Robust Bootstrap Method for Joint Estimation of States and Parameters of a Linear System

Abstract

A robust version of the bootstrap method is presented for the joint on-line estimation of states and parameters of linear systems. Two feasible canonical forms for the state-space model are considered and compared. These state-space models are used in conjunction with the innovations model. The robustified estimation part of the bootstrap algorithm successfully handles the occasional large errors in the data, commonly called “outliers.” The convergence, rate of convergence, etc. of the proposed algorithm are theoretically established. To illustrate the potentiality of the suggested scheme, an example is also provided. Since the data available in real life are not devoid of errors, the robust bootstrap method is extremely useful in practical on-line applications.