Robustness and Accuracy of finite Ensemble Kalman filters in large dimensions

نویسندگان

  • Andrew J. Majda
  • Xin T. Tong
چکیده

Contemporary data assimilation often involves more than a million prediction variables. Finite ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they allow for computationally cheap low ensemble state approximation for extremely large dimensional turbulent dynamical systems. The practical finite ensemble filter like EnKF necessarily involve modifications such as covariance inflation and localization, and it is a genuine mystery why they perform so well with small ensemble sizes in large dimensions. This paper provides the first rigorous stochastic analysis of the accuracy and covariance fidelity of finite EnKF in the practical regime where the ensemble size is much smaller than the large ambient dimension for finite EnKFs with random coefficients. A challenging issue overcome here is that finite EnKF in huge dimensions introduces unavoidable bias and model errors which need to be controlled and estimated.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Performance of Ensemble Kalman filters in large dimensions

Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they allow for computationally cheap low ensemble state approximation for extremely large dimensional turbulent dynamical systems. The practical finite ensemble fil...

متن کامل

The 1000-Member Ensemble Kalman Filtering with the JMA Nonhydrostatic Mesoscale Model on the K Computer

The ensemble Kalman filter (EnKF) approximates background error covariance by using a finite number of ensemble members. Although increasing the ensemble size consistently improves the EnKF analysis, typical applications of the EnKF to realistic atmospheric simulations are conducted with a small ensemble size due to limited computational resources. The finite ensemble size introduces a sampling...

متن کامل

Resampling the ensemble Kalman filter

Ensemble Kalman filters (EnKF) based on a small ensemble tend to provide collapse of the ensemble over time. It is shown that this collapse is caused by positive coupling of the ensemble members due to use of one common estimate of the Kalman gain for the update of all ensemble members at each time step. This coupling can be avoided by resampling the Kalman gain from its sampling distribution i...

متن کامل

Rigorous accuracy and robustness analysis for two-scale reduced random Kalman filters in high dimensions

Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the underlying multiscale structure, applying the full Kalman filtering procedures only to the large scale variables, and estimating the small scale variables with pr...

متن کامل

New Adaptive UKF Algorithm to Improve the Accuracy of SLAM

SLAM (Simultaneous Localization and Mapping) is a fundamental problem when an autonomous mobile robot explores an unknown environment by constructing/updating the environment map and localizing itself in this built map. The all-important problem of SLAM is revisited in this paper and a solution based on Adaptive Unscented Kalman Filter (AUKF) is presented. We will explain the detailed algorithm...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016