Merging particle filter for sequential data assimilation

A new filtering technique for sequential data assimilation, the merging particle filter (MPF), is proposed. The MPF is devised to avoid the degeneration problem, which is inevitable in the particle filter (PF), without prohibitive computational cost. In addition, it is applicable to cases in which a nonlinear relationship exists between a state and observed data where the application of the ensemble Kalman filter (EnKF) is not effectual. In the MPF, the filtering procedure is performed based on sampling of a forecast ensemble as in the PF. However, unlike the PF, each member of a filtered ensemble is generated by merging multiple samples from the forecast ensemble such that the mean and covariance of the filtered distribution are approximately preserved. This merging of multiple samples allows the degeneration problem to be avoided. In the present study, the newly proposed MPF technique is introduced, and its performance is demonstrated experimentally.