Optimal Polarimetric Detection Filter and Its Statistical Tests for a Ship Detector

Abstract

Ship detection is one important task in radar remote sensing. Moreover, Polarimetry shows a valuable contribution to discriminate between targets and clutter. The performance of most polarimetric detectors depends on two important factors: target clutter ratio (TCR) and speckles (or standard deviation to mean ratio of clutter background). The polarimetric matched filter (PMF) is just to maximize the TCR, while the polarimetric whitening filter (PWF) only takes the speckle reduction into consideration. In this paper, the optimal polarimetric detection filter (OPDF) is put forward, which considers maximizing the ratio of TCR to speckle. The approximate expression of the probability density function (PDF) of the OPDF is derived in closed form, so are the probability of false alarm (PFA) and the probability of detection (PD) in Wishart distribution assumption. The threshold of the OPDF detection can be easily obtained in closed form or via the bisection method. Experiments via simulated data validate the correctness of our results. The OPDF detector gives the best performance in most environments, especially in low PFA case and in the case where the statistics of targets is not the ideal Wishart distribution.