Distributed estimation for multi‐agent systems with relative measurements and quantized communication: A feedback quadratic framework

Summary In this paper, the feedback quadratic distributed state estimation problem is investigated for a class of linear discrete time‐varying multi‐agent systems subject to non‐Gaussian noises. For the multi‐agent systems, each agent has access to not only the local measurements but the relative states to its adjacent agents as well. Due to the bandwidth constraints of the digital communication networks, the signals are quantized and then exchanged between two adjacent agents, where the probabilistic uniform quantizations are taken into account. The purpose of the addressed problem is to design a novel quadratic distributed estimator for each agent based on the local information and the predictions received from the neighbors. In particular, an output injection term is introduced to handle the unstable systems. By means of the state/measurement augmentation approach, the underlying system is transformed into an augmented one, which aggregates the original vector and its second‐order Kronecker power. Accordingly, a distributed estimator is constructed such that an upper bound is ensured for the estimation error covariance and the suboptimal estimator parameters, which minimize such an upper bound, are subsequently calculated in terms of the solutions to certain matrix difference equations. Finally, an illustrative example is provided to verify the effectiveness and superiority of the proposed quadratic estimation scheme.