Intensity filters on discrete spaces

Multitarget tracking problems on discrete target state and sensor measurement spaces arise when measurements are grouped into histograms to reduce data volume and when target state space is quantized, or gridded. In such problems more than one target can occupy the same discrete target state, and any number of measurements can be observed in the histogram cells. The joint probability generating function (PGF) for the discrete problem is derived. The generating function of the Bayes posterior is derived by differentiating the joint generating function. Two summary statistics of the Bayes posterior process are given: the distribution of the total number of targets and the intensity function, or expected number of targets in each discrete state. Intensity filters are obtained by assuming these summary statistics are sufficient statistics. Several limiting forms are derived for small cell size.