Bound on errors in particle filtering with incorrect model assumptions and its implication for change detection

We study the errors in particle filtering with incorrect system model parameters. The total error in approximating the posterior distribution of the actual process (state), given noisy observations, can be split into modeling error and particle filtering error in tracking with the incorrect model. We show that the bound on both errors is a monotonically increasing function of the error in the system model per time step. The bound on the particle filtering error blows up very quickly since it has increasing derivatives of all orders. We apply this result to bounding the errors in approximating our statistic for slow change detection in nonlinear systems.