Enhancing Particle Filtering using Gaussian Processes

This contribution presents a novel resampling scheme that leverages Gaussian Processes (GPs) to more accurately approximate the posterior distribution from a set of random measures and, ultimately, enhance resampling by sampling from such approximation. Resampling is a critical step in particle filtering, impacting its estimation performance and parallelization capabilities. The approach can be seen as a kernel-based density approximation. As a byproduct, we are able to i) derive an explicit formula for minimum mean squared error (MMSE) state estimation, and ii) provide a well defined optimization problem for determining the maximum a posteriori (MAP) state estimation. The results on a target tracking problem show the performance improvements of the so-called Gaussian Process Particle Filter (GPPF) when compared to standard particle filtering.