Distributed Parameter Estimation with Adversaries via Multi-Hop Relays

We study resilient distributed parameter estimation in multi-agent systems where some agents may malfunction. The objective is for each nonfaulty agent to locally estimate its parameter while it may interact with adversaries. To this end, we develop an algorithm using multi-hop relaying to achieve the goal in multi-agent networks with directed topologies. With multi-hop relays, agents can access more information of remote agents even though they communicate with only direct neighbors. We characterize a necessary and sufficient graph condition for our algorithm to succeed, which is denoted by the notion of robust following graphs. We prove that our condition with multi-hop relays is more relaxed than the one with one-hop case, and hence, our approach can tolerate more adversaries in the same network when multi-hop relays are applied. Lastly, numerical examples verify the efficacy of our algorithm.