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.

翻译：核学习前向-后向随机微分方程滤波器是一种用于求解非线性滤波问题的迭代式自适应无网格方法。该方法基于描述状态变量概率密度演化的Fokker-Planck方程所对应的前向-后向随机微分方程构建，并采用核密度估计进行密度近似。该算法在收敛速度与高维问题求解效率方面均展现出优于主流粒子滤波方法的性能。然而，该方法的收敛性此前仅通过实证研究得以验证。本文通过严格的理论分析，证明了该方法的局部与全局收敛性，为其经验性结果提供了理论支撑。