Track-to-track association metric I.I.D.-non-poisson cases
Shintaro Mori, Chee-Yee Chong · 2003
In this paper, we consider a general twosensor, track-to-track association problem, in which an unknown number of targets is modeled as an independent, identically distributed (i.i.d.) system of random elements in a given target state space, while the a priori probability distribution of the total number of targets is not necessarily Poisson. We will show that, in order to accommodate not-necessarily-Poisson distributions, we need to modify the well-known, commonly-used track-to-track association hypothesis evaluation formula, by adding an extra multiplier that is a function of the hypothesized number of the detected targets. In order for this multiplier to be constant, thereby allowing us to use the commonly used track association metric, the Poisson assumption is not only sufficient but also necessary. A general multiple target tracking problem is a dynamic state estimation (filtering) problem in which the system state is that of a set of an unknown number of objects and the observations are given as a collection of sets of measurements taken by generally multiple sensors at different times [1] – [5]. In such a problem, the origin of each measurement in any given measurement set is unknown, and the set may exclude some targets (misdetections) or include objects of no interest (false alarms). It was shown that, mathematically, such a problem is best described using random finite sets [6]-[8], or finite point processes [9], [10]. In an early development of a general theory of multiple target tracking [11], and its distributed processing counterpart [12], an equivalent formalism, i.e., random finite sequences with permutable probability distributions, was used. In [11] and [12], it was shown that the commonly used multiplicative hypothesis evaluation formulae (including the original multiple hypothesis tracking formula shown in [13]), for both track-to-measurement and track-to-track association, are at least partly a consequence of the Poisson assumptions on the a priori probability distributions for numbers of targets and false alarms.