Hypothesized Track Sets

Now consider a set of K tracks. Assume tracks can not share detections, and again assume missed detections are possible³. It can be shown that the number of hypothesized track sets is⁴

$$I_n^{'} = \left( \sum_{j=0}^{K} \left( \begin{array}{c} {J_1... ...J_m} \\ j \end{array} \right)}{(K-j)!} \right) \right) \; \; .$$ (4)

Let the i^th hypothesized K-track set be represented as

$$\mbox{\boldmath$\tau$ }_n^i = \{ \mbox{\boldmath$\theta$ }_n^... ..., \cdots, \mbox{\boldmath$\theta$ }_n^{l_K (i)} \} \; \; \; ,$$ (5)

where the superscript l_k (i) denotes the k^th track of the i^thtrack set. ${\cal Z} ( \mbox{\boldmath$\tau$ }_n^i )$ will be used to denote the measurement data associated with the i^th K-track set. Multiple Hypothesis Tracking (MHT) algorithms aim to determine at time nthe best from the I_n^' hypothesized track sets.