Inversion Error Bound Analysis of Scatterer Parameters for Multidimensional SAR

Synthetic aperture radar (SAR) has become a state-of-the-art technology in many applications without being affected by changes in weather and daylight. Since the detection capability of the single-dimensional SAR is limited, the multidimensional (MD) SAR system, e.g., multibaseline and multipolarization, is used to improve its performance. The design of the MDSAR system should be directly related to the specified applications and a quantitatively analytical theory for bound analysis is required to achieve good efficiency. In this article, a mathematical framework for inversion bounds analysis of MDSAR is proposed. First, based on the attributed scattering center (ASC) model, the Fisher information matrix and its corresponding Cramer–Rao lower bound (CRLB) are used to get the error bound of the estimated parameters. Second, considering the discrete sampling (DS) of the parameters, a probability density function-based conversion is conducted to get the DS CRLB. Finally, the mathematical framework for MD acquisitions is established. The simulation-based experimental results show that the theoretical error bound is consistent with the output of the orthogonal matching pursuit (OMP). The error bound of the parameters obtained by the proposed general mathematical framework can be used to evaluate the performance of inversion algorithms under certain MDSAR configurations.