Robust eigenvalue decomposition techniques for high resolution signal estimation and detection

Porges, Richard Graham (1993) Robust eigenvalue decomposition techniques for high resolution signal estimation and detection. University of Southampton, Doctoral Thesis.

Abstract

This work is concerned with methods of detecting and estimating the directions of arrival of plane waves on arrays of sensors, in particular when the noise field is non-isotropic with an arbitrary covariance matrix and when the signals are coherent. The signal model can be either deterministic or stochastic although the computer simulations detailed here predominantly use the former.

A maximum likelihood and a Bayesian approach both result in the estimation method of minimising the determinant of the projection onto the noise subspace of the sampled data covariance matrix. A minimum description length (MDL) approach yields a second, closely related, minimising criterion; the data covariance matrix is projected onto the signal subspace as well as the noise subspace, and the product of the two determinants is minimised.

Here, a third method is proposed: not the product of the two determinants, but their quotient is to be minimised with respect to the signals' steering vectors. Through extensive computer simulation studies the proposed method is shown to compare very favourably with the other two methods, and also with the stochastic maximum likelihood method and MUSIC. The deterministic Cramer-Rao lower bounds are calculated and provide additional comparisons.

An algebraic simplification (applicable to all three main methods) shortens computation time considerably, and an iterative modification provides closer yet shadowing of the Cramer-Rao performance target.

A signal detection process based on an MDL formulation is then derived and shown, by the use of computer simulations, to compare favourably with an existing MDL detection algorithm.

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