scholarly journals Sigma-point Kalman filter data assimilation methods for strongly nonlinear dynamical models.

2009 ◽  
Author(s):  
Jaison Thomas Ambadan
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Dynamical Models ◽  
Nonlinear Dynamical ◽  
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.

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

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 Data assimilation for control of a plane mixing layer

2019 ◽  
Vol 286 ◽  
pp. 07013
Author(s):  
N. Kumar ◽  
F. Kerhervé ◽  
L. Cordier
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Robust Estimation ◽  
Mixing Layer ◽  
Flow State ◽  
Experimental Demonstration ◽  
Dynamical Models ◽  
Control Applications ◽  
Plane Mixing Layer ◽  
Active Model

The design of active model-based flow controllers requires the knowledge of a dynamical model of the flow. However, real-time and robust estimation of the flow state remains a challenging task when only limited spatial and temporal discrete measurements are available. In this study, the objective is to draw upon the methodologies implemented in meteorology to develop dynamic observers for flow control applications. Well established data assimilation (DA) method using Kalman filter is considered. These approaches are extended to both estimate model states and parameters. Simple non-linear dynamical models are first considered to establish quantitative comparisons between the different algorithms. An experimental demonstration for the particular case of a plane mixing layer is then proposed.

Data assimilation with the weighted ensemble Kalman filter

2010 ◽  
Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter
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