An innovation approach to the estimation problem from uncertain observations with correlated signal and noise

This paper presents recursive filtering and fixed-point smoothing algorithms from uncertain observations, when the variables describing the uncertainty are independent, and the signal and observation white noise are correlated. It is assumed that both the autocovariance function of the signal and the crosscovariance function between the signal and the observation noise are expressed in a semi-degenerate kernel form. The estimators are obtained by an innovation approach and do not use the state-space model but only the covariance information of the signal and the observation noise, and the probability that the signal exists in the observed values. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.