Efficiently propagating probability masses

What if there are many targets and events in the system? For a slightly more complicated event observation sequence (Fig. 12), with $5$ targets each in shadow $s_1$ and $s_2$ to start, $135$ joint probability table entries are obtained before the merge step, as shown in Fig. 14. The probability mass entries increase rapidly because of the split events and the FOV events. For a split event, if the originating shadow contains up to $n$ targets, then the number of probability mass entries can multiply by up to a factor of $n + 1$ . For FOV observations, each has certain probability to be enter, exit, and null events, which may cause the number of probability mass entries to triple in the worst case. Therefore, as the number of targets and events increase, the space required to store the probability masses may grow exponentially. Since processing each observation requires going through all the entries, computation time will also explode, which means that the algorithm PROCESS_PROBABILITY_MASS will not work efficiently. On the bright side, as mentioned in subsection VI-D, with many targets in the system, exact algorithm may not be necessary to guarantee accuracy.