Fixed-point smoothing with non-independent uncertainty using covariance information

Abstract

Recursive filtering and fixed-point smoothing algorithms, using covariance information, are designed in systems with uncertain observations, when the variables describing the uncertainty are not necessarily independent. It is assumed that the observations are perturbed by white plus coloured noises, and the autocovariance functions of the signal and coloured noise are given in a semidegenerate kernel form. The estimators are obtained by the orthogonal projection technique and using an invariant imbedding method. The algorithms can be applied for estimating stationary and non-stationary signals.