Covariance-based least-squares filtering algorithm under Markovian measurement delays

Abstract

This paper addresses the least-squares linear filtering problem of signals from measurements which may be randomly delayed by one or two sampling times. The delays are modelled by a homogeneous discrete-time Markov chain to capture the dependence between them. Assuming that the evolution equation generating the signal is not available and that only the first- and second-order moments of the processes involved in the observation model are known, a recursive filtering algorithm is derived using an innovation approach. Recursive formulas for the filtering error variances are also obtained to measure the precision of the proposed estimators.