Asymptotic robustness of Kelly's GLRT and Adaptive Matched Filter detector under model misspecification

TL;DR

This paper investigates the asymptotic robustness of Kelly's GLRT and the Adaptive Matched Filter under model misspecification, particularly in radar signal processing, revealing their behavior when the assumed Gaussian model differs from the true CES distribution.

Contribution

It provides a novel analysis of the robustness of Kelly's GLRT and AMF detectors under model mismatch in radar applications, extending understanding of their asymptotic properties.

Findings

Kelly's GLRT maintains robustness under certain model misspecifications.

AMF exhibits asymptotic robustness when the true data follow CES distribution.

The analysis offers insights into detector performance with model deviations.

Abstract

A fundamental assumption underling any Hypothesis Testing (HT) problem is that the available data follow the parametric model assumed to derive the test statistic. Nevertheless, a perfect match between the true and the assumed data models cannot be achieved in many practical applications. In all these cases, it is advisable to use a robust decision test, i.e. a test whose statistic preserves (at least asymptotically) the same probability density function (pdf) for a suitable set of possible input data models under the null hypothesis. Building upon the seminal work of Kent (1982), in this paper we investigate the impact of the model mismatch in a recurring HT problem in radar signal processing applications: testing the mean of a set of Complex Elliptically Symmetric (CES) distributed random vectors under a possible misspecified, Gaussian data model. In particular, by using this general misspecified framework, a new look to two popular detectors, the Kelly's Generalized Likelihood Ration Test (GLRT) and the Adaptive Matched Filter (AMF), is provided and their robustness properties investigated.