Labeling Uncertainty in Multitarget Tracking

In multitarget tracking, the problem of track labeling (assigning labels to tracks) is an ongoing research topic. The existing literature, however, lacks an appropriate measure of uncertainty related to the assigned labels that has a sound mathematical basis as well as clear practical meaning to the user. This is especially important in a situation where well separated targets move in close proximity with each other and thereafter separate again; in such a situation, it is well known that there will be confusion on target identities, also known as "mixed labeling." In this paper, we specify comprehensively the necessary assumptions for a Bayesian formulation of the multitarget tracking and labeling (MTTL) problem to be meaningful. We provide a mathematical characterization of the labeling uncertainties with clear physical interpretation. We also propose a novel labeling procedure that can be used in combination with any existing (unlabeled) MTT algorithm to obtain a Bayesian solution to the MTTL problem. One advantage of the resulting solution is that it readily provides the labeling uncertainty measures. Using the mixed labeling phenomenon in the presence of two targets as our test bed, we show with simulation results that an unlabeled multitarget sequential Monte Carlo (M-SMC) algorithm that employs sequential importance resampling (SIR) augmented with our labeling procedure performs much better than its "naive" extension, the labeled SIR M-SMC filter

Characterization of uncertainty in Bayesian estimation using sequential Monte Carlo methods

In estimation problems, accuracy of the estimates of the quantities of interest cannot be taken for granted. This means that estimation errors are expected, and a good estimation algorithm should be able not only to compute estimates that are optimal in some sense, but also provide meaningful measures of uncertainty associated with those estimates. In some situations, we might also be able to reduce estimation uncertainty through the use of feedback on observations, an approach referred to as sensor management. Characterization of estimation uncertainty, as well as sensor management, are certainly difficult tasks for general partially observed processes, which might be non-linear, non-Gaussian, and/or have dependent process and observation noises. Sequential Monte Carlo (SMC) methods, also known as particle filters, are numerical Bayesian estimators which are, in principle, able to handle highly general estimation problems. However, SMC methods are known to suffer from a phenomenon called degeneracy, or self-resolving, which greatly impairs their usefulness against certain classes of problems. One of such classes, that we address in the first part of this thesis, is the joint state and parameter estimation problem, where there are unknown parameters to be estimated together with the timevarying state. Some SMC variants have been proposed to counter the degeneracy phenomenon for this problem, but these state-of-the-art techniques are either non-Bayesian or introduce biases on the system model, which might not be appropriate if proper characterization of estimation uncertainty is required. For this type of scenario, we propose using the Rao-Blackwellized Marginal Particle Filter (RBMPF), a combination of two SMC algorithm variants: the Rao-Blackwellized Particle Filter (RBPF) and the Marginal Particle Filter (MPF). We derive two new versions of the RBMPF: one for models with low dimensional parameter vectors, and another for more general models. We apply the proposed methods to two practical problems: the target tracking problem of turn rate estimation for a constant turn maneuver, and the econometrics problem of stochastic volatility estimation. Our proposed methods are shown to be effective solutions, both in terms of estimation accuracy and statistical consistency, i.e. characterization of estimation uncertainty. Another problem where standard particle filters suffer from degeneracy, addressed in the second part of this thesis, is the joint multi-target tracking and labelling problem. In comparison with the joint state and parameter estimation problem, this problem poses an additional challenge, namely, the fact that it has not been properly mathematically formulated in previous literature. Using Finite Set Statistics (FISST), we provide a sound theoretical formulation for the problem, and in order to actually solve the problem, we propose a novel Bayesian algorithm, the Labelling Uncertainty-Aware Particle Filter (LUA-PF) filter, essentially a combination of the RBMPF and the Multi-target Sequential Monte Carlo (M-SMC) filter techniques. We show that the new algorithm achieves significant improvements on both finding the correct track labelling and providing a meaningful measure of labelling uncertainty. In the last part of this thesis, we address the sensor management problem. Although we apply particle filters to the problem, they are not the main focus of this part of the work. Instead, we concentrate on a more fundamental question, namely, which sensor management criterion should be used in order to obtain the best results in terms of information gain and/or reduction of uncertainty. In order to answer this question, we perform an in-depth theoretical and empirical analysis on two popular sensor management criteria based on information theory – the Kullback-Leibler and R´enyi divergences. On the basis of this analysis, we are able to either confirm or reject some previous arguments used as theoretical justification for these two criteria