Distributed input and state estimation for linear discrete-time systems in sensor networks with missing measurements

Abstract

In this paper, the simultaneous unknown input and state estimation problem is investigated for a class of linear discrete time-varying systems in sensor networks with missing measurements. Sensor nodes under consideration are distributed in space according to a fixed network topology, and each sensor receives the information from both the system and its neighbors. The missing measurement phenomenon on each sensor occurs in a random way and is governed by a series of mutually independent random variables obeying a certain Bernoulli distribution. To deal with the sparsity issue of estimator gain matrix, a set of measurement models is established for each sensor to describe all available information from the node itself and its neighbors. Our attention is focused on the design of a recursive estimator for every sensor node to simultaneously estimate unknown input and state in the sense of unbiased minimum-variance. Using direct algebraic operation, we obtain the estimator parameter matrices recursively, and the design algorithm is also provided. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed design scheme.