Models and Algorithms for Tracking Using Variable Dimension Particle Filters

In this paper we discuss modifications to tracking models, and sequential Monte Carlo algorithms for their estimation from sequential and batch data. New models for tracking are proposed which involve a dynamical model on both the hidden state value and its arrival times. In this way we aim to have a more flexible and parsimonious representation of time-varying state characteristics which is more amenable to estimation using Bayesian filtering. In order to perform inference in this scenario new particle filters and smoothers are proposed for cases where the state process arrives at unknown times that are generally different from the observation arrival times.