Importance Sampling With Stochastic Particle Flow and Diffusion Optimization

Particle flow (PFL) is an effective method for overcoming particle degeneracy, the main limitation of particle filtering. In PFL, particles are migrated towards regions of high likelihood based on the solution of a partial differential equation. Recently proposed stochastic PFL introduces a diffusion term in the ordinary differential equation (ODE) that describes particle motion. This diffusion term reduces the stiffness of the ODE and makes it possible to perform PFL with a lower number of numerical integration steps compared to traditional deterministic PFL. In this work, we introduce a general approach to perform importance sampling (IS) based on stochastic PFL. Our method makes it possible to evaluate a "flow-induced" proposal probability density function (PDF) after the parameters of a Gaussian mixture model (GMM) have been migrated by stochastic PFL. Compared to conventional stochastic PFL, the resulting processing step is asymptotically optimal. Within our method, it is possible to optimize the diffusion matrix that describes the diffusion term of the ODE to improve the accuracy-computational complexity tradeoff. Our simulation results in a highly nonlinear 3-D source localization scenario showcase a reduced stiffness of the ODE and an improved estimating accuracy compared to state-of-the-art deterministic and stochastic PFL.