Design of recursive Wiener fixed-point smoothers based on innovations approach in linear discrete-time stochastic systems

This paper designs two kinds of recursive least-squares Wiener fixed-point smoothers based on an innovation approach in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white noise. The proposed fixed-point smoothers require the information of the observation matrix, the system matrix for the state variable, related with the signal, the variance of the state variable, the cross-variance function of the state variable with the observed value and the variance of the white observation noise.