Paper ASAT 16 147 RS, In this paper we analyzed the effect of topography variations of illuminated area in focused. image That we get after range and azimuth compression Then explain proposal method. aperture dependent MOCO for topography correction that applied after second order MOCO. and before azimuth compression, We organize this paper as follows In Section 2 the error duo to topography variations. derived that affected on focused image Then Section 3 used the aperture dependent MOCO. is compensation the phase error of all targets before azimuth compression In Section 4 the. simulated data is used to validate the proposed method Finally conclusions are drawn in. 2 Effect of topography variations on focused image. The Airborne SAR data acquisition geometry is shown in Fig 1 where the linear straight line. Y axis denotes the nominal track and the curve represents the real or actual track In the. ideal case the antenna phase center APC of the radar moves along the nominal path at a. constant velocity V However owing to the displacement of the real track from the nominal. one additional range error from radar to target arises Assume that the pulse repetition. interval is Tr APCs are located at a constant interval of V Tr along the Y axis direction with a. reference height of H The actual and ideal APC positions at the slow time t a are. X ta Y ta Z ta and 0 V ta H respectively The motion error vector defined as the. displacement between the actual and nominal paths is d ta x ta Y ta V ta z ta. where x ta and z ta denote the motion displacements in the normal plane i e the cross. track motion errors The position of the illuminating antenna is now completely described by. the azimuth coordinate y V ta and by the vector d ta the platform displacements from the. nominal track The correction is made assuming a constant reference height plan at zo which. is the reference plan Considering a scatter point at P x y z and in the unsquinted. observation mode broadside the position of that point in reference plan is Po xo yo zo. Then the instantaneous range from the nominal APC position y to the scatter Po is. Rn ta r y xo 2 y yo zo H y yo r2,V ta yo r r R ta r yo. where r xo 2 zo H 2 is the distance of the closest approach with respect to the nominal. The instantaneous range from the actual APC position A to the scatter P is. R ta r y x x 2 y y y zo h H z,xo x h x yo y h y y zo h H z. Rn ta r y R ta r y, where R ta r y is the slant range error h is the difference between actual height and. reference high tog scattered and x h is the shift in X axis due to topography variation and. Paper ASAT 16 147 RS, y h is the shift in Y axis due to topography variation The slant range error can be. approximately as follows,R ta r y R ta r y Rn ta r y. Rn ta r y Rn ta r y Rn ta r y,x ta 2 z ta 2 y ta 2 xo x x h y yo y y h 3. 2 Rn ta r y Rn ta r y Rn ta r y,zo H z ta h x 2h y 2h h 2. Rn ta r y 2 Rn ta r y, Fig 1 SAR system geometry in the presence of trajectory deviation and topography Variations. Let denote the off nadir angle i e the look angle associated with the scatterer P and is. the instantaneous squint angle as a function of azimuth position That can be written as. V ta y cos,sin and cos o,Rn ta r x Rn ta r x r r 4. where a is the azimuth beamwidth Substituting Eq 4 into Eq 3 and ignoring the. higher order terms the range displacement can be approximated as. Paper ASAT 16 147 RS,R ta r x sin y cos sin x cos z. cos sin x h sin y h cos cos h 5,Rref ta r x Rtopo ta r x. where Rref ta r x and Rtopo ta r x are range error related to reference plane and. topographic variation are shown in Eq 6 and Eq 7 respectively. Rref ta r x sin y cos sin x cos z 6,Rtopo ta r x sin y h cos sin x h cos h 7. In Eq 6 and Eq 7 the first terms in are caused by the along track motion error and the. second terms are the cross track error and the last four terms is the effect of topographic. variation Assuming that range compression and range cell migration correction RCMC. have been applied the signal in time domain for a given target has the following expression in. the unsquinted observation mode broadside,s ta t r Ao exp j r 2 V 2 ta tao exp j ta r. sa ta tao src t, where Ao is a complex constant t a is the azimuth time t is the range time r is the closest. approach distance V is the forward