Research on BFSAR Motion Compensation with Second-order Difference Method via Minimum Entropy

‍ ‍Compared with traditional monostatic synthetic aperture radar imaging systems， bistatic forward-looking synthetic aperture radar （BFSAR） systems have increasingly attracted the attention of researchers both domestically and internationally， owing to their unique configuration and imaging advantages. By placing the transmitting and receiving antennas on separate platforms， the BFSAR system enables forward-looking imaging capabilities that are not achievable with monostatic SAR systems. Therefore， the BFSAR system holds significant application value in areas such as maritime surveillance， target detection， and military guidance. However， due to the separation of the transmitter and receiver of the BFSAR system， each radar platform is subjected to motion-induced errors during flight. Compared with monostatic SAR systems， these motion errors introduce more complex phase distortions in the received echo data captured by the system， ultimately resulting in image defocusing of the target. To address this issue， a second-order difference motion compensation algorithm based on the minimum entropy criterion is proposed in this study. First， the echo data of the target， after one-dimensional range compression， is used as the processing object. The second-order difference method is then applied to estimate the phase errors of the echo signals corresponding to each range cell occupied by the target. These estimated phase errors are subsequently used to compensate for the echo signals. Next， the compensated echo signal is compressed in the azimuth direction using the Range Doppler （RD） algorithm to generate the target image. The image entropy is then calculated， and the optimal phase error that minimizes the entropy is selected. Finally， the phase error is used to further compensate the echo signal， and the RD algorithm is applied once more in the azimuth domain to produce a well-focused target image. This algorithm does not rely on inertial navigation data and can directly estimate phase errors from the echo data to perform motion compensation. Simulation results demonstrate that the proposed algorithm effectively mitigates the impact of the platform motion errors on the phase and Doppler characteristics of the echo signal. Consequently， the resulting image exhibits a focusing quality comparable to that of an ideal reference image.