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

Multiple-Object Estimation Techniques for Challenging Scenarios

A series of methods for solving the multi-object estimation problem in the context sequential Bayesian inference is presented. These methods concentrate on dealing with challenging scenarios of multiple target tracking, involving fundamental problems of nonlinearity and non-Gaussianity of processes, high state dimensionality, high number of targets, statistical dependence between target states, and degenerate cases of low signal-to-noise ratio, high uncertainty, lowly observable states or uninformative observations. These difficulties pose obstacles to most practical multi-object inference problems, lying at the heart of the shortcomings reported for state-of-the-art methods, and so elicit novel treatments to enable tackling a broader class of real problems. The novel algorithms offered as solutions in this dissertation address such challenges by acting on the root causes of the associated problems. Often this involves essential dilemmas commonly manifested in Statistics and Decision Theory, such as trading off estimation accuracy with algorithm complexity, soft versus hard decision, generality versus tractability, conciseness versus interpretativeness etc. All proposed algorithms constitute stochastic filters, each of which is formulated to address specific aspects of the challenges at hand while offering tools to achieve judicious compromises in the aforementioned dilemmas. Two of the filters address the weight degeneracy observed in sequential Monte Carlo filters, particularly for nonlinear processes. One of these filters is designed for nonlinear non-Gaussian high-dimensional problems, delivering representativeness of the uncertainty in high-dimensional states while mitigating part of the inaccuracies that arise from the curse of dimensionality. This filter is shown to cope well with scenarios of multimodality, high state uncertainty, uninformative observations and high number of false alarms. A multi-object filter deals with the problem of considering dependencies between target states in a way that is scalable to a large number of targets, by resorting to probabilistic graphical structures. Another multi-object filter treats the problem of reducing the computational complexity of a state-of-the-art cardinalized filter to deal with a large number of targets, without compromising accuracy significantly. Finally, a framework for associating measurements across observation sessions for scenarios of low state observability is proposed, with application to an important Space Surveillance task: cataloging of space debris in the geosynchronous/geostationary belt. The devised methods treat the considered challenges by bringing about rather general questions, and provide not only principled solutions but also analyzes the essence of the investigated problems, extrapolating the implemented techniques to a wider spectrum of similar problems in Signal Processing

Tracking and Fusion Methods for Extended Targets Parameterized by Center, Orientation, and Semi-axes

The improvements in sensor technology, e.g., the development of automotive Radio Detection and Ranging (RADAR) or Light Detection and Ranging (LIDAR), which are able to provide a higher detail of the sensor’s environment, have introduced new opportunities but also new challenges to target tracking. In classic target tracking, targets are assumed as points. However, this assumption is no longer valid if targets occupy more than one sensor resolution cell, creating the need for extended targets, modeling the shape in addition to the kinematic parameters. Different shape models are possible and this thesis focuses on an elliptical shape, parameterized with center, orientation, and semi-axes lengths. This parameterization can be used to model rectangles as well. Furthermore, this thesis is concerned with multi-sensor fusion for extended targets, which can be used to improve the target tracking by providing information gathered from different sensors or perspectives. We also consider estimation of extended targets, i.e., to account for uncertainties, the target is modeled by a probability density, so we need to find a so-called point estimate. Extended target tracking provides a variety of challenges due to the spatial extent, which need to be handled, even for basic shapes like ellipses and rectangles. Among these challenges are the choice of the target model, e.g., how the measurements are distributed across the shape. Additional challenges arise for sensor fusion, as it is unclear how to best consider the geometric properties when combining two extended targets. Finally, the extent needs to be involved in the estimation. Traditional methods often use simple uniform distributions across the shape, which do not properly portray reality, while more complex methods require the use of optimization techniques or large amounts of data. In addition, for traditional estimation, metrics such as the Euclidean distance between state vectors are used. However, they might no longer be valid because they do not consider the geometric properties of the targets’ shapes, e.g., rotating an ellipse by 180 degree results in the same ellipse, but the Euclidean distance between them is not 0. In multi-sensor fusion, the same holds, i.e., simply combining the corresponding elements of the state vectors can lead to counter-intuitive fusion results. In this work, we compare different elliptic trackers and discuss more complex measurement distributions across the shape’s surface or contour. Furthermore, we discuss the problems which can occur when fusing extended target estimates from different sensors and how to handle them by providing a transformation into a special density. We then proceed to discuss how a different metric, namely the Gaussian Wasserstein (GW) distance, can be used to improve target estimation. We define an estimator and propose an approximation based on an extension of the square root distance. It can be applied on the posterior densities of the aforementioned trackers to incorporate the unique properties of ellipses in the estimation process. We also discuss how this can be applied to rectangular targets as well. Finally, we evaluate and discuss our approaches. We show the benefits of more complex target models in simulations and on real data and we demonstrate our estimation and fusion approaches compared to classic methods on simulated data.2022-01-2

Estimation and control of multi-object systems with high-fidenlity sensor models: A labelled random finite set approach

Principled and novel multi-object tracking algorithms are proposed, that have the ability to optimally process realistic sensor data, by accommodating complex observational phenomena such as merged measurements and extended targets. Additionally, a sensor control scheme based on a tractable, information theoretic objective is proposed, the goal of which is to optimise tracking performance in multi-object scenarios. The concept of labelled random finite sets is adopted in the development of these new techniques

Pattern-theoretic foundations of automatic target recognition in clutter

Issued as final reportAir Force Office of Scientific Research (U.S.

