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.

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    ABSTRACT: In many inverse problems of signal processing the problem reduces to a linear system of equations. Accurate and robust estimation of the solution with errors in both measurement vector and coefficient matrix is a challenging task. In this paper a novel formulation is proposed which takes into account the structure (e.g. Toeplitz, Hankel) and uncertainties of the system. A numerical algorithm is provided to obtain the solution. The proposed technique and other methods are compared in a channel equalization example which is a fundamental necessity in communication.
    No preview · Conference Paper · May 2009
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