Normalized Optimal Smoothers for a Class of Hidden Generalized Reciprocal Processes

Abstract

This technical note is a sequel to our earlier work in these Transactions concerning Bayesian smoothers developed for the class of hidden reciprocal chains (RC). Within this Bayesian setting, two important issues remained unsolved, and are the subject of this note. The first, and most significant issue concerns the extent to which the models considered in our earlier work are general in terms of the statistical nature of the processes involved. The second issue concerns the practical implementation of smoothers. In this note we offer answers to both these issues. A new class of processes called generalized reciprocal chains (GRC), which include RC as a proper subclass is defined. The note argues that GRC form a more appropriate class of models from an application point of view, in particular, inference problems in target tracking. The note also describes a method for ensuring the numerical stability of the smoother algorithm. Finally, a simple numerical example is presented, which indicates potential benefits for the use of these new models in target tracking problems when compared to Markov chain or RC models.