Hidden states, hidden structures: Bayesian learning in time series models

This thesis presents methods for the inference of system state and the learning of model structure for a number of hidden-state time series models, within a Bayesian probabilistic framework. Motivating examples are taken from application areas including finance, physical object tracking and audio restoration. The work in this thesis can be broadly divided into three themes: system and parameter estimation in linear jump-diffusion systems, non-parametric model (system) estimation and batch audio restoration. For linear jump-diffusion systems, efficient state estimation methods based on the variable rate particle filter are presented for the general linear case (chapter 3) and a new method of parameter estimation based on Particle MCMC methods is introduced and tested against an alternative method using reversible-jump MCMC (chapter 4). Non-parametric model estimation is examined in two settings: the estimation of non-parametric environment models in a SLAM-style problem, and the estimation of the network structure and forms of linkage between multiple objects. In the former case, a non-parametric Gaussian process prior model is used to learn a potential field model of the environment in which a target moves. Efficient solution methods based on Rao-Blackwellized particle filters are given (chapter 5). In the latter case, a new way of learning non-linear inter-object relationships in multi-object systems is developed, allowing complicated inter-object dynamics to be learnt and causality between objects to be inferred. Again based on Gaussian process prior assumptions, the method allows the identification of a wide range of relationships between objects with minimal assumptions and admits efficient solution, albeit in batch form at present (chapter 6). Finally, the thesis presents some new results in the restoration of audio signals, in particular the removal of impulse noise (pops and clicks) from audio recordings (chapter 7)This work was supported by the Engineering and Physical Sciences Research Council (EPSRC

Efficient, concurrent Bayesian analysis of full waveform LaDAR data

Bayesian analysis of full waveform laser detection and ranging (LaDAR) signals using reversible jump Markov chain Monte Carlo (RJMCMC) algorithms have shown higher estimation accuracy, resolution and sensitivity to detect weak signatures for 3D surface profiling, and construct multiple layer images with varying number of surface returns. However, it is computational expensive. Although parallel computing has the potential to reduce both the processing time and the requirement for persistent memory storage, parallelizing the serial sampling procedure in RJMCMC is a significant challenge in both statistical and computing domains. While several strategies have been developed for Markov chain Monte Carlo (MCMC) parallelization, these are usually restricted to fixed dimensional parameter estimates, and not obviously applicable to RJMCMC for varying dimensional signal analysis. In the statistical domain, we propose an effective, concurrent RJMCMC algorithm, state space decomposition RJMCMC (SSD-RJMCMC), which divides the entire state space into groups and assign to each an independent RJMCMC chain with restricted variation of model dimensions. It intrinsically has a parallel structure, a form of model-level parallelization. Applying the convergence diagnostic, we can adaptively assess the convergence of the Markov chain on-the-fly and so dynamically terminate the chain generation. Evaluations on both synthetic and real data demonstrate that the concurrent chains have shorter convergence length and hence improved sampling efficiency. Parallel exploration of the candidate models, in conjunction with an error detection and correction scheme, improves the reliability of surface detection. By adaptively generating a complimentary MCMC sequence for the determined model, it enhances the accuracy for surface profiling. In the computing domain, we develop a data parallel SSD-RJMCMC (DP SSD-RJMCMCU) to achieve efficient parallel implementation on a distributed computer cluster. Adding data-level parallelization on top of the model-level parallelization, it formalizes a task queue and introduces an automatic scheduler for dynamic task allocation. These two strategies successfully diminish the load imbalance that occurred in SSD-RJMCMC. Thanks to the coarse granularity, the processors communicate at a very low frequency. The MPIbased implementation on a Beowulf cluster demonstrates that compared with RJMCMC, DP SSD-RJMCMCU has further reduced problem size and computation complexity. Therefore, it can achieve a super linear speedup if the number of data segments and processors are chosen wisely

Planning Algorithms for Multi-Robot Active Perception

A fundamental task of robotic systems is to use on-board sensors and perception algorithms to understand high-level semantic properties of an environment. These semantic properties may include a map of the environment, the presence of objects, or the parameters of a dynamic field. Observations are highly viewpoint dependent and, thus, the performance of perception algorithms can be improved by planning the motion of the robots to obtain high-value observations. This motivates the problem of active perception, where the goal is to plan the motion of robots to improve perception performance. This fundamental problem is central to many robotics applications, including environmental monitoring, planetary exploration, and precision agriculture. The core contribution of this thesis is a suite of planning algorithms for multi-robot active perception. These algorithms are designed to improve system-level performance on many fronts: online and anytime planning, addressing uncertainty, optimising over a long time horizon, decentralised coordination, robustness to unreliable communication, predicting plans of other agents, and exploiting characteristics of perception models. We first propose the decentralised Monte Carlo tree search algorithm as a generally-applicable, decentralised algorithm for multi-robot planning. We then present a self-organising map algorithm designed to find paths that maximally observe points of interest. Finally, we consider the problem of mission monitoring, where a team of robots monitor the progress of a robotic mission. A spatiotemporal optimal stopping algorithm is proposed and a generalisation for decentralised monitoring. Experimental results are presented for a range of scenarios, such as marine operations and object recognition. Our analytical and empirical results demonstrate theoretically-interesting and practically-relevant properties that support the use of the approaches in practice