velocity of the platform tao is the zero Doppler time. position c is the speed of light ta r is the uncompensated trajectory for that target src. is the range compressed envelopes and sa is the azimuth compressed envelopes. In chirp scaling algorithms a two step MOCO is commonly applied 12 where rst order. MOCO compensation both envelope and phase for a reference range and height while. second order MOCO corrects for each range after RCMC and range compression Therefore. second order MOCO is carried out multiplying Eq 8 by a complex function containing the. residual range dependent correction z0 ta r where subscript z0 means the correction is. made assuming a constant reference height If the introduced term is equal to the error ta r. MOCO is applied correctly i e the height of the target is equal to the reference one used. during second order MOCO However this is normally not the case if strong topography. variations are present in the scene Therefore a phase error remains along the phase history of. the target which after azimuth compression yields to phase errors and both degradation and. displacement of the impulse response along azimuth direction Consequently although. conventional MOCO has been applied the error depends on the topography making azimuth. compression still space variant The main problem to overcome is the fact that for a given. pulse it is not possible to correct for more than one height The subaperture approach. presented in Section 3 expounds a solution to this problem. The phase offset value due to second order MOCO mismatch can be evaluated analytically. for the maximum of the impulse response Assuming time domain azimuth compression i e. a cross correlation the expression for instant tao is. Paper ASAT 16 147 RS,sc tao t r A exp j r src t sa tao. exp j r exp j z0 r d, where LSAR is the length of the synthetic aperture in seconds The integral in Eq 9 should. have a zero phase value, With the use of an external DEM one could think of computing the integral in Eq 9 for. each pixel of the image and correct the phase The next section expounds a solution that. avoids all harmful effects by modifying the phase history of targets accurately before azimuth. compression,3 Topography Dependent Motion Compensation with. Subaperture, Topography dependent motion compensation started after conventional second order MOCO. using the height information of an external DEM This solution has the drawback that the. correction is only applied at one referable height which could be the mean height of the. antenna footprint for that pulse and which is not able to accommodate for other heights The. system parameters are listed in Table 1 and a synthetic aperture of 350 m in midrange If the. observed scene had strong topography variations the correction would be insuf cient. Table 1 Airborne SAR Sensor Parameters,Nominal height H 12000 m Chirp duration Tp 50 s. Midrange coordinate Ro 18275 m Chirp bandwidth Br 180 MHz. Wavelength 1 875 cm Range pixel dimension Rs c 2 f s 50 cm. Platform velocity V 208 m s Azimuth pixel dimension As V PRF 20 8 cm. Sampling Frequency f s 300 MHz Pulse Repetition Frequency PRF 1000 Hz. The algorithm proposed in this section allows for an angle accommodation to follow a similar. principle than the one presented in 13 15 The distinction between targets in azimuth by. Doppler beam sharpening DBS are shown in Fig 2,Paper ASAT 16 147 RS. Fig 2 Separation targets in azimuth by Doppler beam sharpening DBS. The max number of samples Ns depends on the concept of Doppler Beam Sharpening. DBS DBS technique takes the azimuth fast Fourier transform process to construct DBS. sub images right after range pulse compression Fig 2 shows the geometric relationship. between the point target and airborne SAR in slant range plane In Fig 2 airborne SAR. makes a uniform rectilinear path along the Y axis with the velocity V P is the scatter point. target and is the instantaneous squint angle as a function of azimuth position The slant. ranges of point target is r and r r corresponding to the positions of the airborne SAR A1. and A2 respectively The echo of a point target of P in Fig 2 can be obtained as follows. s A ta r exp j r V ta 2rV ta cos,4 V 2 ta2 cos 2 T T. exp j r V t sin ta c c, where Tc is the integration time in the azimuth direction To