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Adaptive error covariances estimation methods for ensemble Kalman filters

Yicun Zhen, John Harlim
2015 Journal of Computational Physics  
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework  ...  The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when  ...  Acknowledgment The authors thank Tyrus Berry for insightful discussion and sharing the source codes of his method.  ... 
doi:10.1016/j.jcp.2015.03.061 fatcat:okkcbphzsja7notvlewpkjxtui

Page 729 of Journal of the Atmospheric Sciences Vol. 60, Issue 5 [page]

2003 Journal of the Atmospheric Sciences  
In the ensemble transform Kalman filter (ETKF) method, the analysis error covariance matrix for the modified network is con- sistent with the statistics of an ETKF assimilation scheme.  ...  The predicted changes of forecast error variance are identical to those that the ensemble transform Kalman filter method would yield if applied to a set of Hessian singular vectors.  ... 

Adaptive Kalman Filtering for Postprocessing Ensemble Numerical Weather Predictions

Anna Pelosi, Hanoi Medina, Joris Van den Bergh, Stéphane Vannitsem, Giovanni Battista Chirico
2017 Monthly Weather Review  
The proposed method implements a Kalman filtering approach that fully exploits the information content of the ensemble for updating the parameters of the postprocessing equation.  ...  Here, a new adaptive postprocessing technique for ensemble predictions (called AEMOS) is introduced.  ...  Adaptive Kalman filtering applied to ensemble forecasts In this section, we illustrate a new adaptive postprocessing procedure for ensemble forecasts based on a Kalman filtering technique.  ... 
doi:10.1175/mwr-d-17-0084.1 fatcat:ahzolziuivaznolfx75irqpvii

An Adjoint-Based Adaptive Ensemble Kalman Filter

Hajoon Song, Ibrahim Hoteit, Bruce D. Cornuelle, Xiaodong Luo, Aneesh C. Subramanian
2013 Monthly Weather Review  
We introduce a new hybrid EnKF (ensemble Kalman filter)/4D-VAR (four-dimensional variational) approach to mitigate background covariance limitations in the EnKF.  ...  The new method leads to the least root-mean-squared estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds.  ...  We introduce a new hybrid EnKF (ensemble Kalman filter)/4D-VAR (four-dimensional variational) approach to mitigate background covariance limitations in the EnKF.  ... 
doi:10.1175/mwr-d-12-00244.1 fatcat:o7ypqyef5rhu5dkc6fjionbzyi

Kalman Filters for Dynamic and Secure Smart Grid State Estimation

Jinghe Zhang, Greg Welch, Naren Ramakrishnan, Saifur Rahman
2015 Intelligent Industrial Systems  
Combining dynamic state estimation methods such as Kalman filters with real-time data generated/collected by digital meters such as phasor measurement units (PMU) can lead to advanced techniques for improving  ...  In this work, we introduce and compare a novel method, viz. adaptive Kalman Filter with inflatable noise variances, against a variety of classic Kalman filters.  ...  filter (naive RKF), ensemble Kalman filter (EnKF), ensemble adjustment Kalman filter (EAKF), and our proposed adaptive Kalman filter with inflatable noise variances (AKF with InNoVa) with its principles  ... 
doi:10.1007/s40903-015-0009-6 fatcat:ugeftto735h5jbi37qsnozvdpa

Kalman-Takens filtering in the presence of dynamical noise

Franz Hamilton, Tyrus Berry, Timothy Sauer
2017 The European Physical Journal Special Topics  
By combining the Kalman-Takens method with an adaptive filtering procedure we are able to estimate the statistics of the observational and dynamical noise.  ...  If a parametric model is known, methods such as Kalman filtering have been developed for this purpose.  ...  At the kth step, the filter produces an estimate of the state x + k−1 and the covariance matrix P + k−1 , which estimates the covariance of the error between the estimate x + k−1 and the true state.  ... 
doi:10.1140/epjst/e2016-60363-2 fatcat:gqm3f7qnvbe7nhlsekdyc7y4he

Page 1141 of Journal of the Atmospheric Sciences Vol. 60, Issue 9 [page]

2003 Journal of the Atmospheric Sciences  
The ensemble transform Kalman filter (ETKF) theory was first introduced as an adaptive sampling method (Bishop et al. 2001).  ...  Closed form solutions for the ex- act error covariances that would be produced by infinite time Kalman filter scheme for such a system are given in Bishop et al. (2003, hereafter BRT).  ... 

