GAII.05 8 July 2003

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Data Assimilation Methods for Characterizing
Radiation Belt Dynamics
E.J. Rigler1, D.N. Baker1, D. Vassiliadis2, R.S.
Weigel1 (1) Laboratory for Atmospheric and Space
Physics University of Colorado at Boulder (2)
Universities Space Research Association NASA /
Goddard Space Flight Center
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Introduction and Outline

• Using Data Assimilation (DA) algorithms for
  identification of empirical dynamical systems
• Finite Impulse Response (FIR) linear prediction
  filters
• Intuitive model structure
• Robust and proven predictive capabilities
• Adaptive System Identification (RLS vs. EKF)
• Weighted least squares estimates of model
  parameters
• Tracking non-linear systems with adaptive linear
  models
• Better Model Structures
• Multiple input, multiple output (MIMO) models
• Dynamic feedback and noise models (ARMAX,
  Box-Jenkins)
• Combining RB state with dynamical model parameters

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Dynamic Model Identification
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Why Linear Prediction Filters?
SISO Impulse Response
Operational Forecasts (NOAA REFM)
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Recursive System Identification

• RLS minimizes least-squares criterion
  recursively.
• Forgetting factor (?) allows tracking of
  non-time-stationary dynamic processes.
• Weighting factor (q) (de)emphasizes certain
  observations.

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Extended Kalman Filter (EKF)

• Model parameters can be incorporated into a
  state-space configuration.
• Process noise (vt) describes time-varying
  parameters as a random walk.
• Observation error noise (et) measures confidence
  in the measurements.
• Provides a more flexible and robust
  identification algorithm than RLS.

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Adaptive Single-Input, Single-Output
(SISO) Linear Filters
EKF-Derived Model Coefficients (w/o
Process Noise)
EKF-Derived Model Coefficients (with
Process Noise)
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SISO Model Residuals
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Multiple Input / Output (MIMO)
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Average Prediction Efficiencies
MIMO PE
EKF-MIMO PE (w/o process noise)
EKF-MIMO PE (with process noise)
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Alternative Model Structures

• ARMAX, Box-Jenkins, etc.
• Adaptive colored noise filters.
• True dynamic feedback.
• Better separation between driven and recurrent
  dynamics.

Combining the State and Model Parameters

• True data assimilation
• Ideal for on-line, real-time RB specification and
  forecasting.
• Framework is easily adapted to incorporate
  semi-empirical or physics-based dynamics modules.

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Acknowledgements

• Special thanks are extended to Drs. Scot
  Elkington and Alex Klimas for their valuable time
  and feedback.
• The data used for this study was generously
  provided by the National Space Science Data
  Center (NSSDC) OmniWeb project and the SAMPEX
  data team.
• This work was supported by the NSF Space Weather
  Program (grant ATM-0208341), and the NASA
  Graduate Student Research Program (GSRP, grant
  NGT5-132).

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