Error analysis and application of a nonlinear filter

A nonlinear filtering algorithm with online model error estimation and compensation is proposed for a nonlinear system with uncertain model errors and disturbances. The model error is estimated by minimizing the variance of the predictive output residual based on the nonlinear predictive filter (NPF) principle, and then the system state is estimated by the extended Kalman filter (EKF) principle based on the compensated model. Detailed propagation formula of the state estimation error and its variance matrix are derived. Simulation results show the effectiveness of the proposed algorithm on a satellite attitude determination system with uncertain model errors. The simulation shows the robustness of the proposed algorithm for both the initial state error and uncertain model error, and the increasing filtering period may decrease the estimation accuracy. Compared with EKF and NPF, the proposed nonlinear filtering algorithm has the advantage of both improved estimation accuracy and faster convergence.