Motion compensation processing of airborne SAR data - IEEE Xplore
MOTION COMPENSATION PROCESSING OF AIRBORNE SAR DATA P. Guccione, C. Cafforio Politecnico di Bari Dipartimento di Elettrotecnica ed Elettronica via Orabona, 4 - 70125 Bari, Italy ABSTRACT This paper presents a motion compensation algorithm to focus high resolution SAR data taken from an airborne sensor. The basic idea is to fragment the sensor trajectory into smaller segments that can be modelled as linear or quadratic. The synthetic antenna is then considered as an array of smaller subarrays. The algorithm can easily adapt and trade efficiency for sensor path irregularity. In fact the algorithm is more efficient if the segments are longer. Experimental results with real airborne data confirm the correctness of the approach. Index Terms— SAR, Motion compensation, wavenumber domain
tilinear. Each complex image so obtained (let us call it a look) is then interpolated on a uniform output grid that refers to the average rectilinear path. Terrain altimetry is not needed to correctly focus the burst of data, but it is needed to compute the correspondence of the output sampling nodes into each look. The length of the data bursts must be the longer one that still allows an accurate enough match between the modelled and the real path. The range error should be kept within a fraction of a wavelength, as usual. To avoid too small blocks and subsequent computational inefficiency, a quadratic model is considered for the sensor path segment. The main advantage of this blockwise processing is its conceptual simplicity, even though a coherent summation of the focused looks needs accurate processing and precise knowledge of the sensor path.
1. INTRODUCTION
2. DOPPLER HISTORY WITH A PARABOLIC TRAJECTORY
One key step in airborne SAR data focusing and interferometric processing is the compensation of platform motion errors. In their basic embodiment, efficient SAR processing algorithms like Chirp Scaling, Range-Doppler and ω-k [1, 2, 3] are bind to a rectilinear sensor path. Airborne sensors, however, can hardly guarantee such an operational environment, subject as they are to atmospheric turbulence. Any deviation from the assumed sensor path and nominal pointing induces variations in the target phase history, which impair the quality of the processed image. The effects of these errors are a space-variant broadening of the system impulse response and targets mispositioning both in slant range and azimuth directions. The availability of sufficiently precise navigation data as measured by onboard Inertial Navigation Units (INU) and Global Positioning Systems GPS), makes it possible to integrate such information into the raw data processing algorithm. Usual MoCo strategies basically consist in a preliminary compensation w.r.t. a reference trajectory (first order MoCo) and assuming a constant terrain height, followed by a rangedependent compensation (second order MoCo) that can be correctly performed only after range focusing and correction of range migration [4, 5, 6]. In this paper MoCo is obtained by processing raw data in segments so short that the sensor path can be modelled as rec-
978-1-4244-2808-3/08/$25.00 ©2008 IEEE
If the sensor path is known with enough accuracy, MoCo can be, at least in principle, a simple matter: if slant-range vs. time can be computed for all output samples, it is enough to compensate the phase delays to get a well focused output image. However, the computational burden of this approach is prohibitively heavy. Efficient focusing algorithms [1, 2, 3] all assume a straight path with constant velocity and attitude. Much literature has been devoted to the adaptation of these efficient algorithms to deviations from theoretical straight path. However, any sufficiently small trajectory segment can be approximated through a rectilinear path and the corresponding data can processed with a ”traditional” algorithm. The processing is equivalent to that of a burst of data in the ScanSAR mode. It is obvious that the computational efficiency is inversely proportional to the length of the data bursts and that any means to make it larger is welcome. A quadratic model is able to match the real path over a longer segment than a linear one, but focusing operator will need a change. With reference to Fig. 1, let us suppose that a segment of trajectory of Ts seconds long can be approximated by an arc of parabula. The sensor motion equations in the slant range plane will be:
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IGARSS 2008
x(t) = v(t − t0 ) z(t) = ax(t)2 + c
(1)
Here it is supposed that the curvature is small enough so that that the velocity along the x-axis and the velocity along the curvilinear path are almost equal. The x-axis is tangent to the quadratic path at the segment center (so c = 0 with this hypothesis) while the quadratic path is the LMS fit to the real path.
