A Novel Methodology for D-GBSAR Repositioning Error Compensation Based on Maximum Likelihood Estimation

Repositioning error (RE) compensation is one of the key steps in discontinuous ground-based synthetic aperture radar (D-GBSAR) monitoring. The traditional RE compensation is to perform 2-D phase unwrapping, and then remove the RE based on the least-squares method, thereby introducing an extra unwrapping error. Specifically, due to the phase wrapped of the discrete permanent scatterers (PSs), the least-squares method is intractable to be performed directly. Hence, the core idea of this article is to propose a new likelihood function model and straightforwardly estimate the baseline parameters to compensate for the RE, avoiding phase unwrapping. First, we transform the discrete PS phase wrapped into a continuous function model, reducing the complexity of mathematical analysis. Then, based on the novel RE model in the context of Gaussian white noise, we obtain a concise mathematical expression of the Cramer-Rao lower bound (CRLB) for maximum likelihood estimation, which serves as the performance indicator for baseline estimation. Afterward, by introducing the Newton iteration method, we obtain the baseline estimation results and integrate a novel RE compensation deformation inversion processing methodology for D-GBSAR, named maximum likelihood-Newton iteration-RE compensation algorithm (MLNIRECA). Finally, the effectiveness of the proposed method is verified through simulation and real data experiments, where the root mean square error (RMSE) is constantly close to the CRLB with the increase in signal-to-noise ratio (SNR) when the SNR is greater than -10 dB. Particularly, we can extend the spatial baseline to 100 mm under the condition of accuracy requirements and use the proposed methodology to achieve submillimeter deformation monitoring accuracy over actual scenarios in time and space.