Estimation from uncertain observations in distributed parameter systems covariance information

This paper studies the least mean-squared error linear estimation problem in distributed parameter systems from uncertain observations when the observation equation, besides the multiplicative noise component, is also affected by white plus coloured additive noises. Using as information the covariances of the involved processes, and assuming that the autocovariance functions of the signal and coloured noise are given in a semidegenerate kernel form, we propose recursive algorithms for the filter and fixed-point smoother.