Robust Multiple Signal Classification via Probability Measure Transformation

TL;DR

This paper presents a robust measure-transformed MUSIC framework that enhances signal classification robustness by transforming probability measures, effectively handling outliers and coherent signals, and improving estimation accuracy.

Contribution

The paper introduces a novel measure-transformed approach for robust MUSIC, including a new MDL criterion and extensions for coherent signals, with demonstrated advantages over existing methods.

Findings

MT-MUSIC is B-robust with bounded influence function.

The eigendecomposition of MT-covariance determines the noise subspace.

Simulation shows improved robustness and accuracy over existing methods.

Abstract

In this paper, we introduce a new framework for robust multiple signal classification (MUSIC). The proposed framework, called robust measure-transformed (MT) MUSIC, is based on applying a transform to the probability distribution of the received signals, i.e., transformation of the probability measure defined on the observation space. In robust MT-MUSIC, the sample covariance is replaced by the empirical MT-covariance. By judicious choice of the transform we show that: 1) the resulting empirical MT-covariance is B-robust, with bounded influence function that takes negligible values for large norm outliers, and 2) under the assumption of spherically contoured noise distribution, the noise subspace can be determined from the eigendecomposition of the MT-covariance. Furthermore, we derive a new robust measure-transformed minimum description length (MDL) criterion for estimating the number of signals, and extend the MT-MUSIC framework to the case of coherent signals. The proposed approach is illustrated in simulation examples that show its advantages as compared to other robust MUSIC and MDL generalizations.