Real trajectory
Parabolic approx. of a segment of trajectory
x
P(x0,z0) t0=0
z RP(t)
Nominal straight trajectory
As long as the truncation to quadratic terms in Eq. (3) holds, the curved trajectory translates into a change of the curvature of the target echo phase history. If matched filtering is performed assuming a rectilinear sensor path, adjusting the Doppler rate would remove defocusing, but geometric deformations would remain. The first, more evident effect is a stretching (or compression) in azimuth by α. The Doppler centroid for a point target is the same, both for the curved path and for the tangent rectilinear one. As the Doppler rate has been changed by α, the azimuth position of the focused echo is misplaced: it is at fD /KR and differs by the factor α from the correct one. Beyond this, tthe focused echo will be placed at the nearest range distance of the point scatterer from the sensor path. These positioning errors, which are variable both with azimuth and range position of the scatterer, must be corrected to get an undistorted look, if a coherent sum of partial looks has to bring about a full resolution image. In Fig. 1 a is positive and so α is less than 1. A value of α < 1 means that the phase Doppler history has a slope lower than the corresponding one got by a linear trajectory so that a SPOT SAR effect ensues. The converse holds for a value of α > 1.
S(t)
Global mean trajectory
Fig. 1. Determination of the sensor-target distance on the slant range plane for a parabolic segment of trajectory. Supposing t0 = 0 and the target in P (x0 , z0 ), the Doppler history for a parabolic trajectory is: RP (t) = (x(t) − x0 )2 + (z(t) − z0 )2 (2) = (x(t) − x0 )2 + (ax2 + c − z0 )2 After some rearrangments and neglecting the quadratic term in a (supposed small enough), we have: RP (x; x0 , z0 ) z0 + Δz +
assuming the sensor is moving along the tangent rectilinear path.
α 2z0 (x
− x0 )2 +
The curved path adds a complication: the path is quadratic in the three-dimensional space, but its projection in the slant range plane will be different at different slant ranges. We have used the ω − k focusing algorithm and it assumes rectilinear sensor path. To accommodate the different Doppler rate a modification of the assumed sensor speed would be enough. However, assuming a rectilinear sensor path means assuming a given law of change of Doppler rate with slant range. Here, however, Doppler rate does change with range and so much more because of the different projections at different ranges. This amounts to a rate of change with slant range of the Doppler rate that is different from that assumed by the algorithm.
(4)
As Doppler rate changes, for a given step in slant range, more when targets are nearer, less when they are far away, it is possible to assume a modified value for echoes delays so that, adapting both sensor speed and sampling window start time, it is possible to get exactly the right Doppler rate at near and at far range. In between, the inverse proportionality with slant range will dictate the values of Doppler rate at intermediate ranges [3].
The sensor-target distance history assuming the sensor is moving along the curved path differs from the one obtained
Any other focusing algorithm could be used in this piecewise fashion, as long as the correct Doppler rate is used and the azimuth and range deformations are corrected.
