New approach to weighted subspace fitting using subspace perturbation expansions

Abstract

ABSTRACT Weighted Subspace Fitting (WSF) is a method of estimating signal parameters from a of a matrix of received data. WSF was originally derived using the asymptotic (large data length) statistics of sample eigenvectors. This paper presents a new approach to deriving statistically optimal weights for weighted fitting (WSF) algorithms. The approach uses a formula called a subspace perturbation expansion, which shows how the subspaces of a finite-size matrix change when the matrix elements are perturbed. The perturbation is used to derivean optimal WSF cost function for estimating directions of arrival in array signal processing. The resulting costfunction is identical to that obtained using asymptotic statistics.Keywords : Subspace fitting , parameter estimation, D OA estimation , perturbation 1. INTRODUCTION A • variety of parameter estimation problems in signal processing and system identification can be solved usingsubspace methods. These methods rely on the fact that a rank deficient matrix can be formed from noise-freedata. Furthermore, information about the signal or system parameters is embedded in the column space and/orrow space of this matrix. With noisy data, the appropriate is estimated, usually with the singular valuedecomposition, and the parameters are extracted from the estimated subspace.A subspace perturbation expansion is a formula which shows how much of a perturbation is inducedby additive noise in the data. This formula' is called a subspace perturbation expansion. This formula was used