Observed Fisher Information for Radar Clutter Modeled with Sub-Gaussian Α-Stable Distribution

It is well known that the clutter in such applications as synthetic aperture radar (SAR) follows heavy-tailed distributions. In such applications, knowledge of the exact statistical properties and/or errors in estimation of the clutter parameters plays an important role in successful implementation of the related applications like target tracking using SAR. In this study, the observed Fisher information (OFI) matrix will be derived for the received clutter assuming that the statistical behavior of clutter follows a sub-Gaussian α-stable (SGS) distribution along with a density function for an SGS distribution based on a newly proposed expansion. The new expansion is characterized with high speed computation in one hand, and avoids issues related to numerical computation of SGS density function, on the other. The minimum standard error of the clutter parameters, then, will be derived as the OFI matrix is inversely related to the Cramer-Rao lower bound (CRLB) of the clutter's estimated parameters. In order to compute the density function and OFI of the SGS distribution, the performance of the proposed methodology has been tested through numerical simulation where the implemented computer code of the proposed numerical method has been demonstrated to be fast and accurate. The R code is available at https://github.com/mahditeimouri/Sub-Gaussian/blob/main/OFI-sub-Gaussian.r.