State Estimation for Stochastic Non-linear Systems via Backstepping Design

This paper presents a stochastic differential equation based filter design algorithm for system state estimation. Motivated by backstepping procedure and the variance assignment, the non-linear system filtering has been achieved. In particular, the system dynamics have been described by stochastic differential equation which results in the structure of the filter. The estimation error has been stabilised by backstepping design. Then, the non-linear process of the estimation error is converted to Ornstein-Uhlenbeck process using the filter compensative signal. In the ideal case, the estimation error is a Brownian motion, which leads to the variance assignment of Ornstein-Uhlenbeck process, thus the parameter of the proposed filter can be further optimised. The numerical simulation has been given to show the effectiveness of the proposed design algorithm.