Convergence analysis of kernel learning FBSDE filter
This work addresses a theoretical gap for researchers in signal processing and stochastic filtering, but it is incremental as it focuses on analysis rather than new method development.
The paper tackles the lack of theoretical convergence guarantees for the kernel learning forward backward SDE filter, a meshfree method for nonlinear filtering, by providing rigorous local and global convergence analysis to support its empirical performance.
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.