Efficient recursive distributed state estimation of hidden Markov models over unreliable networks

We consider a scenario in which a process of interest, evolving within an environment occupied by several agents, is well-described probablistically via a Markov model. The agents each have local views and observe only some limited partial aspects of the world, but their overall task is to fuse their data to construct an integrated, global portrayal. The problem, however, is that their communications are unreliable: network links may fail, packets can be dropped, and generally the network might be partitioned for protracted periods. The fundamental problem then becomes one of consistency as agents in different parts of the network gain new information from their observations but can only share this with those with whom they are able to communicate. As the communication network changes, different views may be at odds; the challenge is to reconcile these differences. The issue is that correlations must be accounted for, lest some sensor data be double counted, inducing overconfidence or bias. As a means to address these problems, a new recursive consensus filter for distributed state estimation on hidden Markov models is presented. It is shown to be well-suited to multi-agent settings and associated applications since the algorithm is scalable, robust to network failure, capable of handling non-Gaussian transition and observation models, and is, therefore, quite general. Crucially, no global knowledge of the communication network is ever assumed. We have dubbed the algorithm a Hybrid method because two existing pieces are used in concert: the first, iterative conservative fusion is used to reach consensus over potentially correlated priors, while consensus over likelihoods, the second, is handled using weights based on a Metropolis Hastings Markov chain. To attain a detailed understanding of the theoretical upper limit for estimator performance modulo imperfect communication, we introduce an idealized distributed estimator. It is shown that under certain general conditions, the proposed Hybrid method converges exponentially to the ideal distributed estimator, despite the latter being purely conceptual and unrealizable in practice. An extensive evaluation of the Hybrid method, through a series of simulated experiments, shows that its performance surpasses competing algorithms.