Birth and death in multitarget tracking filters

Continuous time birth and death processes are used to model the number of targets in multitarget tracking filters. The general problem is formulated for arbitrary boundary conditions that specify the initial distributions of the numbers of targets and clutter. Three examples are discussed, two of which are new. One uses a pure death process and Poisson numbers of prior and new targetsit gives the PHD intensity filter. The second is a pure death process with a specified number of targets in the prior and a Poisson distributed number of new targets. The third uses the same boundary conditions as the second example but with a combined target birth and death process. The behavior of these filters is compared in the special case when there are no measurements.