Multi-target tracking with Poisson processes observations

This paper considers the problem of Bayesian inference in dynamical models with time-varying dimension. These models have been studied in the context of multiple target tracking problems and for estimating the number of components in mixture models. Traditional solutions for the single target tracking problem becomes infeasible when the number of targets grows. Furthermore, when the number of targets is unknown and the number of observations is influenced by misdetections and clutter, then the problem is complex. In this paper, we consider a marked Poisson process for modeling the time-varying dimension problem. Another solution which has been proposed for this problem is the Probability Hypothesis Density (PHD) filter, which uses a random set formalism for representing the time-varying nature of the state and observation vectors. An important feature of the PHD and the proposed method is the ability to perform sensor data fusion by integrating the information from the multiple observations without an explicit data association step. However, the method proposed here differs from the PHD filter in that uses a Poisson point process formalism with discretized spatial intensity. The method can be implemented with techniques similar to the standard particle filter, but without the need for specifying birth and death probabilities for each target in the update and filtering equations. We show an example based on ultrasound acoustics, where the method is able to represent the physical characteristics of the problem domain.