Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> Much of the literature on target tracking is based on the assumption that the observing sensor produces a single point measurement of the target. In practice, this is often not the case. For example, a high resolution sensor may be able to resolve features on an extended target. An analogous problem is that of tracking a group of point targets moving in formation. In both cases, there is a strong interdependency between the individual sensor measurements. In this paper, we handle both of these cases via the same model of individual motion superposed on a common “bulk” effect. A common approach to tracking groups of (dependent) points is to perform the update operation in two distinct steps. The first stage is to find the “best” match or registration between the set of measurements and the predicted pattern, while the second step is to generate an estimate based on the assumption that the selected association is correct. The complexity of managing multiple hypotheses with strongly interdependent groups is usually avoided. However, particularly in stressing scenarios, where the measurement-object association is highly uncertain, a multiple hypothesis approach should have significant advantages. We present a Bayesian multiple hypothesis solution using the bootstrap or particle filter technique in which the probability distribution of the problem state vector is represented by a set of random samples or “particles”. The great advantage of this approach is that the sample set implicitly includes information on previous hypotheses and so awkward hypothesis management is avoided. Only the feasible association hypotheses for the current update of the filter need to be considered for construction of the measurement likelihood function. (4 pages) <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> In certain applications it is sometimes not necessary to detect and track individual targets with accuracy. Examples include applications with very large track densities, in which the overall distribution of forces is of greater interest than individual targets; or group target processing, in which detection and tracking of force-level objects (brigades, battalions, etc.) is of greater interest than detection and tracking of the individual targets which constitute them. The usual strategy is to attempt to detect and track individual targets first and then deduce group behavior from them. The approach described in this paper employs the opposite philosophy: it detects and tracks target groupings first and sorts out individual targets only as data quantity and quality permits. It is based on a multitarget statistical analog of the simplest approximate single-target filter: the constant-gain Kalman filter. Our approximate multitarget filter propagates a first-order statistical moment of the entire multitarget system. This moment, the probability hypothesis density (PHD), is the density function whose integral in any region of state space is the expected number of targets in the region. We describe the behavior of an implementation of the PHD filter in some simple bulk-tracking scenarios. <s> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> Abstract A truly variance-minimizing filter is introduced and its performance is demonstrated with the Korteweg–DeVries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four-dimensional variational data assimilation (4DVAR)-like methods relying on perfect model dynamics have difficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When observations are available, the so-called importance resampling algorithm is applied. From Bayes's theorem it follows that each ensemble member receives a new weight dependent on its “distance” to the obse... <s> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> It is common practice to represent a target group (or an extended target) as set of point sources and attempt to formulate a tracking filter by constructing possible assignments between measurements and the sources. We suggest an alternative approach that produces a measurement model (likelihood) in terms of the spatial density of measurements over the sensor observation region. In particular, the measurements are modelled as a Poisson process with a spatially dependent rate parameter. This representation allows us to model extended targets as an intensity distribution rather than a set of points and, for a target formation, it gives the option of modelling part of the group as a spatial distribution of target density. Furthermore, as a direct consequence of the Poisson model, the measurement likelihood may be evaluated without constructing explicit association hypotheses. This considerably simplifies the filter and gives a substantial computational saving in a particle filter implementation. The Poisson target-measurement model will be described and its relationship to other filters will be discussed. Illustrative simulation examples will be presented. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> A Bayesian filter has been developed for tracking an extended object in clutter based on two simple axioms: (i) the numbers of received target and clutter measurements in a frame are Poisson distributed (so several measurements may originate from the target) and (ii) target extent is modelled by a spatial probability distribution and each target-related measurement is an independent 'random draw' from this spatial distribution (convolved with a sensor model). Diffuse spatial models of target extent are of particular interest. This model is especially suitable for a particle filter implementation, and examples are presented for a Gaussian mixture model and for a uniform stick target convolved with a Gaussian error. A rather restrictive special case that admits a solution in the form of a multiple hypothesis Kalman filter is also discussed and demonstrated. <s> BIB005 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> This comprehensive resource provides you with an in-depth understanding of finite-set statistics (FISST) - a recently developed method which unifies much of information fusion under a single probabilistic, in fact Bayesian, paradigm. The book helps you master FISST concepts, techniques, and algorithms, so you can use FISST to address real-world challenges in the field. You learn how to model, fuse, and process highly disparate information sources, and detect and track non-cooperative individual/platform groups and conventional non-cooperative targets. You find a rigorous Bayesian unification for many aspects of expert systems theory. Moreover, the book presents systematic integral and differential calculus for multisource-multitarget problems, providing a methodology for devising rigorous new techniques. This accessible and detailed book is supported with over 3,000 equations, 90 clear examples, 70 explanatory figures, and 60 exercises with solutions. <s> BIB006 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> We present an example-based crowd simulation technique. Most crowd simulation techniques assume that the behavior exhibited by each person in the crowd can be defined by a restricted set of rules. This assumption limits the behavioral complexity of the simulated agents. By learning from real-world examples, our autonomous agents display complex natural behaviors that are often missing in crowd simulations. Examples are created from tracked video segments of real pedestrian crowds. During a simulation, autonomous agents search for examples that closely match the situation that they are facing. Trajectories taken by real people in similar situations, are copied to the simulated agents, resulting in seemingly natural behaviors. <s> BIB007 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> Contour tracking for a single source emission is addressed in this paper. This problem is solved by estimating the contour boundary positions using a set of particle filters. The use of Sequential Monte Carlo techniques enables the tracking to performed when the measurements are noisy and the tracking results also includes the estimation uncertainly. The proposed technique is illustrated for a SCIPUFF generated single emission scenario and simulation experiments showed the successful tracking throughout the tracking period. <s> BIB008 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> This correspondence addresses the problem of tracking extended objects, such as ships or a convoy of vehicles moving in urban environment. Two Monte Carlo techniques for extended object tracking are proposed: an interacting multiple model data augmentation (IMM-DA) algorithm and a modified version of the mixture Kalman filter (MKF) of Chen and Liu , called the mixture Kalman filter modified (MKFm). The data augmentation (DA) technique with finite mixtures estimates the object extent parameters, whereas an interacting multiple model (IMM) filter estimates the kinematic states (position and speed) of the manoeuvring object. Next, the system model is formulated in a partially conditional dynamic linear (PCDL) form. This affords us to propose two latent indicator variables characterizing, respectively, the motion mode and object size. Then, an MKFm is developed with the PCDL model. The IMM-DA and the MKFm performance is compared with a combined IMM-particle filter (IMM-PF) algorithm with respect to accuracy and computational complexity. The most accurate parameter estimates are obtained by the DA algorithm, followed by the MKFm and PF. <s> BIB009 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> Collectively moving object clusters are of particular interest in certain applications and have to be tracked as separate aggregated entities consisting of an unknown number of individuals. Tracking of convoys or large vehicles in wide area ground surveillance are practically important examples (GMTI: Ground Moving Target Indicator). In standard tracking algorithms, the objects of interest are usually considered as point source objects; i. e. compared to the sensor resolution their spatial extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, different scattering centers of an extended object cam cause distinct detections. In this sense also collectively moving object groups can be considered as extended objects. Due to the resulting data association and resolution conflicts. any attempt of tracking individual objects within the group is no longer reasonable. In this paper ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated. An important aspect is the incorporation of context information into the Bayesian data processing formalism. We here consider kinematical constraints such as road maps and sensor specific characteristics such as Doppler-blindness. <s> BIB010 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> In algorithms for tracking and sensor data fusion the targets to be observed are usually considered as point source objects; i.e., compared with the sensor resolution their extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, this assumption is often no longer valid as different scattering centers of an object can cause distinct detections when passing the signal processing chain. Examples of extended targets are found in short-range applications (littoral surveillance, autonomous weapons, or robotics). A collectively moving target group can also be considered as an extended target. This point of view is the more appropriate, the smaller the mutual distances between the individual targets are. Due to the resulting data association and resolution conflicts any attempt of tracking the individual objects within the group seems to be no longer reasonable. With simulated sensor data produced by a partly unresolvable aircraft formation the addressed phenomena are illustrated and an approximate Bayesian solution to the resulting tracking problem is proposed. Ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated or tracked. We expect that the resulting tracking algorithms are also relevant for tracking large, collectively moving target swarms. <s> BIB011 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> This paper presents a novel and mathematically rigorous Bayes' recursion for tracking a target that generates multiple measurements with state dependent sensor field of view and clutter. Our Bayesian formulation is mathematically well-founded due to our use of a consistent likelihood function derived from random finite set theory. It is established that under certain assumptions, the proposed Bayes' recursion reduces to the cardinalized probability hypothesis density (CPHD) recursion for a single target. A particle implementation of the proposed recursion is given. Under linear Gaussian and constant sensor field of view assumptions, an exact closed-form solution to the proposed recursion is derived, and efficient implementations are given. Extensions of the closed-form recursion to accommodate mild nonlinearities are also given using linearization and unscented transforms. <s> BIB012 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> In the year 1999 the world population reached 6 billion, doubling the previous census estimate of 1960. Recently, the United States Census Bureau issued a revised forecast for world population showing a projected growth to 9.4 billion by 2050 (US Census Bureau, http://www.census.gov/ipc/www/worldpop.html). Different research disci- plines have studied the crowd phenomenon and its dynamics from a social, psychological and computational standpoint respectively. This paper presents a survey on crowd analysis methods employed in computer vision research and discusses perspectives from other research disciplines and how they can contribute to the computer vision approach. <s> BIB013 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> In this paper we introduce a novel method to detect and localize abnormal behaviors in crowd videos using Social Force model. For this purpose, a grid of particles is placed over the image and it is advected with the space-time average of optical flow. By treating the moving particles as individuals, their interaction forces are estimated using social force model. The interaction force is then mapped into the image plane to obtain Force Flow for every pixel in every frame. Randomly selected spatio-temporal volumes of Force Flow are used to model the normal behavior of the crowd. We classify frames as normal and abnormal by using a bag of words approach. The regions of anomalies in the abnormal frames are localized using interaction forces. The experiments are conducted on a publicly available dataset from University of Minnesota for escape panic scenarios and a challenging dataset of crowd videos taken from the web. The experiments show that the proposed method captures the dynamics of the crowd behavior successfully. In addition, we have shown that the social force approach outperforms similar approaches based on pure optical flow. <s> BIB014 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <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> BIB015 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> In this paper, we address the problem of detection and tracking of multiple contaminant clouds. We develop a stochastic extension of the Gaussian puff model to characterize evolution of the average atmospheric pollutant concentration. To perform the sequential inference on this difficult problem, we propose a Markov Chain Monte Carlo (MCMC)-based Particle algorithm. Numerical simulations illustrate the ability of the algorithm to detect and track multiple contaminant clouds. <s> BIB016 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany †Dept. Sensor Data and Information Fusion, Fraunhofer FKIE, Wachtberg, Germany ‡Data Fusion Algorithms & Software, EADS Deutschland GmbH, Ulm, Germany marcus.baum@kit.edu, {michael.feldmann |wolfgang.koch}@fkie.fraunhofer.de dietrich.fraenken@eads.com, uwe.hanebeck@ieee.org <s> BIB017 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> Recent research into multi-object filtering for non-standard targets introduced alternative approaches for target group representation. In these approaches a measurement model (likelihood) was suggested that led to a representation of the measurements as a spatial point process, namely a Poisson point process. In this paper we take a more traditional approach to extended target tracking. We assume a 'standard' measurement model (at most one measurement generated from a target point), but represent the target group (extended targets) as a spatial cluster process, in particular an independent cluster process with a fixed distribution on the component (daughter) process. With this assumption we are able to derive approximate measurement-update equations for the first order moment density of the extended object Bayes filter in a number of scenarios. Such approximations are Bayes optimal and provide estimates for the number of clusters (extended targets) and their locations. <s> BIB018 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> This paper is about tracking an extended object or a group target, which gives rise to a varying number of measurements from different measurement sources. For this purpose, the shape of the target is tracked in addition to its kinematics. The target extent is modeled with a new approach called Random