Diffusion map-based algorithm for Gain function approximation in the Feedback Particle Filter

Understand

Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings.

• In any numerical implementation of the FPF algorithm, the main challenge is to numerically approximate the so-called gain function.
• A numerical algorithm for gain function approximation is the subject of this paper.
• The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian $\Delta_\rho$.