Poisson Multi-Bernoulli Mixtures for Multiple Object Tracking

Multi-object tracking (MOT) refers to the process of estimating object trajectories of interest based on sequences of noisy sensor measurements obtained from multiple sources. Nowadays, MOT has found applications in numerous areas, including, e.g., air traffic control, maritime navigation, remote sensing, intelligent video surveillance, and more recently environmental perception, which is a key enabling technology in automated vehicles. This thesis studies Poisson multi-Bernoulli mixture (PMBM) conjugate priors for MOT. Finite Set Statistics provides an elegant Bayesian formulation of MOT based on random finite sets (RFSs), and a significant trend in RFSs-based MOT is the development of conjugate distributions in Bayesian probability theory, such as the PMBM distributions. Multi-object conjugate priors are of great interest as they provide families of distributions that are suitable to work with when seeking accurate approximations to the true posterior distributions. Many RFS-based MOT approaches are only concerned with multi-object filtering without attempting to estimate object trajectories. An appealing approach to building trajectories is by computing the multi-object densities on sets of trajectories. This leads to the development of many multi-object filters based on sets of trajectories, e.g., the trajectory PMBM filters. In this thesis, [Paper A] and [Paper B] consider the problem of point object tracking where an object generates at most one measurement per time scan. In [Paper A], a multi-scan implementation of trajectory PMBM filters via dual decomposition is presented. In [Paper B], a multi-trajectory particle smoother using backward simulation is presented for computing the multi-object posterior for sets of trajectories using a sequence of multi-object filtering densities and a multi-object dynamic model. [Paper C] and [Paper D] consider the problem of extended object tracking where an object may generate multiple measurements per time scan. In [Paper C], an extended object Poisson multi-Bernoulli (PMB) filter is presented, where the PMBM posterior density after the update step is approximated as a PMB. In [Paper D], a trajectory PMB filter for extended object tracking using belief propagation is presented, where the efficient PMB approximation is enabled by leveraging the PMBM conjugacy and the factor graph formulation

Multi-Scan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multitarget distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multitarget tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multiscan trajectory PMBM filter and a multiscan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multiscan trajectory MBM01 filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented N-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multiframe assignment problem. The performance of the presented multitarget trackers, applied with an efficient fixed-lag smoothing method, is evaluated in a simulation study

Spatiotemporal Constraints for Sets of Trajectories with Applications to PMBM Densities

In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal contraints on trajectories can be used to answer a range of important questions, including, e.g., "where did the person that were in area A at time t, go afterwards?". We discuss how multiple constraints can be combined into sets of constraints, and we then apply sets of constraints to set of trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM) densities. For Poisson target birth, the exact posterior density is PMBM for both point targets and extended targets. In the paper we show that if the unconstrained set of trajectories density is PMBM, then the constrained density is also PMBM. Examples of constrained trajectory densities motivate and illustrate the key results

Multi-object filtering with second-order moment statistics

The focus of this work lies on multi-object estimation techniques, in particular the Probability Hypothesis Density (PHD) filter and its variations. The PHD filter is a recursive, closed-form estimation technique which tracks a population of objects as a group, hence avoiding the combinatorics of data association and therefore yielding a powerful alternative to methods like Multi-Hypothesis Tracking (MHT). Its relatively low computational complexity stems from strong modelling assumptions which have been relaxed in the Cardinalized PHD (CPHD) filter to gain more flexibility, but at a much higher computational cost. We are concerned with the development of two suitable alternatives which give a compromise between the simplicity and elegance of the PHD filter and the versatility of the CPHD filter. The first alternative generalises the clutter model of the PHD filter, leading to more accurate estimation results in the presence of highly variable numbers of false alarms; the second alternative provides a closed-form recursion of a second-order PHD filter that propagates variance information along with the target intensity, thus providing more information than the PHD filter while keeping a much lower computational complexity than the CPHD filter. The discussed filters are applied on simulated data, furthermore their practicality is demonstrated on live-cell super-resolution microscopy images to provide powerful techniques for molecule and cell tracking, stage drift estimation and estimation of background noise