Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced. © 2013 Elsevier Inc. All rights reserved

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 However, this assumption is no longer valid if targets occupy more than one sensor resolution cell, creating the need for extended targets, modeling the shape in addition to the kinematic parameters.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

Contextual information aided target tracking and path planning for autonomous ground vehicles

Recently, autonomous vehicles have received worldwide attentions from academic research, automotive industry and the general public. In order to achieve a higher level of automation, one of the most fundamental requirements of autonomous vehicles is the capability to respond to internal and external changes in a safe, timely and appropriate manner. Situational awareness and decision making are two crucial enabling technologies for safe operation of autonomous vehicles. This thesis presents a solution for improving the automation level of autonomous vehicles in both situational awareness and decision making aspects by utilising additional domain knowledge such as constraints and influence on a moving object caused by environment and interaction between different moving objects. This includes two specific sub-systems, model based target tracking in environmental perception module and motion planning in path planning module. In the first part, a rigorous Bayesian framework is developed for pooling road constraint information and sensor measurement data of a ground vehicle to provide better situational awareness. Consequently, a new multiple targets tracking (MTT) strategy is proposed for solving target tracking problems with nonlinear dynamic systems and additional state constraints. Besides road constraint information, a vehicle movement is generally affected by its surrounding environment known as interaction information. A novel dynamic modelling approach is then proposed by considering the interaction information as virtual force which is constructed by involving the target state, desired dynamics and interaction information. The proposed modelling approach is then accommodated in the proposed MTT strategy for incorporating different types of domain knowledge in a comprehensive manner. In the second part, a new path planning strategy for autonomous vehicles operating in partially known dynamic environment is suggested. The proposed MTT technique is utilized to provide accurate on-board tracking information with associated level of uncertainty. Based on the tracking information, a path planning strategy is developed to generate collision free paths by not only predicting the future states of the moving objects but also taking into account the propagation of the associated estimation uncertainty within a given horizon. To cope with a dynamic and uncertain road environment, the strategy is implemented in a receding horizon fashion

Tracking multiple moving objects in images using Markov Chain Monte Carlo

A new Bayesian state and parameter learning algorithm for multiple target tracking models with image observations are proposed. Specifically, a Markov chain Monte Carlo algorithm is designed to sample from the posterior distribution of the unknown time-varying number of targets, their birth, death times and states as well as the model parameters, which constitutes the complete solution to the specific tracking problem we consider. The conventional approach is to pre-process the images to extract point observations and then perform tracking, i.e. infer the target trajectories. We model the image generation process directly to avoid any potential loss of information when extracting point observations using a pre-processing step that is decoupled from the inference algorithm. Numerical examples show that our algorithm has improved tracking performance over commonly used techniques, for both synthetic examples and real florescent microscopy data, especially in the case of dim targets with overlapping illuminated regions.Engineering and Physical Sciences Research Council

Tracking Extended Objects with Active Models and Negative Measurements

Beim Tracking von ausgedehnten Objekten (auf Englisch ‚extended object tracking‘, kurz EOT) geht es darum, die Form und Lage eines Zielobjekts anhand von verrauschten Punktmessungen zu schätzen. EOT wird traditionell zur Verfolgung von Großobjekten wie Flugzeugen, Schiffen, oder Autos verwendet. Allerdings ermöglichen Technologiefortschritte bei Tiefenkameras wie Microsoft Kinects mittlerweile sogar Laien, Punktwolken aus ihrer Umgebung aufzunehmen. Das stellt eine neue Herausforderung für EOT-Ansätze dar, die in modernen Anwendungen, wie z.B. Objektmanipulation in Augmented Reality oder in der Robotik, Zielobjekte mit vielen möglichen Formen anhand von Messungen unterschiedlicher Qualität verfolgen müssen. In diesem Kontext ist die Auswahl der Formmodelle ausschlaggebend, denn sie bestimmen, wie robust und leistungsfähig der Schätzer sein wird, was wiederum eine sorgfältige Betrachtung der Modalitäten und Qualität der verfügbaren Informationen erfordert. Solch ein Informationsparadigma kann als ein Spektrum visualisiert werden: auf der einen Seite, eine große Anzahl an genauen Messungen, und auf der anderen Seite, nur wenige verrauschte Beobachtungen. Allerdings haben sich die Verfahren in der Literatur traditionell auf einen schmalen Teil dieses Spektrums konzentriert. Einerseits assoziieren ‚gierige‘ Verfahren, die auf der Methode der kleinsten Quadrate basieren, Messungen mit der nächsten Quelle auf der Form. Diese Verfahren sind effizient und liefern sogar für komplizierte Formen akkurate Ergebnisse, allerdings nur solange das Messrauschen niedrig bliebt. Ansonsten kann nicht gewährleistet werden, dass der nächste Punkt immer noch eine passende Approximation der wahren Quelle ist, was zu verzerrten Ergebnissen führt. Andererseits sind probabilistische Modelle wie Raumverteilungen präzise für einfache Formen, sogar bei extrem hohem Messrauschen, allerdings werden sie schon für wenig komplexe Formen unlösbar oder numerisch instabil. Die Schwierigkeit besteht darin, dass in vielen modernen Trackingszenarien die Menge an verfügbarer Information sich drastisch mit der Zeit ändern kann. Das unterstreicht den Bedarf an Ansätzen, die nicht nur die Stärken beider Modelle kombinieren, sondern auch alle Bereiche des Spektrums und nicht nur dessen Grenzfälle abdecken können. Das Ziel dieser Arbeit ist es, diese Lücke zu füllen und somit die oben angesprochenen Herausforderungen zu lösen. Dazu schlagen wir vier Beiträge vor, die den aktuellen Stand der Technik signifikant erweitern. Zuerst schlagen wir Level-set Partial Information Models vor, einen probabilistischen Ansatz zur erwartungstreuen Formschätzung für Szenarien mit Verdeckungen und hohem Messrauschen. Zusätzlich führen wir Level-set Active Random Hypersurface Models ein, die von Konzepten aus EOT und Computervision inspiriert sind, eine flexible Formparametrisierung für konvexe und nicht-konvexe Formen ermöglichen, und die auch mit wenig Information umgehen können. Darüber hinaus machen Negative Information Models sogenannte ‚negative‘ Information nutzbar, indem Messungen verarbeitet werden, die uns sagen, wo das Zielobjekt nicht sein kann. Schließlich zeigen wir eine einfach zu implementierende Erweiterung von diesen Beiträgen, Extrusion Models, um dreidimensionale Objekte mit realen Sensordaten zu verfolgen

