Ensemble Kalman Filter for Continuous-Discrete State-Space Models

Abstract

The ensemble Kalman filter (EnKF) is well-established for discrete state-space models. In this paper, we provide the methodology of applying the EnKF to continuous-discrete (CD) state-space models. The proposed CD EnKF algorithm is a bank of the CD extended Kalman filters for the time update. Then, the observation update is formulated using the Gaussian-sum distributed predicted state probability density function (PDF). We also provide the observation update based on the Dirac’s delta mixture predicted state PDF. The numerical simulation using a benchmark filtering problem called the satellite reentry is conducted to investigate the performance of the CD EnKFs. The performance comparison with the EnKF applied to the discretized model is also made.