Metric-Based Motion Error Estimation With Ground Cartesian Back-Projection for UAV TTW SAR

Uncrewed aerial vehicle (UAV) through-the-wall (TTW) synthetic aperture radar (SAR) extends the traditional remote sensing into penetration perception of obstructed areas in high-rise buildings with significant advantages. However, the image defocusing caused by motion errors severely hinders the application of UAV TTW SAR. The mismatched signal model in the TTW condition leads to the ineffectiveness of conventional airbone autofocus, while the widebeam and wideband characteristics of the UAV TTW SAR system further aggravate the defocusing issue. In this article, an effective metric-based motion error estimation with ground Cartesian back-projection (GCBP) algorithm is proposed. Unlike conventional SAR scenarios, a parametric signal model of UAV TTW SAR is established by incorporating refraction approximation which is a critical distinction absent in traditional remote sensing. Phase errors are further analyzed from the perspective of geometric, frequency-dependent, time-variant, and space-variant characteristics. Then, the aperture division and subband division are integrated with the GCBP algorithm for efficient imaging. With the constraint of the UAV motion continuity, a metric-based optimization method is designed. Gradient descent combined with the line search strategy constitutes an iterative optimization mechanism. Finally, through the verifications of simulations and experiments, the proposed algorithm realizes precise motion error estimation and achieves fabulous refocusing performance in UAV TTW SAR. This technology holds immense potential for large-scale TTW sensing of high-rise buildings, bridging the gap between traditional remote sensing and concealed space sensing in urban environments.