Joint intra-frame and inter-frame imaging algorithm for spaceborne ISAR imaging of air target

doi:10.23919/JSEE.2025.000014

Abstract

Abstract:

The spaceborne inverse synthetic aperture radar (ISAR) has attracted significant attention due to its extensive observation range and imaging performance. However, the complex motion between spaceborne platform and the air target leads to complex signal modulation. The scattering anisotropy and occlusion lead to the scattering points missing problem. These problems pose a serious challenge to the traditional ISAR imaging algorithms. Aiming at the above problems, this paper proposes a joint intra-frame and inter-frame imaging algorithm based on spaceborne ISAR. In this algorithm, we divide the long coherent processing interval into several sub-apertures using the narrow-band tracking data, and each-order terms of the signal within sub-aperture is derived in detail. Then, the intra-frame algorithm based on the parametric minimized image entropy search is proposed to correct the spatial-variant phase errors caused by the complex relative motion. As to the well-focused images from different views and the rotation parameters obtained in sub-apertures, the inter-frame algorithm based on wavelet transform can perform image registration and image fusion to obtain more detailed target feature information and more complete target structure. In simulated and real-measured data experiments, the effectiveness and superiority of the proposed algorithm are validated.

Key words: spaceborne inverse synthetic aperture radar (ISAR), long coherent processing interval division, intra-frame complex motion compensation, inter-frame image fusion

Yichen ZHOU, Yong WANG. Joint intra-frame and inter-frame imaging algorithm for spaceborne ISAR imaging of air target[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 412-430.

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Parameter	Value
Carrier frequency/${\mathrm{GHz}}$	$10$
Bandwidth/${\mathrm{MHz}}$	$100$
Repetition frequency/${\mathrm{Hz}}$	$1\;000$
Pulse number	1024

Error term	Relevant motion parameter	Boundary value
$ \Delta {\varPsi _{T,1}} $	$ {K_1} $/$({\mathrm{m}}\cdot {{\mathrm{s}}^{ - 1}})$	$1.464\;8$
$ \Delta {\varPsi _{T,2}} $	$ {K_2} $/$({\mathrm{m}}\cdot {{\mathrm{s}}^{ - 2}})$	$1.430\;5$
$ \Delta {\varPsi _{T,3}} $	$ {K_3} $/$({\mathrm{m}}\cdot {{\mathrm{s}}^{ - 3}})$	$1.397\;0$
$ \Delta {\varPsi _{T,4}} $	$ {K_4} $/$({\mathrm{m}}\cdot {{\mathrm{s}}^{ - 4}})$	$1.364\;2$
$ \Delta {\varPhi _{T,1}} $	$ {K_2} $/$ {\mathrm{m}}\cdot {{\mathrm{s}}^{ - 2}}) $	$ 1.788\;1 \times {10^{ - 3}} $
$ \Delta {\varPhi _{T,2}} $	$ {K_3} $/$({\mathrm{m}}\cdot {{\mathrm{s}}^{ - 3}})$	$1.746\;2 \times {10^{ - 3}}$
$ \Delta {\varPhi _{T,3}} $	$ {K_4} $/$({\mathrm{m}}\cdot {{\mathrm{s}}^{ - 4}})$	$1.705\;3 \times {10^{ - 3}}$
$ \Delta {\varPhi _{R,1}} $	$ {\alpha _e} $/$({\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 2}})$	$3.576\;3 \times {10^{ - 4}}$
$ \Delta {\varPhi _{R,2}} $	$ {\omega _1} $/$({\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 1}})$	$1.891\;1 \times {10^{ - 2}}$
$ \Delta {\varPhi _{R,3}} $	$ {\alpha _e}{\omega _1} $/$({\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 3}})$	$3.492\;5 \times {10^{ - 4}}$
$ \Delta {\varPhi _{R,4}} $	$ {\alpha _e} $/$({\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 2}})$	$3.693\;6 \times {10^{ - 2}}$

Parameter	Value
Satellite orbit altitude/km	500
Satellite velocity/(km/s)	8
Initial position of the satellite/km	$(0, - 90)$
Target altitude/km	10
Target velocity/(m/s)	100

Fitting coefficient	Value	Boundary value
$ {K_1} $(first-order)/(${\mathrm{m}} \cdot {{\mathrm{s}}^{ - 1}} $)	$ - 1.102\;8 \times {10^3}$	$1.464\;8$
$ {K_2} $(second-order)/(${\mathrm{m}} \cdot {{\mathrm{s}}^{ - 2}} $)	$ {\text{3}}{\text{.622 5}} \times 10 $	$ 1.788\;1 \times {10^{ - 3}} $
$K_3$(third-order)/(${\mathrm{m}} \cdot {{\mathrm{s}}^{ - 3}} $)	$1.148\;7 \times {10^{ - 1}}$	$1.746\;2 \times {10^{ - 3}}$
$ {K_4} $(fourth-order)/(${\mathrm{m}} \cdot {{\mathrm{s}}^{ - 4}} $)	$ - 3.504\;1 \times {10^{ - 3}}$	$1.705\;3 \times {10^{ - 3}}$
$ {\alpha _e} $(second-order)/${\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 2}} $)	$ - 1.245\;0 \times {10^{ - 3}}$	$3.576\;3 \times {10^{ - 4}}$
$ {\omega _1} $(second-order)/(${\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 1}} $)	$1.895\;0 \times {10^{ - 2}}$	$1.891\;1 \times {10^{ - 2}}$
$ {\alpha _e}{\omega _1} $(third-order)/(${\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 3}} $)	$2.769\;1 \times {10^{ - 5}}$	$3.492\;5 \times {10^{ - 4}}$
$ {\alpha _e} $(fourth-order)/(${\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 2}} $)	$ - 1.245\;0 \times {10^{ - 3}}$	$3.693\;6 \times {10^{ - 2}}$

Parameter	Value
First-order motion component/($ {\mathrm{m}}\cdot {{\mathrm{s}}^{ - 1}} $)	$ 1\;000 $
Second-order motion component/(${\mathrm{m}}\cdot {{\mathrm{s}}^{ - 2}}$)	$20$
Third-order motion component/(${\mathrm{m}}\cdot {{\mathrm{s}}^{ - 3}}$)	$0.1$
Fourth-order motion component/(${\mathrm{m}}\cdot {{\mathrm{s}}^{ - 4}}$)	$0.005$
Rotational velocity/(${\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 1}}$)	$0.05$
Rotational acceleration/(${\mathrm{rad}}\cdot {{\mathrm{s}}^{ - 2}}$)	$0.02$
Bandwidth/${\mathrm{MHz}}$	$100$
Carrier frequency/${\mathrm{GHz}}$	$10$
Pulse repetition frequency/${\mathrm{Hz}}$	$500$
Sampling frequency/${\mathrm{MHz}}$	$200$
Sub-aperture pulse number	1024
SNR/dB	5