A path integral method for data assimilation

Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model initialization.Speedup in the Monte Carlo sampling process is essential if the path integral method has any chance of being a viable estimator on moderately large problems. Here a variety of strategies are proposed and compared for their relative ability to improve the sampling efficiency of the resulting estimator. Provided as well are details useful for its implementation and testing.The method is applied to a problem in which standard methods are known to fail, an idealized flow/drifter problem, which has been used as a testbed for assimilation strategies involving Lagrangian data. It is in this kind of context that the method may prove to be a useful assimilation tool in oceanic studies.