Hypersurface Model (RHM) that assumes varying measurement sources to lie on scaled versions of the shape boundaries. In this paper, a star-convex RHM is introduced for tracking star-convex shape approximations of targets. Bayesian inference for star-convex RHMs is performed by means of a Gaussian-assumed state estimator allowing for an efficient recursive closed-form measurement update. Simulations demonstrate the performance of this approach for typical extended object and group tracking scenarios. <s> BIB019 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Extended objects may give rise to more than one detection per opportunity where the scattering centers may vary from scan to scan. On the other end, group targets (i. e., a number of closely spaced targets moving in a coordinated fashion) often will not cause as many detections as there are individual targets in the group due to limited sensor resolution capabilities. In both cases, tracking and data association under the one target-one detection assumption are no longer applicable. This paper deals with the problem of maintaining a track for an extended object or group target with varying number of detections. Herein, object extension is represented by a random symmetric positive definite matrix. A recently published Bayesian approach to tackling this problem is analyzed and discussed. From there, a new approach is derived that is expected to overcome some of the weaknesses the Bayesian approach suffers from in certain applications. <s> BIB020 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for large groups and extended objects <s> In many group target tracking scenarios, a collection of targets move in a correlated manner as part of a formation, such as a convoy of vehicles. The focus of this paper is in the estimation of the evolution over time of a single-group of targets, referred to as a single-cluster, based on a sequence of partial observation sets. Based on Finite Set Statistics, the paper presents a first-moment recursion for a single-group filter and an analytic solution under linear-Gaussian assumptions. The method is demonstrated on simulated data in a cluttered environment. <s> BIB021
When the number of entities becomes excessively large it is impractical to track them all individually. Thus, instead of tracking separate components, large group techniques identify and track concentrations, e.g. the center of the group and its extent parameter. In this respect groups and extended object tracking are similar problems. The entities forming the concentrations may be objects, measurements or features. This strategy is applied in practice by utilizing extent variables which represent the spatial shape and dynamics of a group. In typical scenarios, groups are characterized by the location and velocity of the group center, their shape and shape deformation BIB019 . Another promising approach for modeling large groups is based on the social force model BIB014  . For large groups (and extended objects), the group density and shape are closely related. The posterior pdf of the joint state and extent parameter vector can, for example, be considered as a mixture of Gaussians BIB015 . This is primarily due to the convenient parametric representation which involves the first two statistical moments of the Gaussians, but other representations are possible. Here, the mean and covariance of the Gaussian mixture are, respectively, the center and shape of the group or extended object. Normally, the extent parameters are considered as both random and dynamic, and as such are governed by appropriate transition kernels. These approaches are capable of simulating complex dynamically evolving shape boundaries, and even compete with sophisticated contour tracking methodologies (see for example BIB008 BIB016 ). The measurement origin uncertainty in group and extended objects can be dealt with in an efficient way BIB004 BIB005 BIB001 BIB015 if the numbers of received target and clutter measurements are considered Poisson distributed (implying that several measurements may originate from each target). A different, albeit related, modeling approach is considered in BIB009 BIB017 BIB010 BIB011 BIB020 where the group extent represents a parameter, estimated as part of an augmented state vector, jointly with the position coordinates of the group center. Except for BIB009 , all other works in this group employ either Kalman filtering techniques [6] or random finite set approaches BIB006 . In general, the extent is considered as a random process and hence is normally assigned a respective prior (e.g., Wishart distribution BIB010 BIB011 BIB020 ) and a transition kernel. The random finite set approach is a powerful tool that has been widely used in recent years BIB006 . Random finite sets are mathematical objects that can elegantly capture the subtleties involved in multiple object tracking and data fusion. It was not until recently that these methods have been employed for group and extended object tracking. The works BIB002 BIB012 BIB018 BIB021 demonstrate the viability of the well-known Probability Hypothesis Density (PHD) filter in solving group tracking problems. These approaches are discussed extensively in the methodological part of this paper. Fluid dynamic models have also been shown to capture well aggregated vehicular traffic phenomena, in combination with SMC 1 In radar applications clutter signifies signal reflected from the environment, instead of from the objects of interest. methods  , for the purposes of freeway traffic tracking. A large body of work is devoted for modeling pedestrians flows in open and enclosed regions, e.g.  BIB007 BIB013 and weather forecasts BIB003 . In what follows, we present the generic SMC framework followed by more sophisticated approaches.