Cross-Range Scaling for Spaceborne Radar Image of Space Target via Novel Method of Rotational Motion Estimation With Analytical Solution

Rotational motion parameters play a critical role in radar imaging, particularly in cross-range scaling, which enables the target's actual size to be reconstructed. However, the motion information is typically unavailable and cannot be reliably estimated from echo data, especially in scenarios of spaceborne radar imaging. In this article, a novel rotational motion estimation method via analytical solutions is proposed and has been successfully applied to the cross-range scaling. First, an accurate cubic phase signal model is established, based on which the high-couple mapping mechanism between the rotational motion parameters and phase coefficients is revealed. Then, the issue of motion parameter estimation is transformed into phase coefficients estimation and multiple variables decouple. On this basis, the closed-form solutions of rotational motion parameters are derived, and the constraint of the unique real solution is analysed. Consequently, the cross-range scaling for spaceborne radar images can be realised with the analytical solutions of rotational motion parameters. The proposed method can achieve high estimation accuracy without relying on iterative search procedures, which typically occur in existing methods and often result in high computational cost or local convergence issues. Results of Monte Carlo experiments and simulated data support the high efficiency and stability of the proposed method.