Suboptimal estimation of signals from uncertain observations using approximations of mixtures

In this paper, we propose a suboptimal filtering algorithm for the estimation of a Gaussian signal from uncertain observations, using covariance information. The suboptimal estimators are obtained as the expectation of the signal, given the observations, when a certain approximation is considered for the conditional distribution. The approximation is carried out via successive approximations of mixtures of Gaussian distributions by Gaussian distributions. On the other hand, by assuming that the uncertainty probability is unknown, a recursive estimation algorithm is proposed for that probability. This algorithm is obtained under a Bayesian viewpoint; specifically, by considering a Beta as the a priori distribution for the unknown parameter, the proposed estimators provide approximations for the mean of the a posteriori distributions.