The Almost Sure Convergence of the Auxiliary Particle Filter

The almost sure convergence of the Auxiliary Particle Filter (APF) is discussed in this dissertation. First, a Modified Auxiliary Particle Filter (MAPF) is constructed. Later, when the recursive time is finite and the interesting function with extended state as independent variable is 4th power integrable with respect to the posterior probability distribution of the extended state, the sufficient condition for APF estimation converges almost surely to the optimal estimation is discussed. A simulation experiment is designed to illustrate the almost sure convergence of APF.