State observers for bilinear state-space systems

This paper studies state estimation algorithms for a bilinear state-space system disturbed by process noise and measurement noise. Because of the special structure of bilinear systems, this paper transforms the considered system into its equivalent linear parameter-varying model and presents the Kalman filter based state estimation algorithm. For the unknown term existing in the linear parameter varying model, we construct an auxiliary model and use its output to take the place of the unknown term, and present the auxiliary model-based state estimation algorithm. Finally, this paper constructs a bilinear state observer and computes the optimal state estimation gain by introducing the delta operator to minimize the covariance matrix of the state estimation error, and derives the delta operator-based state estimation algorithm. The proposed algorithms avoid the poor estimation accuracy caused by the linearization model and improve the state estimation accuracy of bilinear systems. The simulation results show the effectiveness of the proposed algorithms and the state estimation accuracy under different noise conditions. © 2023 Northeast University. All rights reserved.