Least-squares quadratic estimators from nonindependent uncertain observations with coloured noise

A least-squares quadratic filter and fixed-point smoother from uncertain observations of a signal are derived when the variables describing the uncertainty are nonindependent, and the observations are perturbed by white and coloured noise. The proposed estimators do not require knowledge of the state-space model of the signal; the available information is only the moments, up to the fourth one, of the involved processes, the probability that the signal exists in the observations, and the (2,2)-element of the conditional probability matrix of the sequence describing the uncertainty.