Assessing robustness of particle filtering by the Kolmogorov-Smirnov statistics

One of the most criticized aspects of particle filtering algorithms is their dependence on model assumptions. However, a rigorous study of the effect of modeling errors on the performance of such algorithms is still missing. In this paper, the problem of using an inaccurate discrete state-space model is considered and a systematic methodology for studying the effects on its performance is proposed. The methodology is based on the use of the Kolmogorov-Smirnov statistic, which in this case is a distance metric between the posterior characterization when respectively correct and incorrect model assumptions are made. An example with functional and distributional inaccuracies is studied.