Distributed Bayesian Learning of Dynamic States
This work addresses distributed state estimation for networked systems, such as opinion formation in social networks, but it appears incremental as it extends existing Bayesian methods to distributed settings with bounded error guarantees.
The paper tackles the problem of networked agents tracking a dynamic state with partial information by proposing a distributed Bayesian filtering algorithm for finite-state hidden Markov models, showing that disagreement with the optimal centralized solution is asymptotically bounded for geometrically ergodic models.
This work studies networked agents cooperating to track a dynamical state of nature under partial information. The proposed algorithm is a distributed Bayesian filtering algorithm for finite-state hidden Markov models (HMMs). It can be used for sequential state estimation tasks, as well as for modeling opinion formation over social networks under dynamic environments. We show that the disagreement with the optimal centralized solution is asymptotically bounded for the class of geometrically ergodic state transition models, which includes rapidly changing models. We also derive recursions for calculating the probability of error and establish convergence under Gaussian observation models. Simulations are provided to illustrate the theory and to compare against alternative approaches.