Robust estimation of unknowns in a linear system of equations with modeling uncertainties

Abstract

Robust methods of estimation of unknowns in a linear system of equations with modeling uncertainties are proposed. Specifically, when the uncertainty in the model is limited to the statistics of the additive noise, algorithms based on adaptive regularized techniques are introduced and compared with commonly used estimators. It is observed that significant improvements can be achieved at low signal-to-noise ratios. Then, we investigated the case of a parametric uncertainty in the model matrix and proposed algorithms based on non-linear ridge regression, maximum likelihood and Bayesian estimation that can be used depending on the amount of prior information. Based on a detailed comparison study between the proposed and available methods, it is shown that the new approaches provide significantly better estimates for the unknowns in the presence of model uncertainties.