New Normalised Bayesian smoothers for signals modelled by non-causal compositions of reciprocal chains

The present work is a sequel of our paper [1] where a Bayesian unnormalised smoother was proposed for the so-called class of partially observed reciprocal chains (RC). Within this Bayesian setting, an issue remained unsolved concerning practical implementation due to the unnormalised feature of the smoother. Here a normalised Bayesian smoother is developed for a class of signals even more general than RCs, termed Generalised Reciprocal Chains (GRC) which are relevant from an application point of view. A simple numerical example involving target tracking in one dimension is presented which illustrates that a potential benefit of the new models and associated optimal smoothers can be obtained, albeit with increased computational cost. More work is needed to ascertain classes of problems where the new models yield significant benefit.