Robust distributed state estimation for sensor networks with multiple stochastic communication delays

This article is concerned with the robust distributed state estimation problem for a class of uncertain sensor networks with multiple stochastic communication delays. A sequence of mutually independent random variables obeying the Bernoulli distribution is introduced to account for the randomly occurred communication delays. Both the discrete-time target plant and the sensor model are subject to parameter uncertainties as well as stochastic disturbance. The parameter uncertainties are norm-bounded and enter both the system and the measurement matrices. The external stochastic disturbance is given in the form of a scalar Wiener process. Through available output measurements from not only each individual sensor but also its neighbouring sensors, we aim to design distributed state estimators in order to approximate the state of the target plant. By using the Kronecker product, stochastic analysis is carried out to derive a sufficient criterion ensuring the estimation error systems to be convergent in the mean square sense for all randomly occurred delays, admissible stochastic disturbance and parameter uncertainties. Then, an explicit expression of the individual estimator is given in terms of the solution to a convex optimisation problem that can be easily solved by using the semi-definite programme method. A numerical example is given at the end of this article to demonstrate the usefulness of the developed theoretical results.