SKP-shrinkage estimator for SAR multi-baselines applications

The physical properties that can be inferred from Radar data are strictly related to the kind of diversity that characterizes the data itself. Spatial (i.e.: baseline) diversity provides information about target locations, temporal diversity provides information about target displacement, whereas polarimetric diversity provides information about the target electromagnetic behavior. In all cases, covariance matrix estimation is a key issue in the framework of coherent SAR analysis of scenarios characterized by the presence of distributed targets, such as bare or rock surfaces, forested areas, or ice shelves. In this paper we consider the case where two different kinds of diversities are present within the data, such as spatial and temporal or spatial and polarimetric, and investigate the effectiveness of the shrinkage estimator for the data covariance matrix. The shrinkage estimator is obtained as an optimum convex combination between the sample covariance matrix and the structured estimator. The structured estimator is based on the hypothesis of separability of the coherence losses due to the different kinds of diversities within the data, for each target that contributes to the received signal. This hypothesis leads to expressing the data covariance matrix as a Sum of Kronecker Products (SKP), for the estimation of which fast algebraic techniques exist.