Sequential monte carlo methods for multi-target filtering with random finite sets

Abstract

Abstract-Random finite sets are natural representations of multi-target states and observations that allow multi-sensor multi-target filtering to fit in the unifying random set framework for Data Fusion. Although the foundation has been established in the form of Finite Set Statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multi-target filtering is not yet practical due to the inherent computational hurdle. Even the Probability Hypothesis Density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multi-target posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multi-target filter. In addition, a SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving non-linear non-Gaussian dynamics. Convergence results for these filters are also established.

A joint data association, registration, and fusion approach for distributed tracking

“…Many algorithms have been developed for data association including the nearest-neighbor (NN) algorithm, the joint probabilistic data association (JPDA) method [3], the multiple hypothesis tracking approach (MHT) [4], and many others for various types of association [2,5,10,12,17,24,[33][34][35] such as measurement to target association, and track to track association. One issue that has drawn attention is that data association and registration are two correlated processes.…”

Promotion of GM-PHD Filtering Approach for Single-Target Tracking in Raw Data of Synthetic Aperture Radar in Spotlight Imaging Mode

“…The Sequential Monte Carlo (SMC) [3], [4] and the Gaussian Mixture (GM) [5] are the two main approaches in implementing the PHD recursion. As a large number of particles is used to approximate the multi-dimensional integrals in the SMC-PHD filter, the main drawback is its high computational burden.…”

“…To deal with nonlinear target dynamics and measurement models, the nonlinear Kalman filter counterparts can be directly employed. The convergence properties of two implementations were analyzed in [4], [6]. As shown in [6], the true PHD filter to any desired degree of accuracy can be approximated by the GM-PHD filter under the linear Gaussian assumption of the dynamic model.…”

Box-Particle Implementation and Comparison of Cardinalized Probability Hypothesis Density Filter

“…Compared with the PHD filter, the CPHD filter relaxes the Poisson assumptions in target and measurement number to achieve better estimation performance. Plenty of works have been done for their implementations [4][5][6][7], such as the Sequential Monte Carlo (SMC) approximation and the Gaussian mixture (GM) approximation. In order to achieve a satisfactory performance a large number of weighted particles are needed to approximate the intensity function in the SMC implementation.…”