The PHD/CPHD filter for Multiple Extended Target Tracking with Trajectory Set Theory and Explicit Shape Estimation

In this paper, we propose two methods for tracking multiple extended targets or unresolved group targets with elliptical extent shape. These two methods are deduced from the famous Probability Hypothesis Density (PHD) filter and the Cardinality-PHD (CPHD) filter, respectively. In these two methods, Trajectory Set Theory (TST) is combined to establish the target trajectory estimates. Moreover, by employing a decoupled shape estimation model, the proposed methods can explicitly provide the shape estimation of the target, such as the orientation of the ellipse extension and the length of its two axes. We derived the closed Bayesian recursive of these two methods with stable trajectory generation and accurate extent estimation, resulting in the TPHD-E filter and the TCPHD-E filter. In addition, Gaussian mixture implementations of our methods are provided, which are further referred to as the GM-TPHD-E filter and the GM-TCPHD-E filters. We illustrate the ability of these methods through simulations and experiments with real data. These experiments demonstrate that the two proposed algorithms have advantages over existing algorithms in target shape estimation, as well as in the completeness and accuracy of target trajectory generation.

Variation Bayesian Interference for Multiple Extended Targets or Unresolved Group Targets Tracking

In this work, we propose a tracking method for multiple extended targets or unresolvable group targets based on the Variational Bayesian Inference (VBI). Firstly, based on the most commonly used Random Matrix Model (RMM), the joint states of a single target are modeled as a Gamma Gaussian Inverse Wishart (GGIW) distribution, and the multi-target joint association variables are involved in the estimation together as unknown information with a prior distribution. A shape evolution model and VBI are employed to address the shortcomings of the RMM. Through the VBI, we can derive the approximate variational posterior for the exact multi-target posterior. Furthermore, to demonstrate the applicability of the method in real-world tracking scenarios, we present two potential lightweight schemes. The first is based on clustering, which effectively prunes the joint association events. The second is a simplification of the variational posterior through marginal association probabilities. We demonstrate the effectiveness of the proposed method using simulation experiments, and the proposed method outperforms current state-of-the-art methods in terms of accuracy and adaptability. This manuscript is only a preprint version, a completer and more official version will be uploaded as soon as possible