Modeling temporal dependence of spherically invariant random vectors with triplet markov chains

Abstract

Our paper deals with multivariate hidden Markov chains (MHMC) with a view towards segmentation. We propose a new model in which temporal dependencies are modelled using copulas and sensor dependencies are represented by spherically invariant random vector (SIRV). Copulas are very useful and flexible tools, which have been little applied in signal processing problems until now. In particular, for some desirable marginal distributions it is possible to obtain different kind of dependencies. Using some recent results on triplet Markov chains, the new model extends the case of MHMC when the observations are SIRV and independent conditionally on the states. We propose algorithms for computing efficiently the posterior probabilities of the involved triplet Markov chain, in order to propose rapid segmentation and estimation procedures