Linear and quadratic least-squares estimation using measurements with correlated one-step random delay

This paper considers the linear and quadratic least-squares estimation of a discrete-time signal from observations randomly delayed by one sampling time such that the delay at a given time instant depends on a previous delay. It is assumed that the signal is measured with an additive white noise and that the delay in 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. Linear and quadratic recursive filtering and fixed-point smoothing algorithms for such a class of models are constructed using an innovation approach; they do not require full knowledge of the state-space model for the signal process, but just the moments up to the fourth order of the signal (admitting a separable form) and the observation noise, as well as the probability and correlation of the Bernoulli variables modelling the delay. Recursive expressions for the estimation error covariance matrices are also given, and the performance of the different estimators is illustrated by means of a numerical example. (c) 2007 Elsevier Inc. All rights reserved.