realize the coherent. summation the following inequality is indispensable which means that the last phase item of. s A is less 2,4 V 2 cos 2 Tc, Eq 11 is the choosing principle of the coherent processing time in the azimuth. direction the result is the restriction of the integration time in the azimuth direction as. Then constrain of the number of samples can be computed as follows. Paper ASAT 16 147 RS, Due to the parameters of Table 1 the number of samples must meet Ns 90 sample in. azimuth satisfying constrained of the coherent summation in azimuth The number of. samples Ns 64 is used here the resolution during MOCO along azimuth dimension is about. 5 4 m LSAR Ns which allows for an accurate accommodation of topography variations. Fig 3 Analysis of point target echo slant range plane. Fig 4 shows the block diagram of the proposed algorithm The idea is that selecting small. number of samples Ns along azimuth dimension in time domain and applying azimuth FFT. along that same dimension allows for a time frequency or time angle dependent correction. With this principle the authors of 13 15 were able to apply accurate MOCO to low. frequency wide beam data A further step is to apply a topography dependent correction using. the same principle The topography and aperture dependent MOCO the algorithms rely on. the well known time frequency relation of the azimuth SAR signal The mapping between. time and frequency is expressed by,f a ta tao r sin ta tao r 2 V 2 ta tao. where is the azimuth angle corresponding to an azimuth frequency f a The relation. between azimuth frequencies and azimuth angles through the beam is given by the Doppler. i sin 1 f a i 2V 15, where i refers to vector location after azimuth FFT and f a i is the azimuth frequency. related to location or scatter i Eq 15 means that a certain azimuth frequency corresponds. to targets seen from the platform at a certain azimuth angle i The conversion between the. azimuth angles i to azimuth positions y i is given by. Paper ASAT 16 147 RS,y i y0 j r tan i 16, where y0 j is the azimuth center position of subaperture i. Therefore knowing the azimuth position and depending on a DEM that has be back. geocoded to slant range geometry it is possible to know all three coordinates in space of the. target Pi x y z and consequently to compute the correct range error R i. The topography dependent MOCO algorithm applied after conventional second order. MOCO because at that stage range compression has already been applied Therefore it is. possible to perform the following residual range dependent phase correction as follows. H i r exp j,R i Rref i exp j Rtopo i, where R is the true range error computed by determine scatter position that satisfy. azimuth position and close approach range using DEM Rref is the total MOCO correction. already applied to the center of segment j i e rst and second order MOCO corrections. and Rtopo is the range error due to topographic variation Notice that Eq 17 is applied. in the range Doppler domain as depicted in Fig 4, After operation of all range in a certain segments then the segment is azimuth FFT and. stored before continuing to process the next azimuth segment After finishing all segments in. azimuth recombine it Finally matched filtering as standard stripmap SAR processing is. performed the azimuth compression,Paper ASAT 16 147 RS. Fig 4 Block diagram of the topography dependent MOCO algorithm. 4 Simulation Results, An airborne SAR simulation data is utilized in this part to validate the topography. Dependent MOCO The heights or altitudes of scene are change from 375m to 677m The. airborne SAR parameters are shown in Table 1 The scene area contains five point targets. which help to measure the quality of topography Dependent MOCO. Fig 5 shows the position and velocity in N frame The nominal and actual positions in. east north and up are shown in Fig 5 a c and e respectively Then the nominal and. actual velocities in east north and up are shown in Fig 5 b d and f respectively The. invariant range error is shown in Fig 6 a and the along track deviation from nominal path is. Paper ASAT 16 147 RS, shown in Fig 6 b In Fig 7 a and b the topographic variation in scene area in two and. three dimension are shown respectively, Fig 8 a is the focused image without MOCO Then the focused