Signal estimation based on covariance information from observations featuring correlated uncertainty and coming from multiple sensors

Abstract

The linear least-squares estimation problem of signals from observations coming from multiple sensors is addressed when there is a non-zero probability that each observation does not contain the signal to be estimated ( uncertain observations). At each sensor, this uncertainty in the observations is modeled by a sequence of Bernoulli random variables correlated at consecutive sampling times. To estimate the signal, recursive filtering and (fixed-point and fixed-interval) smoothing algorithms are derived without requiring the knowledge of the signal state-space model but only the means and covariance functions of the processes involved in the observation equations, the uncertainty probabilities and the correlation between the variables modeling the uncertainty. To measure the estimation accuracy, recursive expressions for the estimation error covariance matrices are also proposed. The theoretical results are illustrated by a numerical simulation example where a signal is estimated from observations featuring correlated uncertainty and coming from two sensors with different uncertainty characteristics.