On Extended State Based Kalman-Bucy Filter

This paper studies the state estimation problem for a class of continuous-time stochastic systems with unknown nonlinear dynamics and measurement noise. Enlightened by the extended state observer (ESO) in timely estimating both the internal unknown dynamics and the external disturbance of systems, the paper constructs the extended state based KalmanBucy filter (ESKBF) to achieve better filtering performance. It is shown that ESKBF can provide the upper bound of the covariance matrix of estimation error, which is critical in evaluating the filtering precision. Besides, the stability of ESKBF is rigorously proven in the presence of unknown nonlinear dynamics, while the stability of traditional Kalman-Bucy filter is hard to be guaranteed under the same condition. Moreover, the asymptotic optimality of ESKBF for time-invariant system under constant disturbance is given. Finally, numerical simulations show the effectiveness of the method.