Recursive Optimal Smoothing for Finite State Hidden Reciprocal Processes

This technical note addresses modelling and estimation of a class of finite state random processes called hidden reciprocal chains (HRC). A hidden reciprocal chain consists of a finite state reciprocal process, together with an observation process conditioned on the recip- rocal process much as in the case of a hidden Markov model (HMM). The key difference between Markov models and reciprocal models is that reciprocal models are non-causal. The technical note presents a characterization of a HRC by a finite set of hidden Markov bridges, which are HMMs with the final state fixed. The technical note then uses this characterization to derive the optimal fixed interval smoother for a HRC. Performance of linear and optimal smoothers derived for both HMM and HRC are compared (using simulations) for a class of HRC derived