Bayesian Sequential Track Formation

This paper presents a theoretical framework for track building in multiple-target scenarios from the Bayesian point of view. It is assumed that the number of targets is fixed and known. We propose two optimal methods for building tracks sequentially. The first one uses the labelling of the current multitarget state estimate that minimizes the mean-square labeled optimal subpatternassignment error. This method requires knowledge of the posterior density of the vector-valued state. The second assigns the labeling that maximizes the probability that the current multi-targetstate estimate is optimally linked with the available tracks at the previous time step. In this case, we only require knowledge of the random finite-set posterior density without labels

Manouvering target tracking in clutter using particle filters

A particle filter (PF) is a recursive numerical technique which uses random sampling to approximate the optimal solution to target tracking problems involving nonlinearities and/or non-Gaussianity. A set of particle filtering methods for tracking and ma

Explicit filtering equations for labelled random finite sets

We decompose a probability density function (PDF) of a labelled random finite set (RFS) into a probability mass function over a set of labels and a PDF on a vector-valued multitarget state given the labels. Using this decomposition, we write the Bayesian filtering recursion for labelled RFSs in an explicit form. The resulting formulas are of conceptual and practical interest in the RFS approach to multiple target tracking, especially, for track-before-detect particle filter implementations

Target tracking based on estimation of sets of trajectories

In this paper we propose the set of target trajectories as a state variable for target tracking. We argue that target tracking is fundamentally about computing the posterior distribution of the target trajectories, which all existing filtering solutions fail to produce. The new state variable enables us to solve the tracking problem in a principled and straightforward manner, without involving non-physical parameters such as an ordering or labels. We develop all the theoretical tools needed to use the set of trajectories as the state variable in a filtering framework; we adapt standard motion and measurement to random finite sets of trajectories and we also discuss general filtering recursions as well as the involved integrals. Another important component is that we present the exact filtering recursions using a conjugate family of distributions, which ensures that all future predicted and updated filtering distributions belong to the same family of distributions. The paper includes a small numerical example where we illustrate the properties of the proposed approach to trajectory estimation

Target tracking based on estimation of sets of trajectories

In this paper we propose the set of target trajectories as a state variable for target tracking. We argue that target tracking is fundamentally about computing the posterior distribution of the target trajectories, which all existing filtering solutions fail to produce. The new state variable enables us to solve the tracking problem in a principled and straightforward manner, without involving non-physical parameters such as an ordering or labels. We develop all the theoretical tools needed to use the set of trajectories as the state variable in a filtering framework; we adapt standard motion and measurement to random finite sets of trajectories and we also discuss general filtering recursions as well as the involved integrals. Another important component is that we present the exact filtering recursions using a conjugate family of distributions, which ensures that all future predicted and updated filtering distributions belong to the same family of distributions. The paper includes a small numerical example where we illustrate the properties of the proposed approach to trajectory estimation