Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Table 2 <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> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Table 2 <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> BIB002
Sequential MCMC algorithm. Initialize particle set {X -Compute the MH acceptance probability -Compute the MH acceptance probability } with probability ρ p end end end to give an empirical approximation of the posterior distribution of interest at time k, thus seeding the next filtering step at time As shown in BIB002 and in BIB001 , in high dimensional spaces the combination of Metropolis-Hastings with Gibbs sampling gives efficient results and can overcome possible degeneracy problems of PFs. The derived sequential MCMC algorithm has two steps, for 1. Make a joint draw for the pair {X k , X k−1 } using a Metropolis- Then each sub-block can be updated either via a random scan or a deterministic scan using a series of MH-within-Gibbs steps. The script for the MCMC algorithm is given in Table 2 . Other methods such as the particle MCMC methods proposed in  have potential but still have not been studied in the light of the group and extended object tracking problems mainly because these algorithms are used to solve off-line problems. The next section presents methods for tracking small groups.