On weighted structured total least squares

In this contribution we extend the result of (Markovsky et. al, SIAM J. of Matrix Anal. and Appl., 2005) to the case of weighted cost function. It is shown that the computational complexity of the proposed algorithm is preserved linear in the sample size when the weight matrix is banded with bandwidth that is independent of the sample size

Structured least squares with bounded data uncertainties

In many signal processing applications the core problem reduces to a linear system of equations. Coefficient matrix uncertainties create a significant challenge in obtaining reliable solutions. In this paper, we present a novel formulation for solving a system of noise contaminated linear equations while preserving the structure of the coefficient matrix. The proposed method has advantages over the known Structured Total Least Squares (STLS) techniques in utilizing additional information about the uncertainties and robustness in ill-posed problems. Numerical comparisons are given to illustrate these advantages in two applications: signal restoration problem with an uncertain model and frequency estimation of multiple sinusoids embedded in white noise. ©2009 IEEE

Block-Toeplitz/Hankel structured total least squares

A multivariate structured total least squares problem is considered, in which the extended data matrix is partitioned into blocks and each of the blocks is block-Toeplitz/Hankel structured, unstructured, or noise free. An equivalent optimization problem is derived and its properties are established. The special structure of the equivalent problem enables to improve the computational efficiency of the numerical solution via local optimization methods. By exploiting the structure, the computational complexity of the algorithms per iteration is linear in the sample size. Application of the method for system identification and for model reduction is illustrated by simulation examples