A Unifying Framework for Adaptive Radar Detection in the Presence of Multiple Alternative Hypotheses

TL;DR

This paper introduces a unified adaptive radar detection framework based on the Kullback-Leibler Information Criterion, capable of handling multiple hypotheses with unknown parameters, maintaining constant false alarm rate, and demonstrating practical effectiveness.

Contribution

The paper presents a novel decision scheme framework for adaptive radar detection that unifies multiple hypotheses testing with unknown parameters using KL divergence approximations.

Findings

Effective detection schemes for multiple hypotheses with unknown parameters.

Framework maintains constant false alarm rate under certain constraints.

Demonstrated improved performance in practical radar detection scenarios.

Abstract

In this paper, we develop a new elegant framework relying on the Kullback-Leibler Information Criterion to address the design of one-stage adaptive detection architectures for multiple hypothesis testing problems. Specifically, at the design stage, we assume that several alternative hypotheses may be in force and that only one null hypothesis exists. Then, starting from the case where all the parameters are known and proceeding until the case where the adaptivity with respect to the entire parameter set is required, we come up with decision schemes for multiple alternative hypotheses consisting of the sum between the compressed log-likelihood ratio based upon the available data and a penalty term accounting for the number of unknown parameters. The latter rises from suitable approximations of the Kullback-Leibler Divergence between the true and a candidate probability density function. Interestingly, under specific constraints, the proposed decision schemes can share the constant false alarm rate property by virtue of the Invariance Principle. Finally, we show the effectiveness of the proposed framework through the application to examples of practical value in the context of radar detection also in comparison with two-stage competitors. This analysis highlights that the architectures devised within the proposed framework represent an effective means to deal with detection problems where the uncertainty on some parameters leads to multiple alternative hypotheses.