Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

A Gaussian Process Approach for Extended Object Tracking with Random Shapes and for Dealing with Intractable Likelihoods

Tracking of arbitrarily shaped extended objects is a complex task due to the intractable analytical expression of measurement to object associations. The presence of sensor noise and clutter worsens the situation. Although a significant work has been done on the extended object tracking (EOT) problems, most of the developed methods are restricted by assumptions on the shape of the object such as stick, circle, or other axis-symmetric properties etc. This paper proposes a novel Gaussian process approach for tracking an extended object using a convolution particle filter (CPF). The new approach is shown to track irregularly shaped objects efficiently in presence of measurement noise and clutter. The mean recall and precision values for the shape, calculated by the proposed method on simulated data are around 0.9, respectively, by using 1000 particles

Extended Target Tracking and Classification Using Neural Networks

Extended target/object tracking (ETT) problem involves tracking objects which potentially generate multiple measurements at a single sensor scan. State-of-the-art ETT algorithms can efficiently exploit the available information in these measurements such that they can track the dynamic behaviour of objects and learn their shapes simultaneously. Once the shape estimate of an object is formed, it can naturally be utilized by high-level tasks such as classification of the object type. In this work, we propose to use a naively deep neural network, which consists of one input, two hidden and one output layers, to classify dynamic objects regarding their shape estimates. The proposed method shows superior performance in comparison to a Bayesian classifier for simulation experiments

Three-Dimensional Extended Object Tracking and Shape Learning Using Gaussian Processes

In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position, orientation and velocities, together with the shape of the object for online and offline applications. We describe the unknown shape by a radial function in 3D, and induce a correlation structure via a Gaussian process. Furthermore, we propose an efficient algorithm to reduce the computational complexity of working with 3D data. This is accomplished by casting the tracking problem into projection planes which are attached to the object's local frame. The resulting algorithms can process 3D point cloud data and accomplish tracking of a dynamic object. Furthermore, they provide analytical expressions for the representation of the object shape in 3D, together with confidence intervals. The confidence intervals, which quantify the uncertainty in the shape estimate, can later be used for solving the gating and association problems inherent in object tracking. The performance of the methods is demonstrated both on simulated and real data. The results are compared with an existing random matrix model, which is commonly used for extended object tracking in the literature

Channel Prediction and Target Tracking for Multi-Agent Systems

Mobile moving agents as part of a multi-agent system (MAS) utilize the wireless communication channel to disseminate information and to coordinate between each other. This channel is error-prone and the transmission quality depends on the environment as well as on the configuration of the transmitter and the receiver. For resource allocation and task planning of the agents, it is important to have accurate, yet computationally efficient, methods for learning and predicting the wireless channel. Furthermore, agents utilize on-board sensors to determine both their own state and the states of surrounding objects. To track the states over time, the objects’ dynamical models are combined with the sensors’ measurement models using a Bayesian filter. Through fusion of posterior information output by the agents’ filters, the awareness of the agents is increased. This thesis studies the uncertainties involved in the communication and the positioning of MASs and proposes methods to properly handle them.A framework to learn and predict the wireless channel is proposed, based on a Gaussian process model. It incorporates deterministic path loss and stochastic large scale fading, allowing the estimation of model parameters from measurements and an accurate prediction of the channel quality. Furthermore, the proposed framework considers the present location uncertainty of the transmitting and the receiving agent in both the learning and the prediction procedures. Simulations demonstrate the improved channel learning and prediction performance and show that by taking location uncertainty into account a better communication performance is achieved. The agents’ location uncertainties need to be considered when surrounding objects (targets) are estimated in the global frame of reference. Sensor impairments, such as an imperfect detector or unknown target identity, are incorporated in the Bayesian filtering framework. A Bayesian multitarget tracking filter to jointly estimate the agents’ and the targets’ states is proposed. It is a variant of the Poisson multi-Bernoulli filter and its performance is demonstrated in simulations and experiments. Results for MASs show that the agents’ state uncertainties are reduced by joint agent-target state trackingcompared to tracking only the agents’ states, especially with high-resolution sensors. While target tracking allows for a reduction of the agents’ state uncertainties, highresolution sensors require special care due to multiple detections per target. In this case, the tracking filter needs to explicitly model the dimensions of the target, leading to extended target tracking (ETT). An ETT filter is combined with a Gaussian process shape model, which results in accurate target state and shape estimates. Furthermore, a method to fuse posterior information from multiple ETT filters is proposed, by means of minimizing the Kullback-Leibler average. Simulation results show that the adopted ETT filter accurately tracks the targets’ kinematic states and shapes, and posterior fusion provides a holistic view of the targets provided by multiple ETT filters

Decentralized Poisson Multi-Bernoulli Filtering for Vehicle Tracking

A decentralized Poisson multi-Bernoulli filter is proposed to track multiple vehicles using multiple high-resolution sensors. Independent filters estimate the vehicles' presence, state, and shape using a Gaussian process extent model; a decentralized filter is realized through fusion of the filters posterior densities. An efficient implementation is achieved by parametric state representation, utilization of single hypothesis tracks, and fusion of vehicle information based on a fusion mapping. Numerical results demonstrate the performance.Comment: 14 pages, 5 figure

Random Matrix Based Extended Target Tracking with Orientation: A New Model and Inference