(α−1)x0 (x z0
− x0 ) = z0 + Δz +
α 2z0 (x
(3) − x1 )2
being ⎧ ⎨ α = 1 + 2a(c2− z0 ) (α−1)x c2 −c Δz = 2z0 α 0 + 2z 0 ⎩ x1 = x0 /α
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3. BLOCKWISE PROCESSING IN THE WAVENUMBER DOMAIN
Input raw data
The inizial step is the approximation of the sensor trajectory with peacewise linear or quadratic segments. The adopted procedure is suboptimal, as the length of the approximating segment is augmented until the LMS fit to the true navigational data gives an error, in the computed distance, that does exceed a given fraction of a wavelength. The segmentation of the data allows also to take into account the variable attitude of the sensor. The antenna pointing that changes with time does not in itself interfeer with the Doppler history, but certainly changes the weighting effect due to the antenna pattern. The only effect that must be taken care of is the Doppler centroid variation. The first problem to face is the determination of the ”equivalent” speed and sampling window start time. Because of memory management and in order to accommodate a better fit between real Doppler Rates and Doppler rates considered by the ω − k focusing algorithm, data have been partitioned also in the range direction. For each block a scatterer at near and one at far range at antenna beam center are considered. For both the slant range history is computed and a LMS quadratic fit is obtained. As slant range and echo phase delay φD (zn ) are proportional, the quadratic fit can be used to obtain an estimate of the Doppler rate. ⎧ ⎨ φD (zn ) = an t2 + bn t + cn (5) ⎩ fR (zn ) = − λ4 an Collecting the Doppler rates at two ranges allows the determination of the required effective speed and sampling window start time needed to specify the wavenumber domain focusing operator: Hf (ω, kx ; z0 ) = exp jz0
ω+ω0 c/2
2
−
kx2
−
ω+ω0 c/2
(6)
The new parameters will give a well focused image, but their meaning is no longer that of physical geometrical parameters and this must be taken in due account to correctly position the focused output data. As final step, a change of scale in the azimuth direction (see Eqq. (3) and (4)) must be included. This change of scale can be efficiently performed using a CZT with parameters adapted with range, since the scaling is range dependent. To evaluate the scaling factor, α, the range-dependent ratio between the Doppler rates computed with the approximate quadratic path and the tangent rectilinear one is used. After focusing, each look is represented on its slant rangeazimuth plane and makes reference to the terrain height of the
IMU/GPS data
Determination of segments of data
Equivalent params
fDC ,
For each segment
Range focusing
-k focusing & Stolt interpolation
Mean trajectory
range IFFT
azimuth CZT
Interpolation on output grid
Focused & MoCo data
Fig. 2. Processing chain of the ω-k MoCo algorithm. The focusing, the MoCo and the interpolation are performed for each segment of data in which the trajectory has been divided. piece of processed data. It is now necessary to resample these data on the global output sampling grid, that refers to the average rectilinear path. To map the output sampling nodes into each look a DEM of the imaged area, if available, should be used. The mapping is performed determining firstly which are the DEM position corresponding to the common grid nodes (slant range-azimuth pair of coordinates). Since computationally expensive this step can be done only for a larger grid of nodes; the remaining positions will be determined through interpolation. Then, from these ground locations and using the same geometrical relations it is possible to get the positions where the look must be interpolated. However in the experiments here shown the average height over the ground has been used. 4. EXPERIMENTAL RESULTS The algorithm has been tested on both simulated data (point scatterers) and real data from an airborne sensor. In both cases the navigational data (position and attitude) of the real airborne mission have been used. The SAR sensor is SARAT and is the CONAE (Argentinian Space Agency, that we thank for making the data available) L-band, 40MHz bandwidth airborne sensor. Navigational data, apparently accurate enough to allow reasonable processing results, are provided by an onboard INU/GPS system that give access to sensor position, velocity and attitude. Table I summarizes system parameters.
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8500
8450
8450 slant range [m]
slant range [m]
8500
8400
8350
8300
8350
8300
8250 -80
8400
-60
-40
-20
0 azimuth [m]
20
40
60
80
8250 -80
-60
-40
(a)
-20
0 azimuth [m]
20
40
60
80
(b)
Parameter Frequency of operation Swath width Altitude Flight speed Antenna size Antenna pointing angle Pulse Repet. Frequency Sampling frequency Chirp pulse bandwidth Pulse width Spatial resolution
Value 1.3 GHz 14.3 km 4000 m 100 m/s 1.8 x 0.30 m 40° 250 Hz 50 MHz 36 MHz 10 μs 4.8 x 3.0 m (rg x az)
(a)
Fig. 4. Real airborne data. (a) focused using a blockwise ω-k algorithm and no MoCo; (b) with the MoCo ω-k algorithm.
Table I: SARAT System Parameters
Measure 3dB width PSLR ISLR
Method Ideal MoCo -k Ideal MoCo -k Ideal MoCo -k
Azimuth 4.4m 7.7m -13.5dB -7.8dB 10.2dB 8.3dB
(b)
the processing but allow gains in computational efficiency, as longer blocks can be processed. Experimental results, obtained implementing a modified version of the ω-k focusing algorithm, show that the proposed procedure is effective both in terms of sharpness and in terms of good geometric registration of the output focused image.
