Distributed fusion estimation in networked systems with uncertain observations and Markovian random delays

This paper addresses the least-squares linear estimation problem in networked systems with uncertain observations and one-step random delays in the measurements. The uncertainties in the observations and the delays are modeled by sequences of Bernoulli random variables with different characteristics for each sensor; the uncertainties are described by independent random variables whereas the delays are modeled by homogeneous Markov chains. The estimators are obtained by a distributed fusion method; specifically, for each sensor, local estimation algorithms are derived by using the information provided by the covariance functions of the processes involved in the observation model, as well as the probability distributions of the variables modeling the uncertainties and delays. The distributed fusion filter and fixed-point smoother are then obtained as the linear combination of the corresponding local linear estimators verifying that the mean squared error is minimum.