Stochastic Feedback Based Kalman Filter for Nonlinear Continuous-Discrete Systems

For continuous-discrete filtering with unpredictable approximation errors, by proposing the novel stochastic feedback scheme, this note elaborates a closed-loop adaptive Kalman filter for nonlinear continuous-discrete systems. In conventional filters, unknown approximation errors might arise due to the integration/discretization and linearization of continuous model, and ruin the optimality of Kalman theory. As the main contribution of this note, the stochastic feedback based covariance adaption scheme does not require the approximation steps; instead, the posteriori sequence is mined as a feedback to adapt the priori error covariance, so that the unpredictable errors and costly calculations can be reduced or controlled in the novel closed-loop filtering structure. The new approach's advantages in computational cost, adaptability, and accuracy have been demonstrated by the numerical simulations.