Slant range 3.30m 3.68m -21.1dB -21.0dB 14.4dB 14.7dB
Table II: Measurement on the impulse response in figure
Fig. 3. Simulation of a point scatterer. (a) Focusing of ideal target and no motion errors; (b) Focusing with the MoCo ω-k. Blocks have been chosen of the same size in the two cases. Output results for point scatterers are shown in Fig. 3. Fig. 3a shows the contour plot of the ideal 2D impulse response obtained with a conventional ω-k processor, with zero Doppler centroid and no deviations from uniform sensor motion. Fig. 3b shows the response to a point target when the raw data simulation has used the position and attitude data from the navigational data base (a Doppler centroid fDC 70Hz resulted): the processing was ω-k with the described MoCo procedure. Table II compares the relative performances. Finally, Fig. 4 compares the results obtained with and without the MoCo procedure with real data acquired over the Buenos Aires area: image size is about 1.5km in slant range and 0.25km in azimuth. The effectiveness of the MoCo procedure is evident. 5. CONCLUSIONS In this paper a procedure for the motion compensation of airborne SAR data has been presented. Sensor trajectory is approximated with piecewise linear or quadratic segments and a blockwise processing is used. Quadratic segments complicate
6. REFERENCES [1] R. Bamler I. Cumming R. K. Raney, H. Runge and F. H.Wong, “Precision sar processing using chirp scaling,” IEEE Trans. Geosci. Remote Sens., vol. 32, pp. 786–799, July 1994. [2] J. R. Bennett and I. Cumming, “A digital processor for the production of seatsat synthetic aperture radar imagery,” Proc. SURGE Workshop, Frascati ESA-SP-154, 1979. [3] C. Cafforio C. Prati, F. Rocca, “Sar data focusing using seismic migration techniques,” IEEE Trans. on Aeros. and Electr. Syst., vol. 27, pp. 194–207, March 1991. [4] Y. Huang A. Moreira, “Airborne sar processing of highly squinted data using a chirp scaling approach with integrated motion compensation,” IEEE Trans. Geosci. Remote Sens., vol. 32, no.5, September 1994. [5] R. Scheiber K. A. Camara de Macedo, “Precise topography- and aperture-dependent motion compensation for airborne sar,” IEEE Geosci. Remote Sens. Letters, vol. 2, no.2, pp. 172–176, April 2005. [6] A. Moreira, “Extended wavenumber-domain sar focusing with integrated motion compensation,” IEE Proc.-Radar Sonar Navig., vol. 153, no.3, June 2006.
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tilinear. Each complex image so obtained (let us call it a look) is then interpolated on a uniform output grid that refers to the average rectilinear path. Terrain altimetry is not needed to correctly focus the burst of data, but it is needed to compute the correspondence of the output sampling nodes into each look. The length of the data bursts must be the longer one that still allows an accurate enough match between the modelled and the real path. The range error should be kept within a fraction of a wavelength, as usual. To avoid too small blocks and subsequent computational inefficiency, a quadratic model is considered for the sensor path segment. The main advantage of this blockwise processing is its conceptual simplicity, even though a coherent summation of the focused looks needs accurate processing and precise knowledge of the sensor path.
