Iterative solutions of min-max parameter estimation with bounded data uncertainties

TLDR: This paper establishes the existence of a fundamental contraction mapping and uses this observation to propose an approximate recursive algorithm that avoids the need for explicit SVDs and for the solution of the nonlinear equation.

Abstract: This paper deals with the important problem of parameter estimation in the presence of bounded data uncertainties. Its recent closed-form solution leads to more meaningful results than alternative methods (e.g., total least-squares and robust estimation), when a priori bounds about the uncertainties are available. The derivation requires the computation of the SVD of the data matrix and the determination of the unique positive root of a nonlinear equation. This paper establishes the existence of a fundamental contraction mapping and uses this observation to propose an approximate recursive algorithm that avoids the need for explicit SVDs and for the solution of the nonlinear equation. Simulation results are included to demonstrate the good performance of the recursive scheme.