Sequential Bayesian filters, such as particle filters, are often presented as an ideal means of tracking the state of nonlinear systems. Here shadowing filters are demonstrated to perform better than sequential filters at tracking under specific circumstances. The success of shadowing filters is attributed to avoiding both well-known deficiencies of particle filters, and some newly identified problems.
Judd, K., & Stemler, T. (2009). Failures of sequential Bayesian filters and the successes of shadowing filters in tracking of nonlinear deterministic and stochastic systems. Physical Review E, 79(6), Article number 066206, 6pp. https://doi.org/10.1103/PhysRevE.79.066206