1. INTRODUCTION
2. DOPPLER HISTORY WITH A PARABOLIC TRAJECTORY
One key step in airborne SAR data focusing and interferometric processing is the compensation of platform motion errors. In their basic embodiment, efficient SAR processing algorithms like Chirp Scaling, Range-Doppler and ω-k [1, 2, 3] are bind to a rectilinear sensor path. Airborne sensors, however, can hardly guarantee such an operational environment, subject as they are to atmospheric turbulence. Any deviation from the assumed sensor path and nominal pointing induces variations in the target phase history, which impair the quality of the processed image. The effects of these errors are a space-variant broadening of the system impulse response and targets mispositioning both in slant range and azimuth directions. The availability of sufficiently precise navigation data as measured by onboard Inertial Navigation Units (INU) and Global Positioning Systems GPS), makes it possible to integrate such information into the raw data processing algorithm. Usual MoCo strategies basically consist in a preliminary compensation w.r.t. a reference trajectory (first order MoCo) and assuming a constant terrain height, followed by a rangedependent compensation (second order MoCo) that can be correctly performed only after range focusing and correction of range migration [4, 5, 6]. In this paper MoCo is obtained by processing raw data in segments so short that the sensor path can be modelled as rec-
978-1-4244-2808-3/08/$25.00 ©2008 IEEE
If the sensor path is known with enough accuracy, MoCo can be, at least in principle, a simple matter: if slant-range vs. time can be computed for all output samples, it is enough to compensate the phase delays to get a well focused output image. However, the computational burden of this approach is prohibitively heavy. Efficient focusing algorithms [1, 2, 3] all assume a straight path with constant velocity and attitude. Much literature has been devoted to the adaptation of these efficient algorithms to deviations from theoretical straight path. However, any sufficiently small trajectory segment can be approximated through a rectilinear path and the corresponding data can processed with a ”traditional” algorithm. The processing is equivalent to that of a burst of data in the ScanSAR mode. It is obvious that the computational efficiency is inversely proportional to the length of the data bursts and that any means to make it larger is welcome. A quadratic model is able to match the real path over a longer segment than a linear one, but focusing operator will need a change. With reference to Fig. 1, let us suppose that a segment of trajectory of Ts seconds long can be approximated by an arc of parabula. The sensor motion equations in the slant range plane will be:
III - 1154
IGARSS 2008
x(t) = v(t − t0 ) z(t) = ax(t)2 + c
(1)
Here it is supposed that the curvature is small enough so that that the velocity along the x-axis and the velocity along the curvilinear path are almost equal. The x-axis is tangent to the quadratic path at the segment center (so c = 0 with this hypothesis) while the quadratic path is the LMS fit to the real path.
Real trajectory
Parabolic approx. of a segment of trajectory
x
P(x0,z0) t0=0
z RP(t)
Nominal straight trajectory
As long as the truncation to quadratic terms in Eq. (3) holds, the curved trajectory translates into a change of the curvature of the target echo phase history. If matched filtering is performed assuming a rectilinear sensor path, adjusting the Doppler rate would remove defocusing, but geometric deformations would remain. The first, more evident effect is a stretching (or compression) in azimuth by α. The Doppler centroid for a point target is the same, both for the curved path and for the tangent rectilinear one. As the Doppler rate has been changed by α, the azimuth position of the focused echo is misplaced: it is at fD /KR and differs by the factor α from the correct one. Beyond this, tthe focused echo will be placed at the nearest range distance of the point scatterer from the sensor path. These positioning errors, which are variable both with azimuth and range position of the scatterer, must be corrected to get an undistorted look, if a coherent sum of partial looks has to bring about a full resolution image. In Fig. 1 a is positive and so α is less than 1. A value of α < 1 means that the phase Doppler history has a slope lower than the corresponding one got by a linear trajectory so that a SPOT SAR effect ensues. The converse holds for a value of α > 1.
S(t)
Global mean trajectory
Fig. 1. Determination of the sensor-target distance on the slant range plane for a parabolic segment of trajectory. Supposing t0 = 0 and the target in P (x0 , z0 ), the Doppler history for a parabolic trajectory is: RP (t) = (x(t) − x0 )2 + (z(t) − z0 )2 (2) = (x(t) − x0 )2 + (ax2 + c − z0 )2 After some rearrangments and neglecting the quadratic term in a (supposed small enough), we have: RP (x; x0 , z0 ) z0 + Δz +
assuming the sensor is moving along the tangent rectilinear path.
α 2z0 (x
− x0 )2 +
The curved path adds a complication: the path is quadratic in the three-dimensional space, but its projection in the slant range plane will be different at different slant ranges. We have used the ω − k focusing algorithm and it assumes rectilinear sensor path. To accommodate the different Doppler rate a modification of the assumed sensor speed would be enough. However, assuming a rectilinear sensor path means assuming a given law of change of Doppler rate with slant range. Here, however, Doppler rate does change with range and so much more because of the different projections at different ranges. This amounts to a rate of change with slant range of the Doppler rate that is different from that assumed by the algorithm.
