Abstract: In order to improve the immunity of multi-agent system against attack,resilient distributed state estimation under measurement attacks is studied.Each agent makes successive local linear measurements of the system state.The local measurement models are heterogeneous across agents and may be locally unobservable for the system state.An adversary compromises some of the measurement streams and changes their values arbitrarily.The agents' goal is to cooperate with their local measurements and estimate the value of the system state correctly.The challenge of this problem is how to design an algorithm to estimate the real system state without distinguishing the real measurements from the measurements of malicious agents.In order to solve this problem,an adaptive distributed maximum a posteriori probability estimation algorithm is designed.As long as the number of compromised measurement streams is lower than a particular bound,all of the agents' local estimates,including malicious agents' local estimates,can converge to the true system state.Firstly,a centralized maximum a posteriori (MAP) estimation method is proposed based on Kalman filter.Combining a centralized MAP estimation with distributed consensus protocol,a distributed MAP estimation method is derived.Then,considering the measurement attack and analyzing the consistency of distributed estimates,a resilient distributed MAP estimation method is designed by exploiting the saturating adaptive gain,which gives a small gain if the deviation from the practical measurement resulting from the attacks is too large.At last,Numerical simulations are provided to evaluate the effectiveness of the proposed algorithm against measurement attacks.

Key words: Consensus filter, Distributed state estimation, Kalman filter, Maximum a posteriori, Multi-agent system, Resilient estimation