Design of extended recursive Wiener fixed-point smoother and filter in discrete-time stochastic systems

This paper designs the extended recursive Wiener fixed-point smoother and filter in discrete-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. In the estimators, the system matrix phi for the state vector x(k), the observation vector C for the state vector. the variance K (k, k) = K(O) of the state vector, the nonlinear observation function and the variance of the white observation noise are used. phi, C, and K(O) are usually calculated from the autocovariance data of the signal. It is worthwhile, from a simulation example for the estimation of a speech signal in the phase demodulation problem, that the proposed extended recursive Wiener estimators are superior in estimation accuracy to the extended Kalman estimators based on the state-space model. (c) 2006 Elsevier Inc. All rights reserved.