(4)
As Doppler rate changes, for a given step in slant range, more when targets are nearer, less when they are far away, it is possible to assume a modified value for echoes delays so that, adapting both sensor speed and sampling window start time, it is possible to get exactly the right Doppler rate at near and at far range. In between, the inverse proportionality with slant range will dictate the values of Doppler rate at intermediate ranges [3].
The sensor-target distance history assuming the sensor is moving along the curved path differs from the one obtained
Any other focusing algorithm could be used in this piecewise fashion, as long as the correct Doppler rate is used and the azimuth and range deformations are corrected.
(α−1)x0 (x z0
− x0 ) = z0 + Δz +
α 2z0 (x
(3) − x1 )2
being ⎧ ⎨ α = 1 + 2a(c2− z0 ) (α−1)x c2 −c Δz = 2z0 α 0 + 2z 0 ⎩ x1 = x0 /α
III - 1155
3. BLOCKWISE PROCESSING IN THE WAVENUMBER DOMAIN
Input raw data
The inizial step is the approximation of the sensor trajectory with peacewise linear or quadratic segments. The adopted procedure is suboptimal, as the length of the approximating segment is augmented until the LMS fit to the true navigational data gives an error, in the computed distance, that does exceed a given fraction of a wavelength. The segmentation of the data allows also to take into account the variable attitude of the sensor. The antenna pointing that changes with time does not in itself interfeer with the Doppler history, but certainly changes the weighting effect due to the antenna pattern. The only effect that must be taken care of is the Doppler centroid variation. The first problem to face is the determination of the ”equivalent” speed and sampling window start time. Because of memory management and in order to accommodate a better fit between real Doppler Rates and Doppler rates considered by the ω − k focusing algorithm, data have been partitioned also in the range direction. For each block a scatterer at near and one at far range at antenna beam center are considered. For both the slant range history is computed and a LMS quadratic fit is obtained. As slant range and echo phase delay φD (zn ) are proportional, the quadratic fit can be used to obtain an estimate of the Doppler rate. ⎧ ⎨ φD (zn ) = an t2 + bn t + cn (5) ⎩ fR (zn ) = − λ4 an Collecting the Doppler rates at two ranges allows the determination of the required effective speed and sampling window start time needed to specify the wavenumber domain focusing operator: Hf (ω, kx ; z0 ) = exp jz0
ω+ω0 c/2
2
−
kx2
−
ω+ω0 c/2
(6)
The new parameters will give a well focused image, but their meaning is no longer that of physical geometrical parameters and this must be taken in due account to correctly position the focused output data. As final step, a change of scale in the azimuth direction (see Eqq. (3) and (4)) must be included. This change of scale can be efficiently performed using a CZT with parameters adapted with range, since the scaling is range dependent. To evaluate the scaling factor, α, the range-dependent ratio between the Doppler rates computed with the approximate quadratic path and the tangent rectilinear one is used. After focusing, each look is represented on its slant rangeazimuth plane and makes reference to the terrain height of the
IMU/GPS data
Determination of segments of data
Equivalent params
fDC ,
For each segment
Range focusing
-k focusing & Stolt interpolation
Mean trajectory
range IFFT
azimuth CZT
Interpolation on output grid
Focused & MoCo data
Fig. 2. Processing chain of the ω-k MoCo algorithm. The focusing, the MoCo and the interpolation are performed for each segment of data in which the trajectory has been divided. piece of processed data. It is now necessary to resample these data on the global output sampling grid, that refers to the average rectilinear path. To map the output sampling nodes into each look a DEM of the imaged area, if available, should be used. The mapping is performed determining firstly which are the DEM position corresponding to the common grid nodes (slant range-azimuth pair of coordinates). Since computationally expensive this step can be done only for a larger grid of nodes; the remaining positions will be determined through interpolation. Then, from these ground locations and using the same geometrical relations it is possible to get the positions where the look must be interpolated. However in the experiments here shown the average height over the ground has been used. 4. EXPERIMENTAL RESULTS The algorithm has been tested on both simulated data (point scatterers) and real data from an airborne sensor. In both cases the navigational data (position and attitude) of the real airborne mission have been used. The SAR sensor is SARAT and is the CONAE (Argentinian Space Agency, that we thank for making the data available) L-band, 40MHz bandwidth airborne sensor. Navigational data, apparently accurate enough to allow reasonable processing results, are provided by an onboard INU/GPS system that give access to sensor position, velocity and attitude. Table I summarizes system parameters.
