Signal estimation from uncertain observations coming from multiple sensors

In this paper, the least-squares estimation problem of signals from uncertain observations coming from multiple sensors is addressed. Assuming that the probability distribution of the Bernoulli random variables modeling the uncertainty is not necessarily the same for all the sensors, recursive filtering and smoothing (fixed-point and fixed-interval) algorithms are proposed. The derivation of such algorithms does not require the knowledge of the signal state-space model, but only the covariance functions of the processes involved in the observation equations and the uncertainty probabilities. The application of the proposed algorithms is illustrated by a numerical simulation example wherein a signal is estimated from uncertain observations coming from two sensors with different uncertainty characteristics.