Convergence Properties of Particle Filter Algorithm

The basic sampling importance resampling algorithm is the basic for improving particle filter methods which are widely utilized in optimal filtering problems. In our paper, we introduce a modified basic SIR algorithm and analyze the convergence property of the modified basic SIR algorithm. Furthermore, when the recursive time is finite and the forth-order moment of the interesting function w.r.t the posterior joint distribution of the extended state is exist, the sufficient condition for the basic particle filter estimation convergence almost surely to the optimal estimation is discussed.