MSE based optimization of the measure-transformed MUSIC algorithm

Nir Halay, Koby Todros

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Recently, we developed a robust generalization of the MUltiple SIgnal Classification (MUSIC) algorithm. This generalization, called measure-transformed MUSIC (MT-MUSIC), operates by applying a transform to the probability measure (distribution) of the data. The considered transform is structured by a non-negative data-weighting function, called MT-function, that, when properly chosen, mitigates the effect of non-Gaussian heavy-tailed noise that produces outliers. In this paper, we characterize the asymptotic mean-squared-error (MSE) performance of the MT-MUSIC algorithm. Under some mild regularity conditions, we show that the MT-MUSIC estimator is asymptotically normal and unbiased, and obtain an analytic expression for the asymptotic MSE matrix. We go on to develop a strongly consistent estimator for the asymptotic MSE matrix that is constructed via the same sequence of samples being used for implementation of the MT-MUSIC. This paves the way for development of a data-driven procedure for optimal selection of the MT-function parameters that minimizes an empirical estimate of the asymptotic average root MSE (RMSE). The performance advantage of the proposed MSE based optimization of the MT-MUSIC is illustrated in simulation examples.

Original languageEnglish
Pages (from-to)150-163
Number of pages14
JournalSignal Processing
Volume160
DOIs
StatePublished - 1 Jul 2019

Keywords

  • Array processing
  • DOA estimation
  • Probability measure transform
  • Robust statistics

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

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