Modified particle filter methods for assimilating Lagrangian data into a point-vortex model

The process of assimilating Lagrangian (particle trajectory) data into fluid models can fail with a standard linear-based method, such as the Kalman filter. We implement a particle filtering approach that affords a nonlinear estimation and does not impose Gaussianity on either the prior or the posterior distributions at the update step. Several schemes for reinitializing the particle filter, specifically tailored to the Lagrangian data assimilation problem, are applied to a point-vortex system. A comparison with the Extended Kalman Filter (EKF) for the same system demonstrates the effectiveness of particle filters for the assimilation of complex, nonlinear Lagrangian data.