Evaluation of Data Association Hypotheses: Non-Poisson I.I.D. Cases

This paper discusses evaluation of data association hypotheses for a general class of multiple target tracking problems. We assume that the number of targets is random and unknown, and given the number of targets, that the joint target state distribution forms a system of independent, identically distributed (i.i.d.) probability distributions. We are particularly interested in the cases in which the probability distribution of the number of targets is not necessarily Poisson. We will show that the Poisson assumption on the number of targets as well as the number of false alarms is not only sufficient but also necessary for the commonly used standard multiplicative hypothesis evaluation formula. Consequently, we claim that the use of the standard multiplicative hypothesis evaluation formula implies, explicitly or implicitly, the Poisson assumption.