A Method for Designing a Discrete-Time Smoothing Algorithm

This paper addresses the problem of estimating any discrete-time stochastic process of second-order, on the basis of the observations of a discrete-time stochastic signal corrupted by an additive white noise correlated with the signal. A general recursive algorithm is designed for the computation of all types of smoothing estimates (fixed-point, fixed-interval and fixed-lag smoothers). The proposed methodology is based on principal component analysis of stochastic processes and provides an efficient procedure for a suboptimum estimate which can be applied without imposing structural conditions on the correlation functions involved.