Title: Nudging the particle filter,
Abstract: We investigate a new sampling scheme aimed at improving the performance of
particle filters whenever (a) there is a significant mismatch between the
assumed model dynamics and the actual system, or (b) the posterior probability
tends to concentrate in relatively small regions of the state space. The
proposed scheme pushes some particles towards specific regions where the
likelihood is expected to be high, an operation known as nudging in the
geophysics literature. We re-interpret nudging in a form applicable to any
particle filtering scheme, as it does not involve any changes in the rest of
the algorithm. Since the particles are modified, but the importance weights do
not account for this modification, the use of nudging leads to additional bias
in the resulting estimators. However, we prove analytically that nudged
particle filters can still attain asymptotic convergence with the same error
rates as conventional particle methods. Simple analysis also yields an
alternative interpretation of the nudging operation that explains its
robustness to model errors. Finally, we show numerical results that illustrate
the improvements that can be attained using the proposed scheme. In particular,
we present nonlinear tracking examples with synthetic data and a model
inference example using real-world financial data.