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