Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Comparative study <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> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Comparative study <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> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Comparative study <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> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Comparative study <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> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Comparative study <s> In some applications of multi-target tracking, appearing targets are suitably modeled as spawning from existing targets. However, in the original formulation of the cardinalized probability hypothesis density (CPHD) filter, this type of model is not supported; instead appearing targets are modeled by spontaneous birth only. In this paper we derive the necessary equations for a CPHD filter for the case when the process model also includes target spawning. For this generalized filter, the cardinality prediction formula might become computationally intractable for general spawning models. However, when the cardinality distribution of the spawning targets is either Bernoulli or Poisson, we derive expressions that are practical and computationally efficient. Simulations show that the proposed filter responds faster to a change in target number due to spawned targets than the original CPHD filter. In addition, the performance of the filter, considering the optimal subpattern assignment (OSPA), is improved when having an explicit spawning model. <s> BIB005
We provide a performance comparison of three cluster tracking techniques. These refer to: (a) independent Sampling Importance Resampling (SIR) PFs, (b) an extended object PHD filter BIB003 , and (c) a Gaussian mixture MCMC BIB002 . The first tracking approach is suggested in BIB001 for reducing the complexity associated with the joint filtering pdf of the multi-object state. It essentially involves employing an SIR-PF filtering algorithm individually for each target rather than a single joint tracker. The second tracking method considered here amends the PHD filter for extended objects. In virtue of its semi-analytical form, the extended target PHD filter, and in particular its Gaussian mixture implementation, requires significantly less computational resources than any MCMC-based tracking scheme. We have compared the performance of the above mentioned methods in a heavily cluttered environment similar to that in BIB002 . Their performance is illustrated in a typical run in Fig. 9 . This figure shows the actual (black crosses) and estimated (red squares) cluster mean trajectories for the 3 different tracking methods. The MCMC approach exhibits the best tracking accuracy, essentially yielding the least number of false detections. In order to avoid the sensitivity of the PHD filter to parameters such as probability of detection, survival probabilities and measurement noise parameters, these can be estimated jointly with the object states as it is recently shown in BIB004 . The work BIB004 is an important step in dealing with parameter uncertainties which are commonly subject to tuning in each application. In the original formulation of the CPHD filter appearing objects are modeled by spontaneous birth only. Recently, in BIB005 conditions are derived for the CPHD filter when the process model also includes target spawning. Two types of birth models are considered: Bernoulli and Poisson distributions and it is demonstrated that this filter is computationally efficient. The next section summarizes concisely efficient SMC implementations, making them suitable for high-dimensional problems and real time.