Design of a fixed-point smoother based on an innovations theory for white gaussian plus coloured observation noise

The optimal fixed-point smoother is designed based on an innovations theory for the white gaussian plus coloured observation noise in linear continuous systems. The signals to be estimated are non-stationary or stationary stochastic processes. The proposed fixed-point smoothing algorithm calculates estimates sequentially by using the observed value, the autocovariance function of the signal plus the coloured observation noise process and the cross-covariance function of the signal with the observed value.