Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> Abstract In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, patients and data arrive sequentially, and new patient-specific parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for continuous updating of the evolving posterior distribution, but would need to be restarted from scratch at each expansion stage. Thus MCMC methods are often too slow for real-time inference in dynamic contexts. By combining MCMC with importance resampling, we show how real-time sequential updating of posterior distributions can be effected. The proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded, such as when a patient dies or is discharged. We apply the ... <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> Markov chain Monte Carlo (MCMC) sampling is a numerically intensive simulation technique which has greatly improved the practicality of Bayesian inference and prediction. However, MCMC sampling is too slow to be of practical use in problems involving a large number of posterior (target) distributions, as in dynamic modelling and predictive model selection. Alternative simulation techniques for tracking moving target distributions, known as particle filters, which combine importance sampling, importance resampling and MCMC sampling, tend to suffer from a progressive degeneration as the target sequence evolves. We propose a new technique, based on these same simulation methodologies, which does not suffer from this progressive degeneration. <s> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> This paperback edition is a reprint of the 2001 Springer edition. This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as the textbook for a graduate-level course on Monte Carlo methods. Many problems discussed in the alter chapters can be potential thesis topics for masters or Ph.D. students in statistics or computer science departments. Jun Liu is Professor of Statistics at Harvard University, with a courtesy Professor appointment at Harvard Biostatistics Department. Professor Liu was the recipient of the 2002 COPSS Presidents' Award, the most prestigious one for statisticians and given annually by five leading statistical associations to one individual under age 40. He was selected as a Terman Fellow by Stanford University in 1995, as a Medallion Lecturer by the Institute of Mathematical Statistics (IMS) in 2002, and as a Bernoulli Lecturer by the International Bernoulli Society in 2004. He was elected to the IMS Fellow in 2004 and Fellow of the American Statistical Association in 2005. He and co-workers have published more than 130 research articles and book chapters on Bayesian modeling and computation, bioinformatics, genetics, signal processing, stochastic dynamic systems, Monte Carlo methods, and theoretical statistics. "An excellent survey of current Monte Carlo methods. The applications amply demonstrate the relevance of this approach to modern computing. The book is highly recommended." (Mathematical Reviews) "This book provides comprehensive coverage of Monte Carlo methods, and in the process uncovers and discusses commonalities among seemingly disparate techniques that arose in various areas of application. The book is well organized; the flow of topics follows a logical development. The coverage is up-to-date and comprehensive, and so the book is a good resource for people conducting research on Monte Carlo methods. The book would be an excellent supplementary text for a course in scientific computing ." (SIAM Review) "The strength of this book is in bringing together advanced Monte Carlo (MC) methods developed in many disciplines. Throughout the book are examples of techniques invented, or reinvented, in different fields that may be applied elsewhere. Those interested in using MC to solve difficult problems will find many ideas, collected from a variety of disciplines, and references for further study." (Technometrics) <s> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> We describe a multiple hypothesis particle filter for tracking targets that are influenced by the proximity and/or behavior of other targets. Our contribution is to show how a Markov random field motion prior, built on the fly at each time step, can model these interactions to enable more accurate tracking. We present results for a social insect tracking application, where we model the domain knowledge that two targets cannot occupy the same space, and targets actively avoid collisions. We show that using this model improves track quality and efficiency. Unfortunately, the joint particle tracker we propose suffers from exponential complexity in the number of tracked targets. An approximation to the joint filter, however, consisting of multiple nearly independent particle filters can provide similar track quality at substantially lower computational cost. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> We describe a particle filter that effectively deals with interacting targets, targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, significantly reducing tracker failures. We show that this MRF prior can be easily implemented by including an additional interaction factor in the importance weights of the particle filter. However, the computational requirements of the resulting multitarget filter render it unusable for large numbers of targets. Consequently, we replace the traditional importance sampling step in the particle filter with a novel Markov chain Monte Carlo (MCMC) sampling step to obtain a more efficient MCMC-based multitarget filter. We also show how to extend this MCMC-based filter to address a variable number of interacting targets. Finally, we present both qualitative and quantitative experimental results, demonstrating that the resulting particle filters deal efficiently and effectively with complicated target interactions. <s> BIB005 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> This paper adresses real-time automatic tracking and labeling of a variable number of vehicles, using one or more still cameras. The multi-vehicle configuration is tracked through a Markov Chain Monte-Carlo Particle Filter (MCMC PF) method. We show that integrating a simple vehicle kinematic model within this tracker allows to estimate the trajectories of a set of vehicles, with a moderate number of particles, allowing frame-rate computation. This paper also adresses vehicle tracking involving occlusions, deep scale and appearance changes: we propose a global observation function allowing to fairly track far vehicles as well as close vehicles. Experiment results are shown and discussed on multiple vehicle tracking sequences. Though now only tracking light vehicles, the ultimate goal of this research is to track and classify all classes of road users, also including trucks, cycles and pedestrians, in order to analyze road users interactions. <s> BIB006 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> In this paper, we address the problem of detection and tracking of group and individual