Maximum likelihood parameter estimation in time series models using sequential Monte Carlo

Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random variables involved in the definition of the model. When a time series model is to be fitted to some sequentially observed data, it is essential to decide on the value of the parameter that describes the data best, a procedure generally called parameter estimation. This thesis comprises novel contributions to the methodology on parameter estimation in time series models. Our primary interest is online estimation, although batch estimation is also considered. The developed methods are based on batch and online versions of expectation-maximisation (EM) and gradient ascent, two widely popular algorithms for maximum likelihood estimation (MLE). In the last two decades, the range of statistical models where parameter estimation can be performed has been significantly extended with the development of Monte Carlo methods. We provide contribution to the field in a similar manner, namely by combining EM and gradient ascent algorithms with sequential Monte Carlo (SMC) techniques. The time series models we investigate are widely used in statistical and engineering applications. The original work of this thesis is organised in Chapters 4 to 7. Chapter 4 contains an online EM algorithm using SMC for MLE in changepoint models, which are widely used to model heterogeneity in sequential data. In Chapter 5, we present batch and online EM algorithms using SMC for MLE in linear Gaussian multiple target tracking models. Chapter 6 contains a novel methodology for implementing MLE in a hidden Markov model having intractable probability densities for its observations. Finally, in Chapter 7 we formulate the nonnegative matrix factorisation problem as MLE in a specific hidden Markov model and propose online EM algorithms using SMC to perform MLE

Track-before-detect for active sonar.

The detection and tracking of underwater targets with active sonar is a challenging problem because of high acoustic clutter, fluctuating target returns and a relatively low measurement update rate. In this thesis, a Bayesian framework for the detection and tracking of underwater targets using active sonar is formulated. In general, Bayesian tracking algorithms are built on two statistical models: the target dynamics model and the measurement model. The target dynamics model describes the evolution of the target state with time and is almost always assumed to be a Markov process. The typical measurement model approximates the sensor image with a collection of discrete points at each frame and allows point measurement tracking to be performed. This thesis investigates alternative target and measurement models and considers their application to active sonar tracking. The Markov process commonly used for target modelling assumes that the state evolves without knowledge of its future destination. Random realisations of a Markov process can also display a large amount of variability and do not, in general, resemble realistic target trajectories. An alternative is the reciprocal process, which assumes conditioning on a known destination state. The first key contribution is the derivation and implementation of a Maximum Likelihood Sequence Estimator (MLSE) for a Hidden Reciprocal Process (HRP). The performance of the proposed algorithm is demonstrated in simulated scenarios and shown to give improved state estimation performance over Markov processes for scenarios featuring reciprocal targets. In point measurement tracking, reducing the sensor data to point detections results in the loss of valuable information. This method is generally sufficient for tracking high Signal-to-Noise Ratio (SNR) targets but can fail in the case of low SNR targets. The alternative to point measurement tracking is to provide the sensor intensity map, an image, as an input into the tracker. This paradigm is referred to as Track-Before-Detect (TkBD). This thesis will focus on a particular TkBD algorithm based on Expectation-Maximisation (EM) data association called the Histogram-Probabilistic Multi-Hypothesis Tracker (H-PMHT) as it handles multiple targets with low complexity. In the second key contribution, we demonstrate a Viterbi implementation of the H-PMHT algorithm, and show that it outperforms the Kalman Filter in the linear non-Gaussian case. A problem with H-PMHT is that it fails to model fluctuating target amplitude, which can degrade performance in realistic sensing conditions. The third key contribution addresses this by replacing the multinomial measurement model with a Poisson mixture process. The new Poisson mixture is shown to be consistent with the original H-PMHT modelling assumptions but it now allows for a randomly evolving mean target amplitude state with instantaneous fluctuations. This new TkBD algorithm is referred to as the Poisson H-PMHT. The Bayesian prior on the target state is also modified to ensure more robust performance. The fourth contribution is a novel TkBD algorithm based on the application of EM data association to a new measurement model that directly describes continuous valued intensity maps and avoids using an intermediate quantisation stage like the H-PMHT. This model is referred to as the Interpolated Poisson measurement model and is integrated into the Probabilistic Multi-Hypothesis Tracker (PMHT) framework to derive a TkBD algorithm for continuous data called the Interpolated Poisson-PMHT (IP-PMHT). The performance of the Poisson H-PMHT and IP-PMHT algorithms are verified through simulations and are shown to outperform the standard H-PMHT in terms of SNR estimation, particularly for scenarios featuring targets with highly fluctuating amplitude. The final key contribution is the application of several TkBD algorithms based on EM data association to the active sonar problem through a comparative study using trial data from an active towed array sonar. The TkBD algorithms are modified to incorporate changes in target appearance with received array bearing, and are shown to give improved SNR and state estimation performance compared with a conventional point measurement tracking algorithm. The thesis concludes by discussing the limitations of the proposed algorithms and possible avenues for future work.Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 201