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

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.