Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> Taxonomy of methods for multiple groups and extended object tracking <s> We develop methods for performing filtering and smoothing in nonlinear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described. <s> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> We address the problem of multitarget tracking (MTT) encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies in the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> In algorithms for tracking and sensor data fusion the targets to be tracked are usually considered as point source objects; i.e., compared to the sensor resolution their extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, this assumption is often not valid: 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). As an extended target also a collectively moving, loosely structured group can be considered. This point of view is all 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 is no longer reasonable. With simulated sensor data produced by a partly resolvable aircraft formation the addressed phenomena are illustrated and a Bayesian solution to the resulting tracking problem is proposed. Ellipsoidal object extensions are modeled by random matrices and treated as additional state variables to be estimated or 'tracked'. We expect that the resulting tracking algorithms are relevant also for tracking large, collectively moving target swarms. <s> BIB005 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB006 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB007 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> We present Monte Carlo methods for multi-target tracking and data association. The methods are applicable to general nonlinear and non-Gaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data association problem that arises due to unlabelled measurements in the presence of clutter, and the curse of dimensionality that arises due to the increased size of the state-space associated with multiple targets. We develop a number of algorithms to achieve this. The first, which we refer to as the Monte Carlo joint probabilistic data association filter (MC-JPDAF), is a generalisation of the strategy proposed by Schulz et al. (2001) and Schulz et al. (2003). As is the case for the JPDAF, the distributions of interest are the marginal filtering distributions for each of the targets, but these are approximated with particles rather than Gaussians. We also develop two extensions to the standard particle filtering methodology for tracking multiple targets. The first, which we refer to as the sequential sampling particle filter (SSPF), samples the individual targets sequentially by utilising a factorisation of the importance weights. The second, which we refer to as the independent partition particle filter (IPPF), assumes the associations to be independent over the individual targets, leading to an efficient component-wise sampling strategy to construct new particles. We evaluate and compare the proposed methods on a challenging synthetic tracking problem. <s> BIB008 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as nonGaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signal-to-noise ratio (SNR). <s> BIB009 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> Random finite sets (RFSs) are natural representations of multitarget states and observations that allow multisensor multitarget filtering to fit in the unifying random set framework for data fusion. Although the foundation has been established in the form of finite set statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multitarget filtering is not yet practical due to the inherent computational hurdle. Even the probability hypothesis density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multitarget posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multitarget filter. In addition, an SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving nonlinear nonGaussian dynamics. Convergence results for these filters are also established. <s> BIB010 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB011 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> This paper deals with target tracking for extended objects in a track before detect context. In the scope of this paper a target is called extended if its physical size is large enough to occupy multiple (radar) resolution cells, e.g. in range and/or azimuth. We show how the existing track before detect approach can be amended in order to deal with extended targets. The algorithm, that we propose, will jointly estimate on-line both the standard kinematic parameters of the target, i.e. position and velocity, as well as the size or extent of the target. The estimation is performed by means of a particle filter. It is shown that the extended target approach is significantly superior in terms of performance to a point target approach in case the target is extended. <s> BIB012 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> In this article we propose a new Rao-Blackwellized particle filtering based algorithm for tracking an unknown number of targets. The algorithm is based on formulating probabilistic stochastic process models for target states, data associations, and birth and death processes. The tracking of these stochastic processes is implemented using sequential Monte Carlo sampling or particle filtering, and the efficiency of the Monte Carlo sampling is improved by using Rao-Blackwellization. <s> BIB013 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB014 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB015 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB016 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB017 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB018 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB019 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB020 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB021 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB022 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB023 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB024 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB025 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <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> BIB026 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> This paper proposes a novel online two-level multitarget tracking and detection (MTTD) algorithm. The algorithm focuses on multitarget detection and tracking for the case of multiple measurements per target and for an unknown and varying number of targets. Information is continuously exchanged in both directions between the two levels. Using the high level target position and shape information, the low level clusters the measurements. Furthermore, the low level features automatic relevance detection (ARD), as it automatically determines the optimal number of clusters from the measurements taking into account the expected target shapes. The high level's data association allows for a varying number of targets. A joint probabilistic data association algorithm looks for associations between clusters of measurements and targets. These associations are used to update the target trackers and the target shapes with the individual measurements. No information is lost in the two-level approach since the measurement information is not summarized into features. The target trackers are based on an underlying motion model, while the high level is supplemented with a filter estimating the number of targets. The algorithm is verified using both simulations and experiments using two sensor modalities, video and laser scanner, for detection and tracking of people and ants. <s> BIB027 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> In this paper we address the problem of tracking multiple targets based on raw measurements by means of Particle filtering. This strategy leads to a high computational complexity as the number of targets increases, so that an efficient implementation of the tracker is necessary. We propose a new multitarget Particle Filter (PF) that solves such challenging problem. We call our filter Interacting Population-based MCMC-PF (IP-MCMC-PF) since our approach is based on parallel usage of multiple population-based Metropolis-Hastings (M-H) samplers. Furthermore, to improve the chains mixing properties, we exploit genetic alike moves performing interaction between the Markov Chain Monte Carlo (MCMC) chains. Simulation analyses verify a dramatic reduction in terms of computational time for a given track accuracy, and an increased robustness w.r.t. conventional MCMC based PF. <s> BIB028 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> This tutorial paper summarizes the motivations, concepts and techniques of finite-set statistics (FISST), a system-level, “top-down,” direct generalization of ordinary single-sensor, single-target engineering statistics to the realm of multisensor, multitarget detection and tracking. Finite-set statistics provides powerful new conceptual and computational methods for dealing with multisensor-multitarget detection and tracking problems. The paper describes how “multitarget integro-differential calculus” is used to extend conventional single-sensor, single-target formal Bayesian motion and measurement modeling to general tracking problems. Given such models, the paper describes the Bayes-optimal approach to multisensor-multitarget detection and tracking: the multisensor-multitarget recursive Bayes filter. Finally, it describes how multitarget calculus is used to derive principled statistical approximations of this optimal filter, such as PHD filters, CPHD filters, and multi-Bernoulli filters. <s> BIB029 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> Bernoulli filters are a class of exact Bayesian filters for non-linear/non-Gaussian recursive estimation of dynamic systems, recently emerged from the random set theoretical framework. The common feature of Bernoulli filters is that they are designed for stochastic dynamic systems which randomly switch on and off. The applications are primarily in target tracking, where the switching process models target appearance or disappearance from the surveillance volume. The concept, however, is applicable to a range of dynamic phenomena, such as epidemics, pollution, social trends, etc. Bernoulli filters in general have no analytic solution and are implemented as particle filters or Gaussian sum filters. This tutorial paper reviews the theory of Bernoulli filters as well as their implementation for different measurement models. The theory is backed up by applications in sensor networks, bearings-only tracking, passive radar/sonar surveillance, visual tracking, monitoring/prediction of an epidemic and tracking using natural language statements. More advanced topics of smoothing, multi-target detection/tracking, parameter estimation and sensor control are briefly reviewed with pointers for further reading. <s> BIB030 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> This chapter presents a novel framework for identifying and tracking dominant agents in groups. The proposed approach relies on a causality detection scheme that is capable of ranking agents with respect to their contribution in recognizing the system’s collective behavior based exclusively on the agents’ observed trajectories. Further, the reasoning paradigm is made robust to multiple emissions and clutter by employing a class of recently introduced Markov chain Monte Carlo-based group tracking methods. Examples are provided that demonstrate the strong potential of the proposed scheme in identifying actual leaders in swarms of interacting agents and moving crowds. <s> BIB031 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Taxonomy of methods for multiple groups and extended object tracking <s> Exploitation of external knowledge through constrained filtering guarantees improved performance. In this paper we show how multiscan processing of such information further enhances the track accuracy. This can be achieved using a Fixed-Lag Smoothing procedure, and a proof of improvement is given in terms of entropy reduction. Such multiscan algorithm, i.e., named KB-Smoother (“Fixed-lag smoothing for Bayes optimal exploitation of external knowledge,” F. Papi , Proc. 15th Int. Conf. Inf. Fusion, 2012) can be implemented by means of a SIR-PF. In practice, the SIR-PF suffers from depletion problems, which are further amplified by the Smoothing technique. Sequential MCMC methods represent an efficient alternative to the standard SIR-PF approach. Furthermore, by borrowing techniques from genetic algorithms, a fully parallelizable multitarget tracker can be defined. Such approach, i.e., named Interacting Population (IP)-MCMC-PF, was first introduced in “Multitarget tracking with interacting population-based MCMC-PF” (M Bocquel , Proc. 15th Int. Conf. Inf. Fusion, 2012). In this paper, we propose and analyze a combination of the KB-Smoother along with the IP-MCMC-PF. As will be shown, the combination of the two methods yields an improved track accuracy while mitigating the loss of particles diversity. Simulation analyses for single and multitarget tracking scenarios confirm the benefits of the proposed approach. <s> BIB032
Over the past decade various methods have been developed for group and extended object tracking. These can be divided into two broad classes depending on the underlying complexities: 1. Methods for a relatively small number of groups, with a small number of group components BIB023 BIB024 BIB005 6 ]. 2. Methods for groups comprised of hundreds or thousands of objects (normally referred to as cluster/extended object/crowd tracking): track before detect methods for extended objects BIB012  , Poisson likelihood approaches BIB006 BIB007 BIB001 BIB019 , groups' extent parameter estimation and random matrix techniques BIB014 BIB021 BIB015 BIB016 BIB025 , parametric level curves BIB017 BIB020 , and random finite sets BIB003 BIB018 BIB022 BIB026  BIB029 , including the Bernouli random finite set filters BIB030  . Figs. 1 and 2 present the taxonomy of methods for tracking small groups and respectively large groups/extended objects. Details are given in the next sections. Results for small groups with a fixed number of targets are presented in BIB004 BIB006 BIB008 BIB002 . These SMC algorithms exploit point process formulations for properly assigning measurements to their originating targets. As part of this, smart procedures are used to eliminate non-probable association hypotheses. Other SMC schemes adopt various approaches for dealing with the high dimensionality problem BIB013 BIB009 . An extension of the SMC technique to a varying number of targets is introduced in BIB010 and BIB011 . In BIB011 BIB024 sequential Markov Chain Monte Carlo (MCMC) techniques are developed for tracking varying numbers of interacting objects. The MCMC approach has advantages over the conventional particle filter (PF) due to its efficient sampling mechanism BIB031 BIB019 BIB024 . Interacting population MCMC algorithms are presented in BIB032  BIB028 . The approach proposed in BIB027 represents an extension of the MCMC method proposed in BIB011 . However, in BIB027 measurement clustering is combined with nonparametric prior information and the variational Bayes approach.