STRUCTURED TOTAL LEAST SQUARES Analysis, Algorithms and Applications

Abstract

In this paper an overview is given of the Structured Total Least Squares (STLS) approach and its recent extensions. The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) problem when constraints on the matrix structure need to be im­ posed. Similar to the ordinary TLS approach, the STLS approach can be used to determine the parameter vector of a linear model, given some noisy measurements. In many signal processing applications, the imposition of this matrix structure constraint is necessary for obtaining Maximum Likelihood (ML) estimates of the parameter vector. A basic algorithmic scheme leading to fast implementations of the STLS approach through the exploitation of the low displacement rank structure is presented. An example illustrates the possible benefit of using the STLS approach.