Joint target-detection and tracking smoothers

A multi-object Bayes filter analogous to the single-object Bayes filter can be derived using Finite Set Statistics for the estimation of an unknown and randomly varying number of target states from random sets of observations. The joint target-detection and tracking (JoTT) filter is a truncated version of the multi-object Bayes filter for the single target detection and tracking problem. Despite the success of Finite-Set Statistics for multi-object Bayesian filtering, the problem of multi-object smoothing with Finite Set Statistics has yet to be addressed. I propose multi-object Bayes versions of the forward-backward and two-filter smoothers and derive optimal nonlinear forward-backward and two-filter smoothers for jointly detecting, estimating and tracking a single target in cluttered environments. I also derive optimal Probability Hypothesis Density (PHD) smoothers, restricted to a maximum of one target and show that these are equivalent to their Bayes filter counterparts. © 2009 SPIE.