State Tracking in the Presence of Heavy-tailed Observations

Abstract

In this paper, we define a state-space model with discrete latent states and a multivariate heavy-tailed observation density for applications in tracking the state of a system with observations including extreme deviations from the median. We use a Gaussian distribution with an unknown variance parameter which has a Gamma distribution prior depending on the state of the system to model the observation density. The key contribution of the paper is the theoretical formulation of such a state-space model which makes use of scale mixtures of Gaussians to yield an exact inference method. We derive the framework for estimation of the states and how to estimate the parameters of the model. We demonstrate the performance of the model on synthetically generated data sets.