Auxiliary-Filter-Free Incompressible Particle Flow Filtering Using Direct Estimation of the Log-Density Gradient with Target Tracking Examples

Abstract

This paper presents an incompressible particle flow filtering method that does not require an auxiliary filter by estimating log-density gradients directly from particles. Particle flow filter (PFF) is likely to avoid particle impoverishment and degeneracy problems that occur in particle filters because particles themselves move toward desired density to perform measurement updates. There are various implementation forms for PFF depending on the assumptions made about the flow. This paper deals with PFF using incompressible flow. Incompressible PFF requires the log-density gradient to calculate the flow. The well-known gradient estimation method for incompressible PFF is a finite difference method collaborating with k nearest neighbors(kNN) method. Since this method requires the prior knowledge about the prior density value in each particle, it is necessary to use an auxiliary filter or a density estimation technique. As a result, the performance of an auxiliary filter or a density estimation technique can directly affect the PFF performance, and the finite difference method is more likely to be inaccurate than directly estimating the log-density gradient. Therefore, this paper presents a PFF structure applying least-squares log-density gradient (LSLDG) method that estimates the log-density gradient directly from particles. In order to verify the performance of the presented structure, this paper performs both single and multiple target tracking simulations. Simulation results demonstrate that the presented structure has a relatively good estimation performance and works more robustly for various situations.