Decentralized filtering a multi-agent system with local parametric couplings based on Kalman filter

In this paper, decentralized filtering of multi-agent systems with coupling uncertainties is proposed and investigated. The considered multi-agent system is composed of many agents, each of which evolves with a discrete-time stochastic linear time-varying dynamics, and every agent can be locally influenced by its neighbor agents. Therefore the states evolution of each agent is not only related with its previous states but also related with its neighbors' previous states in the linear dynamic system. Communication limitations existing in the considered multi-agent system restrict that each agent can only observe its own measurements (outputs) and its neighbor agents' outputs while the states are invisible to any agent. Because of communication limitations and information constraints, without knowing the coupling gains of the local interactions, it is not easy for each agent to estimate its states by traditional kalman filter or other state observers, which were extensively discussed in the literature. In this preliminary study, for the considered coupled linear discrete-time multi-agent system with uncertain linear local couplings, based on the key idea of state augmentation and the certainty-equivalence principle borrowed from the area of adaptive control, we propose an efficient decentralized kalman filtering scheme, for each agent, to simultaneously estimate the unknown states and coupling parameters, and extensive simulations are conducted, which have clearly verified the effectiveness of the proposed decentralized filtering scheme.