Random finite sets in multi-target tracking - efficient sequential MCMC implementation

Over the last few decades multi-target tracking (MTT) has proved to be a challenging and attractive research topic. MTT applications span a wide variety of disciplines, including robotics, radar/sonar surveillance, computer vision and biomedical research. The primary focus of this dissertation is to develop an effective and efficient multi-target tracking algorithm dealing with an unknown and time-varying number of targets. The emerging and promising Random Finite Set (RFS) framework provides a rigorous foundation for optimal Bayes multi-target tracking. In contrast to traditional approaches, the collection of individual targets is treated as a set-valued state. The intent of this dissertation is two-fold; first to assert that the RFS framework not only is a natural, elegant and rigorous foundation, but also leads to practical, efficient and reliable algorithms for Bayesian multi-target tracking, and second to provide several novel RFS based tracking algorithms suitable for the specific Track-Before-Detect (TBD) surveillance application. One main contribution of this dissertation is a rigorous derivation and practical implementation of a novel algorithm well suited to deal with multi-target tracking problems for a given cardinality. The proposed Interacting Population-based MCMC-PF algorithm makes use of several Metropolis-Hastings samplers running in parallel, which interact through genetic variation. Another key contribution concerns the design and implementation of two novel algorithms to handle a varying number of targets. The first approach exploits Reversible Jumps. The second approach is built upon the concepts of labeled RFSs and multiple cardinality hypotheses. The performance of the proposed algorithms is also demonstrated in practical scenarios, and shown to significantly outperform conventional multi-target PF in terms of track accuracy and consistency. The final contribution seeks to exploit external information to increase the performance of the surveillance system. In multi-target scenarios, kinematic constraints from the interaction of targets with their environment or other targets can restrict target motion. Such motion constraint information is integrated by using a fixed-lag smoothing procedure, named Knowledge-Based Fixed-Lag Smoother (KB-Smoother). The proposed combination IP-MCMC-PF/KB-Smoother yields enhanced tracking

Probability hypothesis density filter with adaptive parameter estimation for tracking multiple maneuvering targets

AbstractThe probability hypothesis density (PHD) filter has been recognized as a promising technique for tracking an unknown number of targets. The performance of the PHD filter, however, is sensitive to the available knowledge on model parameters such as the measurement noise variance and those associated with the changes in the maneuvering target trajectories. If these parameters are unknown in advance, the tracking performance may degrade greatly. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation (APE) method in the PHD filter so that the model parameters, which may be static and/or time-varying, can be estimated jointly with target states. The resulting APE-PHD algorithm is implemented using the particle filter (PF), which leads to the PF-APE-PHD filter. Simulations show that the newly proposed algorithm can correctly identify the unknown measurement noise variances, and it is capable of tracking multiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches

Simplified multitarget tracking using the PHD filter for microscopic video data

The probability hypothesis density (PHD) filter from the theory of random finite sets is a well-known method for multitarget tracking. We present the Gaussian mixture (GM) and improved sequential Monte Carlo implementations of the PHD filter for visual tracking. These implementations are shown to provide advantages over previous PHD filter implementations on visual data by removing complications such as clustering and data association and also having beneficial computational characteristics. The GM-PHD filter is deployed on microscopic visual data to extract trajectories of free-swimming bacteria in order to analyze their motion. Using this method, a significantly larger number of tracks are obtained than was previously possible. This permits calculation of reliable distributions for parameters of bacterial motion. The PHD filter output was tested by checking agreement with a careful manual analysis. A comparison between the PHD filter and alternative tracking methods was carried out using simulated data, demonstrating superior performance by the PHD filter in a range of realistic scenarios

A Survey of Recent Advances in Particle Filters and Remaining Challenges for Multitarget Tracking

[EN]We review some advances of the particle filtering (PF) algorithm that have been achieved in the last decade in the context of target tracking, with regard to either a single target or multiple targets in the presence of false or missing data. The first part of our review is on remarkable achievements that have been made for the single-target PF from several aspects including importance proposal, computing efficiency, particle degeneracy/impoverishment and constrained/multi-modal systems. The second part of our review is on analyzing the intractable challenges raised within the general multitarget (multi-sensor) tracking due to random target birth and termination, false alarm, misdetection, measurement-to-track (M2T) uncertainty and track uncertainty. The mainstream multitarget PF approaches consist of two main classes, one based on M2T association approaches and the other not such as the finite set statistics-based PF. In either case, significant challenges remain due to unknown tracking scenarios and integrated tracking management

Sequential Monte Carlo Methods for Option Pricing

In the following paper we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used, successfully, for a wide class of applications in engineering, statistics, physics and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.Comment: 37 Pages, 2 Figure

Robust Multi-Object Tracking: A Labeled Random Finite Set Approach

The labeled random finite set based generalized multi-Bernoulli filter is a tractable analytic solution for the multi-object tracking problem. The robustness of this filter is dependent on certain knowledge regarding the multi-object system being available to the filter. This dissertation presents techniques for robust tracking, constructed upon the labeled random finite set framework, where complete information regarding the system is unavailable