On the Maximal Invariant Statistic for Adaptive Radar Detection in Partially-Homogeneous Disturbance with Persymmetric Covariance

TL;DR

This paper derives the Maximal Invariant Statistic for adaptive radar detection in partially-homogeneous, persymmetric Gaussian noise, demonstrating that key tests can be expressed in terms of it, ensuring CFAR performance.

Contribution

The paper introduces a suitable invariance group and derives the MIS for adaptive detection in complex noise environments, unifying key tests under this framework.

Findings

MIS derived for the problem setting

Tests expressed in terms of MIS ensure CFAR

Unified framework for adaptive detection methods

Abstract

This letter deals with the problem of adaptive signal detection in partially-homogeneous and persymmetric Gaussian disturbance within the framework of invariance theory. First, a suitable group of transformations leaving the problem invariant is introduced and the Maximal Invariant Statistic (MIS) is derived. Then, it is shown that the (Two-step) Generalized-Likelihood Ratio test, Rao and Wald tests can be all expressed in terms of the MIS, thus proving that they all ensure a Constant False-Alarm Rate (CFAR).