Design of Extended Recursive Wiener Fixed-Point Smoother and Filter in Continuous-Time Stochastic Systems pp. 197-224
Authors: (Seiichi Nakamori, Department of Technology, Faculty of Education, Kagoshima University, Kohrimoto, Kagoshima, Japan)
Abstract: This paper, at first, designs the extended recursive Wiener fixed-point smoother and filter in continuous-time wide-sense stationary stochastic systems. It is assumed that the signal is observed with the nonlinear mechanism of the signal and with the additional white observation noise. The estimators use the information of the system matrix F for the state vector x(t) , the observation vector C for the state vector, the variance K(t,t) = K(0) of the state vector, the nonlinear observation function and the variance R of the white observation noise. F , C and K(0) are usually obtained from the autocovariance function of the signal. Secondly, by using the covariance information of the signal and the observation noises, the extended fixed-point smoother and filter for white plus colored observation noise are proposed. Numerical simulation examples are shown to demonstrate the validity of the proposed estimation algorithms.