On some Extensions of the Sequential Monte Carlo methods in high-order Hidden Markov Models

We analyze some extensions of the Sequential Monte Carlo (SMC) methods in the context of nonlinear state space models. Namely, we tailor the SMC  methods to handle high-order HMM through the customary recursions of  posterior distributions. It proceeds on mimicking the two-step procedure that is, the prediction step and the update step, in the derivation of the filter  distribution. Once stated, we extend some smoothing recursions as the  Forward-Backward algorithm and the Backward smoother to deal with the actual smoothing distributions in high-order HMM. Finally, we give few examples as an application of these extensions.Key words: Sequential Monte Carlo, high-order HMM, Smoothing, Filtering