Morphing Ensemble Kalman Filters

Two novel costs for determining the tuning parameters of the Kalman Filter

The Kalman filter (KF) and the extended Kalman filter (EKF) are well established techniques for state estimation. However, the choice of the filter tuning parameters still poses a major challenge for the engineers [1]. In the present work, two new costs have been proposed for determining the filter tuning parameters on the basis of the innovation covariance. This provides a cost function based method for the selection of suitable combination(s) of filter tuning parameters in order to ensure the design of a KF or an EKF having an optimally balanced RMSE performance. Index Terms-Kalman filter, t…

Wavelet Ensemble Kalman Filters

We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an example.

State estimation under non-Gaussian Levy noise: A modified Kalman filtering method

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian Lévy noise is devised. It works effectively with reasonable computational cost. Simulation results are presented to illustrate this non-Gaussian filtering method.

Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise

The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman-Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ens…

平均场集合卡尔曼滤波器：近高斯设定

The Mean Field Ensemble Kalman Filter: Near-Gaussian Setting

本文首次分析了平均场集合卡尔曼滤波器在高斯设定之外的精度，通过引入加权全变差度量证明其稳定性，并证明在高斯问题邻域内误差很小。

混沌与机器学习动力系统集合卡尔曼滤波器的长时间精度

Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems

本文研究高维动力系统的在线状态估计问题，确立了集合卡尔曼滤波器在混沌系统及机器学习替代动力学模型中的长时间精度，证明了其估计误差在长时间范围内保持较小，验证了机器学习预测模型在集合数据同化中的有效性。