Bayesian filtering without an observation model

For the past half century and more, Bayesian methods such as the Wiener filter, the Kalman filter, and the particle filter have been successfully employed to incorporate observational information into sequential estimates of a time-varying state. However, there are significant difficulties in the application of these methods to distributed, potentially non-engineered systems. First, the methods generally require knowledge of an `observation model´ which specifies the likelihood of any possible observation given any possible state. Specifying such a model, especially in a distributed system, can be extremely difficult. Second, local information dynamics can lead to differences of opinion among distributed agents, particularly when local observation models are autonomously generated and obscured from the rest of the system. In this paper, we use information geometry to develop a decentralized Bayesian inference mechanism for sequential filtering based not on local probability distributions or known observation models, but on local expert state estimates. We demonstrate the efficacy of the proposed mechanism through simulation.