V.,Optimal Receding Horizon Filter for Continuous-Time Nonlinear Stochastic Systems

Abstract: A receding horizon filtering problem for nonlinear continuous-time stochastic systems is considered. The paper presents the optimal receding horizon filtering equations. Derivation of the equations is based on the Kushner-Stratonovich and Fokker-Planck-Kolmogorov equations for conditional and unconditional density functions. This result could be a theoretical basis for the optimal control in nonlinear stochastic systems with incomplete information over the most recent time interval. The approximate solutions of the optimal receding horizon filtering equations are discussed. In particular, for linear stochastic systems, the optimal linear receding horizon filter represents the combination of the Kalman and Lyapunov equations. Simulation result is provided. Key-Words: receding horizon filter, Kushner-Stratonovich equation, Kalman filter, conditional densit