III - 1156
8500
8450
8450 slant range [m]
slant range [m]
8500
8400
8350
8300
8350
8300
8250 -80
8400
-60
-40
-20
0 azimuth [m]
20
40
60
80
8250 -80
-60
-40
(a)
-20
0 azimuth [m]
20
40
60
80
(b)
Parameter Frequency of operation Swath width Altitude Flight speed Antenna size Antenna pointing angle Pulse Repet. Frequency Sampling frequency Chirp pulse bandwidth Pulse width Spatial resolution
Value 1.3 GHz 14.3 km 4000 m 100 m/s 1.8 x 0.30 m 40° 250 Hz 50 MHz 36 MHz 10 μs 4.8 x 3.0 m (rg x az)
(a)
Fig. 4. Real airborne data. (a) focused using a blockwise ω-k algorithm and no MoCo; (b) with the MoCo ω-k algorithm.
Table I: SARAT System Parameters
Measure 3dB width PSLR ISLR
Method Ideal MoCo -k Ideal MoCo -k Ideal MoCo -k
Azimuth 4.4m 7.7m -13.5dB -7.8dB 10.2dB 8.3dB
(b)
the processing but allow gains in computational efficiency, as longer blocks can be processed. Experimental results, obtained implementing a modified version of the ω-k focusing algorithm, show that the proposed procedure is effective both in terms of sharpness and in terms of good geometric registration of the output focused image.
Slant range 3.30m 3.68m -21.1dB -21.0dB 14.4dB 14.7dB
Table II: Measurement on the impulse response in figure
Fig. 3. Simulation of a point scatterer. (a) Focusing of ideal target and no motion errors; (b) Focusing with the MoCo ω-k. Blocks have been chosen of the same size in the two cases. Output results for point scatterers are shown in Fig. 3. Fig. 3a shows the contour plot of the ideal 2D impulse response obtained with a conventional ω-k processor, with zero Doppler centroid and no deviations from uniform sensor motion. Fig. 3b shows the response to a point target when the raw data simulation has used the position and attitude data from the navigational data base (a Doppler centroid fDC 70Hz resulted): the processing was ω-k with the described MoCo procedure. Table II compares the relative performances. Finally, Fig. 4 compares the results obtained with and without the MoCo procedure with real data acquired over the Buenos Aires area: image size is about 1.5km in slant range and 0.25km in azimuth. The effectiveness of the MoCo procedure is evident. 5. CONCLUSIONS In this paper a procedure for the motion compensation of airborne SAR data has been presented. Sensor trajectory is approximated with piecewise linear or quadratic segments and a blockwise processing is used. Quadratic segments complicate
6. REFERENCES [1] R. Bamler I. Cumming R. K. Raney, H. Runge and F. H.Wong, “Precision sar processing using chirp scaling,” IEEE Trans. Geosci. Remote Sens., vol. 32, pp. 786–799, July 1994. [2] J. R. Bennett and I. Cumming, “A digital processor for the production of seatsat synthetic aperture radar imagery,” Proc. SURGE Workshop, Frascati ESA-SP-154, 1979. [3] C. Cafforio C. Prati, F. Rocca, “Sar data focusing using seismic migration techniques,” IEEE Trans. on Aeros. and Electr. Syst., vol. 27, pp. 194–207, March 1991. [4] Y. Huang A. Moreira, “Airborne sar processing of highly squinted data using a chirp scaling approach with integrated motion compensation,” IEEE Trans. Geosci. Remote Sens., vol. 32, no.5, September 1994. [5] R. Scheiber K. A. Camara de Macedo, “Precise topography- and aperture-dependent motion compensation for airborne sar,” IEEE Geosci. Remote Sens. Letters, vol. 2, no.2, pp. 172–176, April 2005. [6] A. Moreira, “Extended wavenumber-domain sar focusing with integrated motion compensation,” IEE Proc.-Radar Sonar Navig., vol. 153, no.3, June 2006.
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