scholarly journals Comments on “Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems”

2009 ◽  
Vol 66 (11) ◽  
pp. 3498-3500 ◽  
Author(s):  
Thomas M. Hamill ◽  
Jeffrey S. Whitaker ◽  
Jeffrey L. Anderson ◽  
Chris Snyder
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Data Assimilation ◽  
Sigma Point ◽  
Strongly Nonlinear

Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems

2009 ◽  
Vol 66 (2) ◽  
pp. 261-285 ◽  
Author(s):  
Jaison Thomas Ambadan ◽  
Youmin Tang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Kalman Filters ◽  
Joint Estimation ◽  
Sigma Point ◽  
Strongly Nonlinear ◽  
Data Assimilation Scheme ◽  
Higher Dimensional ◽  
Highly Nonlinear ◽  
Assimilation Scheme

Abstract Performance of an advanced, derivativeless, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced sigma-point subspace model is proposed and investigated for higher-dimensional systems. A low-dimensional Lorenz 1963 model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The results of SPKF data assimilation schemes are compared with those of standard EKF and EnKF, in which a highly nonlinear chaotic case is studied. It is shown that the SPKF is capable of estimating the model state and parameters with better accuracy than EKF and EnKF. Numerical experiments showed that in all cases the SPKF can give consistent results with better assimilation skills than EnKF and EKF and can overcome the drawbacks associated with the use of EKF and EnKF.

Data Assimilation for Strongly Nonlinear Problems by Transformed Ensemble Kalman Filter

SPE Journal ◽  
2014 ◽  
Vol 20 (01) ◽  
pp. 202-221 ◽  
Author(s):  
Qinzhuo Liao ◽  
Dongxiao Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Homogeneous Medium ◽  
Forward Model ◽  
Dynamic State ◽  
Initial Time ◽  
Static State ◽  
Strongly Nonlinear

Summary The ensemble Kalman filter (EnKF) has been widely used for data assimilation. It is challenging, however, when the relation of state and observation is strongly nonlinear. For example, near the flooding front in an immiscible flow, directly updating the saturation by use of the EnKF may lead to nonphysical results. One possible solution, which may be referred to as the restarted EnKF (REnKF), is to update the static state (e.g., permeability and porosity) and rerun the forward model from the initial time to obtain the updated dynamic state (e.g., pressure and saturation). However, it may become time-consuming, especially when the number of assimilation steps is large. In this study, we develop a transformed EnKF (TEnKF), in which the state is represented by displacement as an alternative variable. The displacement is first transformed from the forecasted state, then updated, and finally transformed back to obtain the updated state. Because the relation between displacement and observation is relatively linear, this new method provides a physically meaningful updated state without resolving the forward model. The TEnKF is tested in the history matching of multiphase flow in a 1D homogeneous medium, a 2D heterogeneous reservoir, and a 3D PUNQ-S3 model. The case studies show that the TEnKF produces physical results without the oscillation problem that occurs in the traditional EnKF, whereas the computational effort is reduced compared with the REnKF.

scholarly journals An Iterative EnKF for Strongly Nonlinear Systems

2012 ◽  
Vol 140 (6) ◽  
pp. 1988-2004 ◽  
Author(s):  
Pavel Sakov ◽  
Dean S. Oliver ◽  
Laurent Bertino
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Extended Kalman Filter ◽  
Large Scale ◽  
Lorenz Model ◽  
Model Framework ◽  
Simple Modification ◽  
Strongly Nonlinear ◽  
Perfect Model ◽  
Scale Models

Abstract The study considers an iterative formulation of the ensemble Kalman filter (EnKF) for strongly nonlinear systems in the perfect-model framework. In the first part, a scheme is introduced that is similar to the ensemble randomized maximal likelihood (EnRML) filter by Gu and Oliver. The two new elements in the scheme are the use of the ensemble square root filter instead of the traditional (perturbed observations) EnKF and rescaling of the ensemble anomalies with the ensemble transform matrix from the previous iteration instead of estimating sensitivities between the ensemble observations and ensemble anomalies at the start of the assimilation cycle by linear regression. A simple modification turns the scheme into an ensemble formulation of the iterative extended Kalman filter. The two versions of the algorithm are referred to as the iterative EnKF (IEnKF) and the iterative extended Kalman filter (IEKF). In the second part, the performance of the IEnKF and IEKF is tested in five numerical experiments: two with the 3-element Lorenz model and three with the 40-element Lorenz model. Both the IEnKF and IEKF show a considerable advantage over the EnKF in strongly nonlinear systems when the quality or density of observations are sufficient to constrain the model to the regime of mainly linear propagation of the ensemble anomalies as well as constraining the fast-growing modes, with a much smaller advantage otherwise. The IEnKF and IEKF can potentially be used with large-scale models, and can represent a robust and scalable alternative to particle filter (PF) and hybrid PF–EnKF schemes in strongly nonlinear systems.

scholarly journals Cubature Ensemble Kalman Filter for Highly Dimensional Strongly Nonlinear Systems

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 144892-144907
Author(s):  
Qingwen Meng ◽  
Harry Leib ◽  
Xuyou Li
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Ensemble Kalman Filter ◽  
Strongly Nonlinear
Sign in / Sign up

Export Citation Format

Share Document