images with MOCO. based on the navigation data Case 1 are shown in Fig 8 b Finally the focused images with. the topography dependent motion compensation with subaperture Case 2 are shown in Fig. 8 c The rectangle area for PT1 5 in Fig 8 b and c are comparison in Fig 9. Fig 5 Nominal and actual for position and velocity a East position a East velocity b North position. b North velocity b Up position b Up velocity,Paper ASAT 16 147 RS. Fig 6 Cross track and along track motion errors in real data a Range error b Along track phase. perturbation, Fig 7 The altitude of scene area a Two dimension b Three dimension. Paper ASAT 16 147 RS, Fig 8 The Focused image in different cases a The focused image without MOCO b The focused image. with MOCO Case 1 c The foucuse image with the topography dependent motion compensation with. subaperture Case 2,Paper ASAT 16 147 RS, Fig 9 Foucsed in rectagle area in Fig 8 a PT1 in case 1 b PT1 in case2 c PT2 in case 1 d PT2 in case. 2 e PT3 in case1 f PT3 in case 2 g PT4 in case 1 h PT4 in case2 i PT5 in case 1 j PT5 in case 2. Paper ASAT 16 147 RS, Fig 10 Amplitude response of PT1 5 a PT1 b PT2 c PT3 d PT4 e PT5. Table 2The high power reflector point analysis,IRW m PSLR dB ISLR dB. Case 1 3 629 0 9480 2 2419,Case 2 0 5428 12 0758 9 2566. Case 1 2 1233 0 8106 3 0523,Case 2 0 5366 13 7097 9 1289. Case 1 4 2945 0 2577 5 2835,Case 2 0 5449 13 6557 11 2690. Case 1 4 6938 1 4532 1 5943,Case 2 0 5469 15 2301 11 5954. Case 1 1 5161 0 8041 2 7302,Case 2 0 5407 11 5886 8 0250. Paper ASAT 16 147 RS,Table 3 Performance comparison. Sharpness Entropy Contrast Dynamic range dB,without MOCO 3 2136 16 1712 1 6742 122 9383. Fig 8 Case1 6 2916 16 1161 1 8008 131 6332,Case2 42 092 15 8959 15 8959 138 4912. Case1 1 4110 11 1770 1 2301 76 7046,Case2 25 314 10 8533 3 1698 83 3716. Case1 5 4331 11 0641 1 5184 66 2890,Case2 26 816 10 6618 5 9457 85 7173. Case1 4 7045 10 9799 1 8273 81 1616,Fig 9 Case2 28 475 10 6538 8 0850 91 6325. Case1 3 7843 11 0248 1 8117 79 0089,Case2 27 572 10 5189 9 6950 89 7266. Case1 1 3046 11 0914 1 4162 71 7318,Case2 24 988 10 7616 4 2708 81 3056. The focused image and the amplitude responses of PT1 5 are compared in Fig 9 and Fig 10. for different cases respectively Case1 is the red color plot for MOCO depends on navigation. data Case2 is the blue color plot for the topography dependent motion compensation with. subaperture In Fig 9 and Fig 10 it is proved that the topography dependent motion. compensation with subaperture method case 2 can well compensate the motion error for. airborne SAR due to topographic variation To make it clearer The point target analysis for. impulse response width IRW peak sidelobe ratio PSLR and integrated sidelobe ratio. ISLR measured in azimuth direction of PT1 5 is listed in Table 2. In Table 2 Fig 9 and Fig 10 it can be observed that IRW PSLR and ISLR of PT1 5 in. azimuth direction are improved and the focusing quality in azimuth for case 2 is largely. enhanced in visualization and measurement parameters In Table 3 it can be observed that the. focused image with the topography dependent motion compensation with subaperture method. case 2 has the larger image sharpness higher contrast bigger dynamic range and minimum. entropy than the focused image MOCO using navigation data Therefore the topography. dependent motion compensation with subaperture case 2 is well suitable for the motion. compensation of airborne SARs for topographic variation scene area. 5 Conclusions, The focused image affected by topography variation of scene area For this reason we should. take topography variation of illuminated area in consideration and computed accurate phase. error for every point in scene area depend on digital elevation model The strategy used for. compensation topography variation is the aperture dependent MOCO is discussed The. simulation data shows the validity of the topography dependent motion compensation with. subaperture algorithm and proves to be feasible for airborne SARs to compensation. topography variation,6 References, 1 A Moreira and H Yonghong Airborne SAR processing of highly squinted data. using a chirp scaling approach with integrated motion compensation Geoscience and. Remote Sensing IEEE Transactions on vol 32 pp 1029 1040 1994.

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