Recursive fixed-point smoothing algorithm from covariances based on uncertain observations with correlation in the uncertainty

Abstract

This paper considers the least-squares linear estimation problem of a discrete-time signal from noisy observations in which the signal can be randomly missing. The uncertainty about the signal being present or missing at the observations is characterized by a set of Bernoulli variables which are correlated when the difference between times is equal to a certain value m. The marginal distribution of each one of these variables, specified by the probability that the signal exists at each observation, as well as their correlation function, are known. A linear recursive filtering and fixed-point smoothing algorithm is obtained using an innovation approach without requiring the state-space model generating the signal, but just the covariance functions of the processes involved in the observation equation.