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

In this paper recursive least mean-squared error quadratic filtering and fixed-point smoothing algorithms to estimate signals from uncertain observations are obtained for the case of white plus coloured observation noises. It is assumed that the state-space model of the signal is not known and only the information on the moments, up to the fourth one, of the involved processes and the probability that the signal exists in the observations are available. The estimators require the covariance functions of the signal and coloured noise, as well as the covariance functions of its second-order powers in a semi-degenerate kernel form. (C) 2003 Elsevier Inc. All rights reserved.