State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

Abstract

This study presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state‐space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO‐based recursive least squares (BSO‐RLS) algorithm is developed. For comparison with the BSO‐RLS algorithm, by dividing the system into three fictitious subsystems on the basis of the decomposition–coordination principle, a BSO‐based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO‐based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.