In this study, we propose a novel extended target tracking algorithm which is capable of representing the extent of dynamic objects as an ellipsoid with a time-varying orientation angle. A diagonal positive semi-definite matrix is defined to model objects' extent within the random matrix framework where the diagonal elements have inverse-Gamma priors. The resulting measurement equation is non-linear in the state variables, and it is not possible to find a closed-form analytical expression for the true posterior because of the absence of conjugacy. We use the variational Bayes technique to perform approximate inference, where the Kullback-Leibler divergence between the true and the approximate posterior is minimized by performing fixed-point iterations. The update equations are easy to implement, and the algorithm can be used in real-time tracking applications. We illustrate the performance of the method in simulations and experiments with real data. The proposed method outperforms the state-of-the-art methods when compared with respect to accuracy and robustness.Comment: 12 pages, 6 figures, submitted to IEEE TS

Variational Inference and Learning of Piecewise-linear Dynamical Systems

International audienceModeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many real-world processes that cannot be characterized by a single linear behavior. Alternatively, it is possible to consider a piecewise-linear model which, combined with a switching mechanism, is well suited when several modes of behavior are needed. Nevertheless, switching dynamical systems are intractable because their computational complexity increases exponentially with time. In this paper, we propose a variational approximation of piecewise linear dynamical systems. We provide full details of the derivation of two variational expectation-maximization algorithms, a filter and a smoother. We show that the model parameters can be split into two sets, static and dynamic parameters, and that the former parameters can be estimated off-line together with the number of linear modes, or the number of states of the switching variable. We apply the proposed method to a visual tracking problem, namely head-pose tracking, and we thoroughly compare our algorithms with several state of the art trackers

Interactions between gaussian processes and bayesian estimation

L’apprentissage (machine) de modèle et l’estimation d’état sont cruciaux pour interpréter les phénomènes sous-jacents à de nombreuses applications du monde réel. Toutefois, il est souvent difficile d’apprendre le modèle d’un système et de capturer les états latents, efficacement et avec précision, en raison du fait que la connaissance du monde est généralement incertaine. Au cours des dernières années, les approches d’estimation et de modélisation bayésiennes ont été extensivement étudiées afin que l’incertain soit réduit élégamment et de manière flexible. Dans la pratique cependant, différentes limitations au niveau de la modélisation et de l’estimation bayésiennes peuvent détériorer le pouvoir d’interprétation bayésienne. Ainsi, la performance de l’estimation est souvent limitée lorsque le modèle de système manque de souplesse ou/et est partiellement inconnu. De même, la performance de la modélisation est souvent restreinte lorsque l’estimateur Bayésien est inefficace. Inspiré par ces faits, nous proposons d’étudier dans cette thèse, les connections possibles entre modélisation bayésienne (via le processus gaussien) et l’estimation bayésienne (via le filtre de Kalman et les méthodes de Monte Carlo) et comment on pourrait améliorer l’une en utilisant l’autre. À cet effet, nous avons d’abord vu de plus près comment utiliser les processus gaussiens pour l’estimation bayésienne. Dans ce contexte, nous avons utilisé le processus gaussien comme un prior non-paramétrique des modèles et nous avons montré comment cela permettait d’améliorer l’efficacité et la précision de l’estimation bayésienne. Ensuite, nous nous somme intéressé au fait de savoir comment utiliser l’estimation bayésienne pour le processus gaussien. Dans ce cadre, nous avons utilisé différentes estimations bayésiennes comme le filtre de Kalman et les filtres particulaires en vue d’améliorer l’inférence au niveau du processus gaussien. Ceci nous a aussi permis de capturer différentes propriétés au niveau des données d’entrée. Finalement, on s’est intéressé aux interactions dynamiques entre estimation bayésienne et processus gaussien. On s’est en particulier penché sur comment l’estimation bayésienne et le processus gaussien peuvent ”travailler” de manière interactive et complémentaire de façon à améliorer à la fois le modèle et l’estimation. L’efficacité de nos approches, qui contribuent à la fois au processus gaussien et à l’estimation bayésienne, est montrée au travers d’une analyse mathématique rigoureuse et validée au moyen de différentes expérimentations reflétant des applications réelles.Model learning and state estimation are crucial to interpret the underlying phenomena in many real-world applications. However, it is often challenging to learn the system model and capture the latent states accurately and efficiently due to the fact that the knowledge of the world is highly uncertain. During the past years, Bayesian modeling and estimation approaches have been significantly investigated so that the uncertainty can be elegantly reduced in a flexible probabilistic manner. In practice, however, several drawbacks in both Bayesian modeling and estimation approaches deteriorate the power of Bayesian interpretation. On one hand, the estimation performance is often limited when the system model lacks in flexibility and/or is partially unknown. On the other hand, the modeling performance is often restricted when a Bayesian estimator is not efficient and/or accurate. Inspired by these facts, we propose Interactions Between Gaussian Processes and Bayesian Estimation where we investigate the novel connections between Bayesian model (Gaussian processes) and Bayesian estimator (Kalman filter and Monte Carlo methods) in different directions to address a number of potential difficulties in modeling and estimation tasks. Concretely, we first pay our attention to Gaussian Processes for Bayesian Estimation where a Gaussian process (GP) is used as an expressive nonparametric prior for system models to improve the accuracy and efficiency of Bayesian estimation. Then, we work on Bayesian Estimation for Gaussian Processes where a number of Bayesian estimation approaches, especially Kalman filter and particle filters, are used to speed up the inference efficiency of GP and also capture the distinct input-dependent data properties. Finally, we investigate Dynamical Interaction Between Gaussian Processes and Bayesian Estimation where GP modeling and Bayesian estimation work in a dynamically interactive manner so that GP learner and Bayesian estimator are positively complementary to improve the performance of both modeling and estimation. Through a number of mathematical analysis and experimental demonstrations, we show the effectiveness of our approaches which contribute to both GP and Bayesian estimation