ Srow ( ) P d (5) R a a sn ( φ ) =, local Earth s radus of curvature 3.3 Calculatng satellte postons For two satellte magng the target pont P, ther postons need to be calculated. Accordng to the geolocaton prncple of SAR mage, the mage coordnates of a target pont (row and column numbers) can be calculated from ts Cartesan coordnates (P x, P y, P z ) by solvng a system of the range equaton and the Doppler equaton. Assume that the target pont P =(P x, P y, P z ) s n a SAR mage and has coordnates (row, col). We know that the satellte poston s a functon of azmuth tme, namely rows number, and the satellte state vectors can be expressed by mage coordnates (row, col) of the target P. So the range equaton and the Doppler equaton can be converted to an equaton system wth two ndependent varables: row & col. Let the tme of the frst state vector be the reference tme orgn. For the sngle look complex (SLC) data, the absolute tme of the mage rows s known by means of the PRF (Pulse Repeat Frequency, gven n SLC header fle) row t ( row ) = + dt () PRF where dt = the dfference of tme of the frst mage row wth respect to the tme of the frst state vector PRF = Pulse Repeat Frequency row = ndex of SAR mage n azmuth drecton where the symbol stands by the nner product of two vectors. By assumng the Doppler frequency s equal to zero, the mage coordnates (row, col) of the pont are retreved usng a mnmzaton method wth the par of mage center coordnates (rowc, colc) as an ntal guess. So satellte poston (S x, S y, S z ) n the Earth center Cartesan coordnates system can be obtaned by the magery tme whch s decded by row numbers of the target pont. Here we calculate the slave statellte poston wth respect to the targe pont by the coregstraton warp functon of master and slave mages. Ths approach not only can decrease the geolocaton errors n synthetc nterferogram but also can elmnate the phase errors caused by coregstraton when synthetc nterferogram s used n D-InSAR processng. For the smulaton example (see the next secton), the geolocaton errors are about n a resoluton cell of ERS-/ mage, namely 3.9m n azmuth drecton and 7.9m n range drecton. Because the accuracy of co-regstraton s sub-pxel level, the poston accuracy of the target pont n slave SAR mage s better than that of geolocaton. The ndex of the target pont P n slave SAR mage equals to row a a a S 0 = rowm cols b0 b b col M (6) The satellte poston and ts velocty can be expressed as where rowm, col M = ndex of target pont P n master mage functon of the mage rows: rows, col S = ndex of target pont P n slave mage and S (row) = [Sx (t (row)), Sy (t (row)), Sz (t (row))] () Vs (row) = [Vx (t (row)), Vy (t (row)), Vz (t (row))] (3) where (S x (t),s y (t),s z (t)) and (V x (t),v y (t),v z (t)) are satellte poston and velocty respectvely nterpolated from the state vectors gven n SLC header fle wth a cubc splne nterpolaton at the tme t. a0 a a b0 b b = warp matrx of master to slave mage From the known postons of a target and the satelltes n the Cartesan coordnates system, the dstance of the target to each of the two satelltes can be derved. Thus, the nterferogram can be smulated. In radar mage coordnates, row and col ndex of the target ponts form an rregular grd. In order to get a phase mage n 3

4 regular grd, a regrddng nterpolaton processng s necessary. [Eneder M., 003]. RESULTS Three groups of terran data are randomly generated wth fbm model, and each comprses three types of terran, the flat regon ( σ = 3, H = 0.9 ), the hll regon ( σ = 0, H = 0.6 ) and mountan regon ( σ = 30, H = 0.3 ). In the vsual sense, these smulated terran models are obvously dfferent n terms of roughness and shape. The smulaton results are shown n Fgure. In the study case, the orbt parameters of a par of ERS-/ tandem data are assumed and a locaton for synthetc DEM n common area of two SAR mages s assgned. Here the geographc locaton of left-low corner pont of synthetc DEM s(30.500,.65 )and the space of pxels s.5 arcsecond (about 5 meter n ground). The dfference of the elevaton can change arbtrarly. Other parameters for the smulaton are gven n Table. Item DEM pxel spacng Table. The smulaton parameters 5 m 5 m DEM data sze DEM locaton Orbt of ERS-/ Imagery tme of ERS-/ / PRF Wavelength azmuth range pxel spacng Nearest slant range Parallel and normal components of the baselne Master to Slave Warp Matrx Parameters LAT: ~ LON:. 65 ~.737 ERS- orbt = 5070 ERS- orbt = 5397 FRAME = Hz m m m km B p = 5m B n = 0m wth real orbt parameters and geometry model. It s a good assstant tool not only for valdaton of phase-to-heght converon and geocodng processng, but also for D-InSAR processng. References: Curlander J. C., 98, Locaton of Spaceborne SAR Imagery, IEEE Trans. on Geoscence and Remote Sensng, Vol. GE-0, No.3, pp Eneder M., 003, Effcent Smulaton of SAR Interferograms of Large Ares and of Rugged Terran, IEEE Trans. on Geoscence and Remote Sensng, vol., No.6, pp.5-7 Franceschett G., Iodce A., Mglacco M. and Rcco D., 998, A novel across-track SAR nterferometry smulator, IEEE Trans. on Geoscence and Remote Sensng, vol.36, No.5, pp Jn Y. W. and Lu S. J., 998. Prncple of fractal geometry and ts applcaton, Zhejang Unversty Press Petgen Henz-Otto etc., 988. The Scence Of Fractal Image, Sprnger-Verlag SAR Toolbox algorthm specfcaton, Earthnet onlne, ESA Wary L. S., Wlknson A. J., and Inggs M.R., 000, Synthetc Aperture Radar Images Smulator for Interferometry, ISRSE 000, Cape Town, pp. 7, March. Xu W.and Cummng B., 997, Smulator for repeat-pass satellte InSAR studes, IEEE Proc. IGARSS 97, Sngapore, pp Zhu Q., 995. Fractal theory and ts applcaton n dgtal terran analyss and smulaton, Ph.D Thess, North Jaotong Unversty. Acknowledgements The present work s supported by 863 programs (00AA35070) of the Mnstry of Scence and Technology, Chna. The authors would lke to express ther grattude to Prof. Zhong LIU for hs help. We choose the synthetc hll regon ( σ = 0, H = 0.6 ) to test the nterferogram smulaton algorthm wth dfferent elevaton dfferences. Assume the look angle s 3 degree for ERS data. It s found that the heght ambguty approxmates 90.m when the normal baselne equals to0m. Fgure 3(a) shows the synthetc DEM wth the elevaton changes from 6m to 536m. Fgure 3(b) gves the correspondng nterferogram after removng the flat phase. It s seen that the synthetc nterferogram can well reveal the varety of DEM. Fgures 3(c) and (d) gve another example wth the elevaton changes from 63m to 367m. 5. CONCULSION An nterferogram smulator combnng DEM smulaton and nterferometrc phase smulaton has been developed and tested

5 (a) (b) (c) Fgure (a) The synthetc flat regon wth σ = 3, H = 0.9 (b) The synthetc hll regon wth σ = 0, H = 0.6 (c) The synthetc mountan regon wth σ = 30, H = 0.3 (a) (b) Fgure 3 (a) The synthetc DEM wth σ = 0, H = 0.6, elevaton changes from 5m to 536m (b) The synthetc nterferogram correspondng to DEM shown n (a) (c) (d) Fgure 3 (c) The synthetc DEM wth σ = 0, H = 0.6, elevaton changes from 63m to 367m (d) The synthetc nterferogram correspondng to DEM shown n (c) 5