Linear estimation from uncertain observations with white plus coloured noises using covariance information

This paper considers the least mean-squared error linear estimation problems, using covariance information, in linear discrete-time stochastic systems with uncertain observations for the case of white plus coloured observation noises. The different kinds of estimation problems treated include one-stage prediction, filtering, and fixed-point smoothing. The recursive algorithms are derived by employing the Orthogonal Projection Lemma and assuming that both, the signal and the coloured noise autocovariance functions, are given in a semi-degenerate kernel form.  2003 Elsevier Science (USA). All rights reserved.