Comparison of several filtering methods for linear multi-agent systems with local unknown parametric couplings

In this paper, several filtering methods for a class of discrete-time stochastic linear time-varying multi-agent systems with local coupling uncertainties have been investigated. Every 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 existing in the considered multi-agent system. Because of the 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. Noting of the existence of coupling uncertainties in many practical applications, this paper introduces one general framework of decentralized filtering problem of multi-agent systems. For the considered system, based on the key idea of state augmentation and the certainty-equivalence principle borrowed from principles in adaptive control, we introduce several filtering methods to resolve the fundamental problem considered in this paper. By conducting extensive simulations, the consuming time and estimation errors of every method are compared for one typical example, which suggests which method is more precise and faster.