Dimensionless score function for multiple hypothesis tracking

This paper discusses several theoretical issues related to the score function for the measurement-to-track association/assignment decision in the track-oriented version of the multiple hypothesis tracker (MHT). This score function is the likelihood ratio: the ratio of the probability density function (pdf) of a measurement having originated from a track, to the pdf of this measurement having a different origin. The likelihood ratio score is derived rigorously starting from the fully Bayesian MHT (hypothesis oriented, based on combinatorial analysis of the general multitarget problem), which is shown to be amenable under some (reasonable) assumptions to the track-oriented MHT (TOMHT). The latter can be implemented efficiently using multidimensional assignment (MDA). The main feature of a likelihood ratio is the fact that it is a (physically) dimensionless quantity and, consequently, can be used for the association of different numbers of measurements and/or measurements of different dimension. The explicit forms of the likelihood ratio are discussed both for the commonly used Kalman tracking filter, as well as for the interacting multiple model (IMM) estimator. The issues of measurements of different dimension and different coordinate systems together with the selection of certain MHT design parameters - the spatial densities of the false measurements and new targets - are also discussed.