A Study of Poisson Multi-Bernoulli Mixture Conjugate Prior in Multiple Target Estimation

Multiple target tracking (MTT) denotes the process of estimating the set of target trajectories based on a sequence of noise-corrupted measurements including missed detections and false alarms. Nowadays, MTT has found applications in numerous areas, such as air traffic control, autonomous vehicles and robotics, computer vision and biomedical research. In recent years, a significant research trend in MTT is the development of conjugate distributions in Bayesian probability theory based on random finite set. Two popular frameworks have been studied so far, one is based on labelled multi-Bernoulli conjugate prior, and the other is based on unlabelled multiBernoulli conjugate prior. The first contribution of this thesis is a performance comparison study of filters based on multi-Bernoulli conjugate prior. In this part of work, we focus on point target tracking that each target is assumed to give rise to at most one measurement per time scan. The simulation results show that the Poisson multi-Bernoulli filters arguably provide the best overall performance. Due to the rapid development of high-resolution sensors equipped on autonomous vehicles, e.g., near-field radar and lidar, a target may occupy multiple sensor cells on any given scan, leading to the so-called extended target. Solving the multiple extended target tracking problem is mainly complicated by the unknown correspondence between targets and measurements that a huge number of data association events need to be considered. Methods of how to solve the data association in a single step that maximises the desired likelihood function using sampling methods are presented. The second contribution of this thesis is the performance evaluation of different sampling algorithms, which are integrated into the Poisson multi-Bernoulli mixture (PMBM) filter. As an approximation of the PMBM filter, the Poisson multi-Bernoulli (PMB) filter has shown superior performance in point target tracking, but it is not yet clear how to adapt this algorithm to extended target tracking. The third contribution of this thesis is that we present an extended target PMB filter, along with its gamma Gaussian inverse Wishart implementation. The simulation results show that the PMB filter can retain most of the advantages of the PMBM filter.