Convergence analysis of kernel learning FBSDE filter

TL;DR

This paper provides a rigorous convergence analysis of the kernel learning FBSDE filter, an adaptive meshfree method for nonlinear filtering, confirming its empirical effectiveness with theoretical guarantees.

Contribution

It offers the first theoretical proof of local and global convergence for the kernel learning FBSDE filter, supporting its superior performance over particle filters.

Findings

Proves local and global convergence of the method

Supports empirical results with theoretical analysis

Enhances understanding of high-dimensional filtering efficiency

Abstract

Kernel learning forward backward SDE filter is an iterative and adaptive meshfree approach to solve the nonlinear filtering problem. It builds from forward backward SDE for Fokker-Planker equation, which defines evolving density for the state variable, and employs KDE to approximate density. This algorithm has shown more superior performance than mainstream particle filter method, in both convergence speed and efficiency of solving high dimension problems. However, this method has only been shown to converge empirically. In this paper, we present a rigorous analysis to demonstrate its local and global convergence, and provide theoretical support for its empirical results.