Distributed consensus-based Kalman filtering in sensor networks with quantised communications and random sensor failures

This study investigates the signal estimation problem in noisy sensor networks with quantised communications. The sensors are subject to random sensor failures, and synchronously take noisy measurements to produce local estimates by using a Kalman filtering scheme at each sampling instant. A quantiser is considered to be embedded in each sensor, and the probabilistic quantisation strategy is adopted to reduce the energy consumption. In between two sampling instants, each sensor collects quantised local estimates from its neighbours and runs a consensus-based fusion algorithm to generate a fused estimate. The process noises and measurement noises are considered to be spatially uncorrelated, a recursive equation is presented to calculate the estimation error covariance matrix and an upper bound is derived for the estimation performance index. Moreover, a sufficient condition for the convergence of the upper bound of the estimation performance index is also presented. Two types of optimisation problems are constructed for cases of infinite and finite recursions, respectively, where the former one focuses on minimising the derived upper bound of the estimation performance index, and the latter one aims to minimise the energy consumption subject to a constraint on the estimation performance. Illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.