targets. In particular, we focus on a group model with a virtual leader which models the bulk or group parameter. To perform the sequential inference, we propose a Markov Chain Monte Carlo (MCMC)-based Particle algorithm with a marginalisation scheme using pairwise Kalman filters. Numerical simulations illustrate the ability of the algorithm to detect and track targets within groups, as well as infer both the correct group structure and the number of targets over time. <s> BIB007 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> We present a novel filtering algorithm for tracking multiple clusters of coordinated objects. Based on a Markov chain Monte Carlo (MCMC) mechanism, the new algorithm propagates a discrete approximation of the underlying filtering density. A dynamic Gaussian mixture model is utilized for representing the time-varying clustering structure. This involves point process formulations of typical behavioral moves such as birth and death of clusters as well as merging and splitting. For handling complex, possibly large scale scenarios, the sampling efficiency of the basic MCMC scheme is enhanced via the use of a Metropolis within Gibbs particle refinement step. As the proposed methodology essentially involves random set representations, a new type of estimator, termed the probability hypothesis density surface (PHDS), is derived for computing point estimates. It is further proved that this estimator is optimal in the sense of the mean relative entropy. Finally, the algorithm's performance is assessed and demonstrated in both synthetic and realistic tracking scenarios. <s> BIB008 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> This paper proposes a technique for motion estimation of groups of targets based on evolving graph networks. The main novelty over alternative group tracking techniques stems from learning the network structure for the groups. Each node of the graph corresponds to a target within the group. The uncertainty of the group structure is estimated jointly with the group target states. New group structure evolving models are proposed for automatic graph structure initialization, incorporation of new nodes, unexisting nodes removal, and the edge update. Both the state and the graph structure are updated based on range and bearing measurements. This evolving graph model is propagated combined with a sequential Monte Carlo framework able to cope with measurement origin uncertainty. The effectiveness of the proposed approach is illustrated over scenarios for group motion estimation in urban environments. Results with challenging scenarios with merging, splitting, and crossing of groups are presented with high estimation accuracy. The performance of the algorithm is also evaluated and shown on real ground moving target indicator (GMTI) radar data and in the presence of data origin uncertainty. <s> BIB009 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Sequential Bayesian inference using Markov Chain Monte Carlo methods <s> In this paper, we describe models and algorithms for detection and tracking of group and individual targets. We develop two novel group dynamical models within a continuous time setting using stochastic differential equations (SDE) that aim to mimic behavioural properties of groups. We also describe a possible way of modeling interactions between closely spaced targets using repulsive forces. These can be combined with a group structure transition model to create realistic evolving group models. We use a Markov chain Monte Carlo (MCMC)-particles algorithm to perform sequential inference. Computer simulations demonstrate the ability of the algorithm to detect and track targets within groups as well as to infer the correct group structure over time. The group tracking model is also applied to two sets of real ground moving target indicator (GMTI) radar data with group targets. The results show significant improvement in tracking accuracy over tracking without group models. <s> BIB010
The Bayesian framework provides efficient ways of computing the desired posterior distribution. Unfortunately, in many applications, this distribution is analytically intractable. SMC methods such as particle filtering can be used to carry out the inference by sequentially approximating this posterior distribution as in BIB009 . MCMC methods are generally more effective than PFs in high-dimensional spaces. Their traditional formulation, however, allows sampling from probability distributions in a non-sequential fashion. Recently, advanced sequential MCMC schemes were proposed in BIB001 BIB005 BIB010 BIB007 . These approaches are distinct from the Resample-Move scheme BIB002 where the MCMC algorithm is used to rejuvenate degenerate samples following importance sampling resampling. These methods BIB010 BIB005 BIB001 use neither resampling nor importance sampling. In attempting to circumvent the degeneracy problems that can possibly arise in PFs in high dimensions (e.g. with more than 20 states), the Markov Chain Monte Carlo (MCMC) framework BIB008 BIB004  BIB006 BIB005 is investigated and is shown to be effective. The MCMC technique arise first in statistical physics BIB003  . The underlying principle consists in constructing a Markov chain whose long-term equilibrium is close to a desired probability distribution. The addition of the MCMC steps affords moving the "cloud of particles" into more likely regions which improves significantly the performance of the obtained sequential filters. The MCMC step also allows simulation of complicated systems that are difficult to deal with directly, including interactions between group components. Another advantage is that the MCMC step leads to flexibility and one can sample only a part of the state conditional upon the rest, thus facilitating efficient samples. There are many different ways to perform the MCMC steps. One of the most common MCMC algorithms is the Metropolis-Hastings (MH) move step, where first a likelihood ratio test is calculated (based on particles from two subsequent iterations) and the particle is selected if the likelihood exceeds a certain threshold. For small groups tracking the MH step was proposed in BIB010 and in BIB009 and shows efficient results. The method from BIB010 aims at sequentially approximating the following joint posterior distribution where the state vector X k 2 comprises the objects' instantaneous position, velocity and extent parameters at time k. Since the closed form expression of the distribution p(X k−1 | Z 0:k−1 ) is generally unknown, the proposed scheme approximates it by using N p unweighted particles where δ(.) is the Dirac delta function and ( j) is the particle index. Then, by applying this particle approximation to (3), an appropriate MCMC scheme can draw samples from the joint posterior pdf p(X k , X k−1 |Z 0:k ). The converged MCMC outputs are then extracted 2 Note that we will denote the state vector in the reminder of the paper with a capital letter to emphasize that it contains both states and extent parameters.