A fast iterative solution for worst-case parameter estimation with bounded model uncertainties

Deals with the problem of worst-case parameter estimation in the presence of bounded uncertainties in a linear regression model. The problem has been formulated and solved in Chandrasekaran et al. (1997). It distinguishes itself from other estimation schemes, such as total-least-squares and H_∞, methods, in that it explicitly incorporates an a-priori bound on the size of the uncertainties. The closed-form solution in the above mentioned articles, however, 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