Synthetic-aperture-radar motion compensation and feature extraction by means of a relaxation-based algorithm

Zheng-She Liu; Jian Li

doi:10.1364/JOSAA.15.000599

Journal of the Optical Society of America A
Vol. 15,
Issue 3,
pp. 599-610
(1998)
•https://doi.org/10.1364/JOSAA.15.000599

Synthetic-aperture-radar motion compensation and feature extraction by means of a relaxation-based algorithm

Zheng-She Liu and Jian Li

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Zheng-She Liu and Jian Li, "Synthetic-aperture-radar motion compensation and feature extraction by means of a relaxation-based algorithm," J. Opt. Soc. Am. A 15, 599-610 (1998)

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Abstract

We study the problem of extracting target features by means of synthetic-aperture radar (SAR) in the presence of uncompensated aperture motion errors. A parametric data model for a spotlight-mode SAR system is established. The Cramér–Rao bounds (CRB’s) for the parameters of the data model are also derived. The CRB analysis shows that the unknown motion errors can significantly affect the accuracy of a common shift of the scatterer positions in the cross-range direction but have little effect on other target parameters, including the accuracy of the relative positions in the range direction. A relaxation-based motion compensation RELAX (MCRELAX) algorithm for estimating both target features and motion errors is devised. Simulation results show that the mean squared errors of the parameter estimates obtained by using the MCRELAX algorithm can approach the corresponding CRB’s. We also use a couple of examples to show that MCRELAX can simply be used for motion compensation only and can give good motion-compensation results.

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	kth Scatterer
	1	2	3	4	5	6	7	8
$Re (α_{k})$	9.2643	$- 3.5000$	4.4339	$- 2.1447$	$- 1.4363$	1.7064	1.1555	1.2068
$Im (α_{k})$	$- 4.9633$	$- 9.6967$	$- 1.4916$	0.3269	$- 1.2229$	$- 0.6923$	$- 0.7064$	$- 0.6122$
$f_{k}$	0.1016	0.1406	0.1016	0.0078	0.1016	0.0312	$- 0.1328$	0.0938
${\tilde{f}}_{k}$	$- 0.0293$	0.0488	$- 0.0059$	$- 0.0059$	0.1191	$- 0.0215$	$- 0.0371$	$- 0.0684$

	kth Scatterer
	1	2	3	4	5	6	7	8
CRB’s of ${α_{k}}$ obtained by assuming the motion errors unknown (CRB1) and known (CRB2)
CRB1	$- 2.13$	$- 7.78$	$- 2.28$	$- 9.58$	$- 9.85$	$- 9.48$	$- 11.15$	$- 8.62$
CRB2	$- 3.32$	$- 11.19$	$- 3.13$	$- 9.72$	$- 11.04$	$- 9.58$	$- 11.24$	$- 9.54$
CRB’s of ${f_{k}}$ and ${{\overset{˘}{f}}_{k}},$ obtained by assuming the motion errors unknown (CRB1 and CRB3, respectively) and known (CRB2 and CRB4, respectively)
CRB1	$- 74.71$	$- 75.49$	$- 67.94$	$- 58.38$	$- 60.77$	$- 56.66$	$- 57.97$	$- 57.61$
CRB2	$- 74.80$	$- 75.53$	$- 67.98$	$- 58.39$	$- 60.85$	$- 56.67$	$- 57.98$	$- 57.92$
CRB3	$- 68.31$	$- 68.84$	$- 66.75$	$- 58.70$	$- 61.30$	$- 57.23$	$- 58.92$	$- 58.54$
CRB4	$- 68.43$	$- 68.97$	$- 66.88$	$- 58.71$	$- 61.38$	$- 57.24$	$- 58.94$	$- 58.81$
CRB’s of ${{\bar{f}}_{k}}$ and ${{\overset{˘}{\bar{f}}}_{k}},$ obtained by assuming the motion errors unknown (CRB1 and CRB3, respectively) and known (CRB2 and CRB4, respectively)
CRB1	$- 44.20$	$- 44.25$	$- 44.16$	$- 44.14$	$- 43.87$	$- 44.09$	$- 44.07$	$- 43.85$
CRB2	$- 67.11$	$- 75.58$	$- 59.51$	$- 60.03$	$- 60.52$	$- 58.46$	$- 57.98$	$- 55.27$
CRB3	$- 65.83$	$- 68.27$	$- 57.61$	$- 60.41$	$- 60.19$	$- 59.01$	$- 58.81$	$- 54.72$
CRB4	$- 66.10$	$- 68.97$	$- 58.71$	$- 60.55$	$- 61.23$	$- 59.07$	$- 58.88$	$- 56.02$
CRB’s of δ and $\bar{δ},$ obtained by assuming the motion errors unknown (CRB1 and CRB3, respectively) and known (CRB2 and CRB4, respectively)
CRB1		CRB2			CRB3			CRB4

