Linear least-squares estimation based on covariances from multiple correlated uncertain observations

Abstract

In this paper, the linear least-squares estimation problem of signals from correlated uncertain observations coming from multiple sensors is addressed. It is assumed that, at each sensor, the signal is measured in the presence of additive white noise and that the uncertainty in the observations is characterized by a set of Bernoulli random variables which are only correlated at consecutive time instants. Assuming that the probability and correlation of such variables are not necessarily the same for all the sensors, a recursive filtering and fixed-point smoothing algorithm is proposed. The derivation of such algorithm does not require the 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 probability and correlation of the Bernoulli variables modeling the uncertainty. Recursive expressions for the estimation error covariance matrices are also provided, and the performance of the estimators is illustrated by a numerical simulation example wherein a signal is estimated from correlated uncertain observations coming from two sensors with different uncertainty characteristics.