Least-squares linear filtering using observations coming from multiple sensors with one- or two-step random delay

Abstract

This paper discusses the least-squares linear filtering problem of discrete-time signals using observations from multiple sensors which can be randomly delayed by one or two sampling times. It is assumed that, at each sensor, the signal is measured in the presence of additive white noise, that the Bernoulli random variables modelling the delays are independent and that the delay probabilities are not necessarily the same for all the sensors. A recursive filtering algorithm is proposed, and derivation of this does not require knowledge of the signal state-space model, but only the covariance functions of the processes involved in the observation equation of each sensor, as well as the delay probabilities. Recursive expressions for the filtering error covariance matrices are also provided, and the performance of the proposed estimator is illustrated by a numerical simulation example in which a scalar signal is estimated from one- or two-step randomly delayed observations from two sensors with different delay characteristics.