Error analysis for numerical formulation of particle filter
Xiaoying Han, Jinglai Li, Dongbin Xiu · Discrete and Continuous Dynamical Systems - B · 2015
As an approximation of the optimal stochastic filter,particle filter is a widely used tool for numerical prediction ofcomplex systems when observation data are available.In this paper, we conduct an error analysis from a numerical analysisperspective. That is, we investigate the numerical error, which is definedas the difference between the numerical implementation of particlefilter andits continuous counterpart, and demonstrate that the error consists ofdiscretization errorsfor solving the dynamic equations numerically and samplingerrors for generating the random particles.We then establish convergence of the numerical particle filterto the continuous optimal filterand provide bounds for the convergence rate.Remarkably, our analysis suggests that morefrequent data assimilation maylead to larger numerical errors of the particle filter.Numerical examples are provided to verify the theoretical findings.