Distributed estimation of latent parameters in state space models using separable likelihoods

Motivated by object tracking applications with networked sensors, we consider multi sensor state space models. Estimation of latent parameters in these models requires centralisation because the parameter likelihood depend on the measurement histories of all of the sensors. Consequently, joint processing of multiple histories pose difficulties in scaling with the number of sensors. We propose an approximation with a node-wise separable structure thereby removing the need for centralisation in likelihood computations. When leveraged with Markov random field models and message passing algorithms for inference, these likelihoods facilitate decentralised estimation in tracking networks as well as scalable computation schemes in centralised settings. We establish the connection between the approximation quality of the proposed separable likelihoods and the accuracy of state estimation based on individual sensor histories. We demonstrate this approach in a sensor network self-localisation example.