$- 69.75$		$- 69.86$			$- 44.22$			$- 69.88$

	kth Scatterer
	1	2	3	4	5	6	7	8
For ${α_{k}}$
MSE1	5.03	6.58	1.76	$- 5.64$	$- 2.29$	$- 5.36$	$- 8.44$	$- 7.86$
MSE2	$- 2.95$	$- 6.71$	$- 2.56$	$- 9.39$	$- 8.72$	$- 9.45$	$- 11.50$	$- 9.20$
CRB	$- 2.13$	$- 7.78$	$- 2.28$	$- 9.58$	$- 9.85$	$- 9.48$	$- 11.15$	$- 8.62$
For ${{\overset{˘}{f}}_{k}}$
MSE1	$- 58.67$	$- 58.53$	$- 59.18$	$- 54.83$	$- 52.04$	$- 44.88$	$- 56.04$	$- 57.68$
MSE2	$- 69.72$	$- 70.14$	$- 67.11$	$- 58.65$	$- 61.44$	$- 56.85$	$- 59.05$	$- 58.45$
CRB	$- 68.31$	$- 68.84$	$- 66.75$	$- 58.70$	$- 61.30$	$- 57.23$	$- 58.92$	$- 58.54$
For ${\overset{˘}{\bar{f}}}$
MSE1	$- 57.04$	$- 56.37$	$- 54.64$	$- 54.81$	$- 51.48$	$- 47.00$	$- 54.50$	$- 49.15$
MSE2	$- 65.82$	$- 68.49$	$- 57.77$	$- 60.86$	$- 60.12$	$- 58.56$	$- 59.21$	-54.92
CRB	$- 65.83$	$- 68.27$	$- 57.61$	$- 60.41$	$- 60.19$	$- 59.01$	$- 58.81$	$- 54.72$
For δ and $\bar{δ}$
	δ	$\bar{δ}$

MSE1	$- 59.21$	$- 10.54$
MSE2	$- 63.69$	$- 42.36$
CRB	$- 69.75$	$- 44.22$

	kth Scatterer
	1	2	3	4	5	6	7	8
$Re (α_{k})$	9.2643	$- 3.5000$	4.4339	$- 2.1447$	$- 1.4363$	1.7064	1.1555	1.2068
$Im (α_{k})$	$- 4.9633$	$- 9.6967$	$- 1.4916$	0.3269	$- 1.2229$	$- 0.6923$	$- 0.7064$	$- 0.6122$
$f_{k}$	0.1016	0.1406	0.1016	0.0078	0.1016	0.0312	$- 0.1328$	0.0938
${\tilde{f}}_{k}$	$- 0.0293$	0.0488	$- 0.0059$	$- 0.0059$	0.1191	$- 0.0215$	$- 0.0371$	$- 0.0684$

	kth Scatterer
	1	2	3	4	5	6	7	8
CRB’s of ${α_{k}}$ obtained by assuming the motion errors unknown (CRB1) and known (CRB2)
CRB1	$- 2.13$	$- 7.78$	$- 2.28$	$- 9.58$	$- 9.85$	$- 9.48$	$- 11.15$	$- 8.62$
CRB2	$- 3.32$	$- 11.19$	$- 3.13$	$- 9.72$	$- 11.04$	$- 9.58$	$- 11.24$	$- 9.54$
CRB’s of ${f_{k}}$ and ${{\overset{˘}{f}}_{k}},$ obtained by assuming the motion errors unknown (CRB1 and CRB3, respectively) and known (CRB2 and CRB4, respectively)
CRB1	$- 74.71$	$- 75.49$	$- 67.94$	$- 58.38$	$- 60.77$	$- 56.66$	$- 57.97$	$- 57.61$
CRB2	$- 74.80$	$- 75.53$	$- 67.98$	$- 58.39$	$- 60.85$	$- 56.67$	$- 57.98$	$- 57.92$
CRB3	$- 68.31$	$- 68.84$	$- 66.75$	$- 58.70$	$- 61.30$	$- 57.23$	$- 58.92$	$- 58.54$
CRB4	$- 68.43$	$- 68.97$	$- 66.88$	$- 58.71$	$- 61.38$	$- 57.24$	$- 58.94$	$- 58.81$
CRB’s of ${{\bar{f}}_{k}}$ and ${{\overset{˘}{\bar{f}}}_{k}},$ obtained by assuming the motion errors unknown (CRB1 and CRB3, respectively) and known (CRB2 and CRB4, respectively)
CRB1	$- 44.20$	$- 44.25$	$- 44.16$	$- 44.14$	$- 43.87$	$- 44.09$	$- 44.07$	$- 43.85$
CRB2	$- 67.11$	$- 75.58$	$- 59.51$	$- 60.03$	$- 60.52$	$- 58.46$	$- 57.98$	$- 55.27$
CRB3	$- 65.83$	$- 68.27$	$- 57.61$	$- 60.41$	$- 60.19$	$- 59.01$	$- 58.81$	$- 54.72$
CRB4	$- 66.10$	$- 68.97$	$- 58.71$	$- 60.55$	$- 61.23$	$- 59.07$	$- 58.88$	$- 56.02$
CRB’s of δ and $\bar{δ},$ obtained by assuming the motion errors unknown (CRB1 and CRB3, respectively) and known (CRB2 and CRB4, respectively)
CRB1		CRB2			CRB3			CRB4

$- 69.75$		$- 69.86$			$- 44.22$			$- 69.88$

Abstract

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Equations (67)

Journal of the Optical Society of America A