An adaptive-covariance-rank algorithm for the unscented Kalman filter

Lauren E. Padilla, Clarence W. Rowley
2010 49th IEEE Conference on Decision and Control (CDC)  
The Unscented Kalman Filter (UKF) is a nonlinear estimator that is particularly well suited for complex nonlinear systems.  ...  In the UKF, the error covariance is estimated by propagating forward a set of "sigma points," which sample the state space at intelligently chosen locations.  ...  The authors are grateful to Professor Geoff Vallis for introducing us to the Lorenz 96 model, and for many enlightening discussions.  ... 
doi:10.1109/cdc.2010.5717549 dblp:conf/cdc/PadillaR10 fatcat:w5pcsvhb25ccboptvqkgxrwzim

An Adaptive Ensemble Kalman Filter

Herschel L. Mitchell, P. L. Houtekamer
2000 Monthly Weather Review  
In this study, a method of estimating and accounting for model error in the context of an ensemble Kalman filter technique is developed.  ...  It is found that, with temporal smoothing of the model-error parameter estimates, the adaptive ensemble Kalman filter produces fairly good estimates of the parameters and accounts rather well for the model  ...  We thank Dick Dee for making us aware of relevant literature on model-error estimation as well as for several important critical comments on an early version of the estimation algorithm.  ... 
doi:10.1175/1520-0493(2000)128<0416:aaekf>2.0.co;2 fatcat:5lav632hsrbzlowydxq7kam3jq

Dynamic State Estimation for Synchronous Machines Based on Adaptive Ensemble Square Root Kalman Filter

Dongliang Nan, Weiqing Wang, Kaike Wang, Rabea Jamil Mahfoud, Hassan Haes Alhelou, Pierluigi Siano
2019 Applied Sciences  
In this paper, an adaptive ensemble square root Kalman filter (AEnSRF) is proposed, in which the ensemble square root filter (EnSRF) and Sage–Husa algorithm are utilized to estimate measurement noise online  ...  Simulation results obtained by applying the proposed method show that the estimation accuracy of AEnSRF is better than that of ensemble Kalman filter (EnKF), and AEnSRF can track the measurement noise  ...  Author Contributions: D.N. created models, developed methodology, wrote the initial draft, and designed computer programs; W.W. supervised and was responsible for leading the research activity planning  ... 
doi:10.3390/app9235200 fatcat:43bcmhfjf5be5defj6krongsca

Ensemble Square Root Filters*

Michael K. Tippett, Jeffrey L. Anderson, Craig H. Bishop, Thomas M. Hamill, Jeffrey S. Whitaker
2003 Monthly Weather Review  
Ensemble data assimilation methods assimilate observations using state-space estimation methods and low-rank representations of forecast and analysis error covariances.  ...  error covariance equation.  ...  Ensemble size limits the number of degrees of freedom used to represent forecast and analysis errors, and Kalman filter error covariance calculations are practical for modest-sized ensembles.  ... 
doi:10.1175/1520-0493(2003)131<1485:esrf>2.0.co;2 fatcat:gh4ch6i6c5du5ffhuat5jn5a4e

Page 2937 of Journal of the Atmospheric Sciences Vol. 62, Issue 8 [page]

2005 Journal of the Atmospheric Sciences  
Evensen, 1998: Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev., 126, 1719-1724. Daley, R., 1992: Estimating model-error covariances for applica- tion to atmospheric data assimilation.  ...  Houtekamer, 2000: An adaptive en- semble Kalman filter. Mon. Wea. Rev., 128, 416-433. , and G. Pellerin, 2002: Ensemble size, balance, and model-error representation in an ensemble Kalman filter.  ... 

A Nonparametric Adaptive Nonlinear Statistical Filter [article]

Michael Busch, Jeff Moehlis
2014 arXiv   pre-print
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems.  ...  Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.  ...  ACKNOWLEDGMENTS This work was supported by the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the U.S.  ... 
arXiv:1411.0707v1 fatcat:mblrxrk76zehbf5n3yydj2xbau

A nonparametric adaptive nonlinear statistical filter

Michael Busch, Jeff Moehlis
2014 53rd IEEE Conference on Decision and Control  
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems.  ...  Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.  ...  This work was supported by the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the U.S.  ... 
doi:10.1109/cdc.2014.7039700 dblp:conf/cdc/BuschM14 fatcat:hj4atrq5ynhpdeaotmlby5vmkm

Processing arctic eddy-flux data using a simple carbon-exchange model embedded in the ensemble Kalman filter

Edward B. Rastetter, Mathew Williams, Kevin L. Griffin, Bonnie L. Kwiatkowski, Gabrielle Tomasky, Mark J. Potosnak, Paul C. Stoy, Gaius R. Shaver, Marc Stieglitz, John E. Hobbie, George W. Kling
2010 Ecological Applications  
Identifying and compensating for errors in the NEE time series can be automated using a signal processing filter like the ensemble Kalman filter (EnKF).  ...  Because of the covariance among model variables, the EnKF can also update estimates of variables for which there is no direct measurement.  ...  Performance of the ensemble Kalman filter (EnKF) with large and small model noise estimates. The PLIRTLE model (Eq. 1; TABLE 2 . 2 Adaptive noise estimation.  ... 
doi:10.1890/09-0876.1 pmid:20666250 fatcat:agmv35bhmndmfidg6b2jryjkdm
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