Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <s> It is suggested that the motion of pedestrians can be described as if they would be subject to ``social forces.'' These ``forces'' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can also be applied to the description of other behaviors. In the presented model of pedestrian behavior several force terms are essential: first, a term describing the acceleration towards the desired velocity of motion; second, terms reflecting that a pedestrian keeps a certain distance from other pedestrians and borders; and third, a term modeling attractive effects. The resulting equations of motion of nonlinearly coupled Langevin equations. Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically. <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <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 small groups <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> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <s> Part I Theoretical concepts: introduction suboptimal nonlinear filters a tutorial on particle filters Cramer-Rao bounds for nonlinear filtering. Part II Tracking applications: tracking a ballistic object bearings-only tracking range-only tracking bistatic radar tracking tracking targets through blind Doppler terrain aided tracking detection and tracking of stealthy targets group and extended object tracking. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <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> Methods for small groups <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 small groups <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, that aim to mimic behavioural properties of groups. We also describe two possible ways of modeling interactions between closely spaced targets using Markov Random Field (MRF) and repulsive forces. These can be combined together 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 infer the correct group structure over time. <s> BIB007 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <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> BIB008 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <s> This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from nonlocality and anisotropy of the interactions among individuals. A mathematical technique by time-evolving measures is introduced to deal with both macroscopic and microscopic scales within a unified modeling framework. Then self-organization issues are investigated and numerically reproduced at the proper scale, according to the kind of agents under consideration. <s> BIB009 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <s> This paper addresses the use of social behavior models for the prediction of a pedestrian's future motion. Recently, such models have been shown to outperform simple constant velocity models in cases where data association becomes ambiguous, e.g. in case of occlusion, bad image quality, or low frame rates. However, to account for the multiple alternatives a pedestrian can choose from, one has to go beyond the currently available deterministic models. To this end, we propose a stochastic extension of a recently proposed simulation-based motion model. This new instantiation can cater for the possible behaviors in an entire scene in a multi-hypothesis approach, using a principled modeling of uncertainties. In a set of experiments for prediction and template-based tracking, we compare it to a deterministic instantiation and investigate the general value of using an advanced motion prior in tracking. <s> BIB010 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <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> BIB011 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <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> BIB012 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Methods for small groups <s> In Bayesian multi-target filtering we have to contend with two notable sources of uncertainty, clutter and detection. Knowledge of parameters such as clutter rate and detection profile are of critical importance in multi-target filters such as the probability hypothesis density (PHD) and Cardinalized PHD (CPHD) filters. Naive application of the CPHD (and PHD) filter with mismatches in clutter and detection model parameters results in biased estimates. In this paper we show how to use the CPHD (and PHD) filter in unknown clutter rate and detection profile. <s> BIB013
The methods for tracking small groups can be further divided into: (1) methods that take into account the interactions between group components and (2) methods that ignore such interactions. The latter class of methods are the standard Bayesian techniques that track each object separately (e.g., generic particle filters, Extended Kalman filters, Unscented Kalman Filters, Multiple Hypothesis Tracking (MHT) filters [6] and others). These methods have been extensively studied in the literature BIB004 BIB006 . The former class of methods which consider object' interactions is much more compelling (see e.g. BIB003  BIB008 BIB005 ). Although it has received attention in recent years, there is still a wealth of challenges most of which concern the group structure evolution and transitions BIB006  . The predominant strategy consists in incorporating local interaction rules into the object state dynamics. Normally, individual objects are labeled BIB011 and tracked along with the group structure BIB012 . For a small number of objects, one obtains only a few likely group structures. The object states are updated at every time step using models for appearance (birth) of an object, or disappearance (death) of an object and spawning objects BIB006  BIB007 BIB002 BIB013 . Analogously, the group structure is updated taking into account only a few admissible transitions which are determined from physical constraints such as groups' spatial extent and proximity. Interactions at the group level are subject to transitions in addition to the aforementioned ones. Thus, apart from birth and Fig. 3 . Dynamics of a small group structure over time. Splitting takes place from time t 1 to t 2 , resulting with a new group (white). From time t 2 , the white group splits again and merges with the red and blue groups, giving rise to entirely new (green and grey) configurations. The arrows represent the entities movement direction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) disappearance, two additional moves that are commonly attributed to groups are splitting and merging. Alternatively, group structure dynamics can be modeled by means of graph-theoretic approaches and evolving networks BIB012 . In this approach, group components take the role of vertices in a graph where edges embody interrelations among objects. As the group evolves over time, the graph is adapted to reflect the instantaneous structure. This essentially involves removing or adding nodes and updating edges accordingly. Markov random fields can be used in a similar fashion for modeling group interactions BIB003  BIB008 BIB005 . Other works use the multi-goal social force model  BIB010 for pedestrian tracking which extends the social force model proposed in BIB001 or macroscopic models BIB009 . Fig. 3 illustrates the time evolution of a few groups depicted with distinct colors. The event of one group creating another group is called spawning or splitting. The opposite event when multiple groups are combined into a single group is called merging. At time step t 1 there are two groups: group 1 with three components (the upper group, indicated in red) and group 2, with three components (the lower group, indicated in blue). The empty circles correspond to noisy measurements (e.g. clutter 1 ). Splitting and merging is demonstrated in the 2nd and 3rd time-steps, respectively. For clarity, objects' interrelations are mostly omitted in this depiction. They are, nevertheless, suggested for the last time-step in the right-hand-side ellipses.