How to count targets given only the number of measurements

摘要

The Bayes-optimal distribution of the number of targets is derived, given only the numbers of measurements in a sequence of K consecutive sensor scans. Target states and spatial properties of measurements are completely ignored. A backward recursion for the joint probability generating function of the target-measurement count is derived using a branching process model and independent causal influence assumptions. The counting model can be generalized to spatial branching processes.