Sampling Errors in Ensemble Kalman Filtering. Part I: Theory

Sacher, William; Bartello, Peter
August 2008
Monthly Weather Review;Aug2008, Vol. 136 Issue 8, p3035
Academic Journal
This paper discusses the quality of the analysis given by the ensemble Kalman filter in a perfect model context when ensemble sizes are limited. The overall goal is to improve the theoretical understanding of the problem of systematic errors in the analysis variance due to the limited size of the ensemble, as well as the potential of the so-called double-ensemble Kalman filter, covariance inflation, and randomly perturbed analysis techniques to produce a stable analysis—that is to say, one not subject to filter divergence. This is achieved by expressing the error of the ensemble mean and the analysis error covariance matrix in terms of the sampling noise in the background error covariance matrix (owing to the finite ensemble estimation) and by comparing these errors for all methods. Theoretical predictions are confirmed with a simple scalar test case. In light of the analytical results obtained, the expression of the optimal covariance inflation factor is proposed in terms of the limited ensemble size and the Kalman gain.


Related Articles

  • Speed estimation and control in a belt-driven system for a web production process. Part 2: control strategy. Makin, E; Acarnley, P // Proceedings of the Institution of Mechanical Engineers -- Part E;2004, Vol. 218 Issue 1, p25 

    This paper addresses the problem of estimating and controlling the speed of a belt-driven casting drum in a web production process, where direct measurement of drum speed is infeasible. Techniques for estimating web tension and casting drum speed, using measured values of brake and drive torque...

  • Outlier-Tolerant Kalman Filter of State Vectors in Linear Stochastic System. Hu Shaolin; Meinke, Karl; Huajiang Ouyang; Sun Guoji // International Journal of Advanced Computer Science & Application;Dec2011, Vol. 2 Issue 12, p37 

    The Kalman filter is widely used in many different fields. Many practical applications and theoretical results show that the Kalman filter is very sensitive to outliers in a measurement process. In this paper some reasons why the Kalman Filter is sensitive to outliers are analyzed and a series...

  • Stochastic Real-Time Optimal Control for Bearing-Only Trajectory Planning. Ross, Steven M.; Cobb, Richard G.; Baker, William P. // International Journal of Micro Air Vehicles;Mar2014, Vol. 6 Issue 1, p1 

    A method is presented to simultaneously solve the optimal control problem and the optimal estimation problem for a bearing-only sensor. For bearing-only systems that require a minimum level of certainty in position relative to a source for mission accomplishment, some amount of maneuver is...

  • Guaranteed estimation of signals with bounded variances of derivatives. Kulakova, V.; Nebylov, A. // Automation & Remote Control;Jan2008, Vol. 69 Issue 1, p76 

    Consideration is given to the problem of signal estimation against the background of the white noise when the information about the signal is represented in the form of numerical characteristics such as constraints on the variance of the signal itself and variances of some its derivatives. We...

  • Angular Rate Estimation Using a Distributed Set of Accelerometers. Sungsu Park; Sung Kyung Hong // Sensors (14248220);2011, Vol. 11 Issue 11, p10444 

    A distributed set of accelerometers based on the minimum number of 12 accelerometers allows for computation of the magnitude of angular rate without using the integration operation. However, it is not easy to extract the magnitude of angular rate in the presence of the accelerometer noises, and...

  • Deterministic Method to Assess Kalman Filter Passive Ranging Solution Reliability. Yannone, Ronald M. // Enformatika;2006, Vol. 13, p282 

    For decades, the defense business has been plagued by not having a reliable, deterministic method to know when the Kalman filter solution for passive ranging application is reliable for use by the fighter pilot. This has made it hard to accurately assess when the ranging solution can be used for...

  • An application of Ensemble Kalman Filter in integral-balance subsurface modeling. Qiang Shu; Kemblowski, Mariush W.; McKee, Mac // Stochastic Environmental Research & Risk Assessment;Nov2005, Vol. 19 Issue 5, p361 

    Data assimilation method provides a framework to decrease the uncertainty of hydrological modeling by sequentially incorporating observations into numerical model. Such a process involves estimating statistical moments of different order based on the evolution of conditional probability...

  • Estimation of the Limit Accuracy of Discrete Systems for a Class of Dynamic Controllers Relative to the Output. Sadomtsev, Yu.; Torgashova, O. // Automation & Remote Control;Sep2005, Vol. 66 Issue 9, p1423 

    A problem is considered for the estimation of the limit accuracy of multidimensional discrete systems for a definite class of dynamic controllers relative to the output, which differ in the fact that certain of the poles of a closed system prove to be zero ones, while the remaining poles are...

  • Kalman Filter Based Adaptive Reduction of Motion Artifact from Photoplethysmographic Signal. Seyedtabaii, S.; Seyedtabaii, L. // Proceedings of World Academy of Science: Engineering & Technolog;Feb2008, Vol. 39, p173 

    Artifact free photoplethysmographic (PPG) signals are necessary for non-invasive estimation of oxygen saturation (SpO2) in arterial blood. Movement of a patient corrupts the PPGs with motion artifacts, resulting in large errors in the computation of Sp02. This paper presents a study on using...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics