Stationary priors for Bayesian target tracking

A dynamically-based birth/death process is proposed for use in Bayesian single-target tracking. The underlying dynamics are based on an integrated Ornstein-Uhlenbeck process, which is stationary in velocity but not in position. Target birth and death events are defined in terms of a given spatial region of interest. Target death (or, escape) occurs when the dynamics move the target outside this region. Target birth (or, entrance) is specified statistically to achieve a desired stationary probability distribution, which then serves as a Bayesian prior. An implementation of this process for both grid and particle based distribution representations is outlined, and numerical examples are provided to illustrate convergence.