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Assessing the performance of dynamical trajectory estimates

Bröcker, J. (2014) Assessing the performance of dynamical trajectory estimates. Physical Review E, 89 (6). 062919. ISSN 1550-2376

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To link to this item DOI: 10.1103/PhysRevE.89.062919


Estimating trajectories and parameters of dynamical systems from observations is a problem frequently encountered in various branches of science; geophysicists for example refer to this problem as data assimilation. Unlike as in estimation problems with exchangeable observations, in data assimilation the observations cannot easily be divided into separate sets for estimation and validation; this creates serious problems, since simply using the same observations for estimation and validation might result in overly optimistic performance assessments. To circumvent this problem, a result is presented which allows us to estimate this optimism, thus allowing for a more realistic performance assessment in data assimilation. The presented approach becomes particularly simple for data assimilation methods employing a linear error feedback (such as synchronization schemes, nudging, incremental 3DVAR and 4DVar, and various Kalman filter approaches). Numerical examples considering a high gain observer confirm the theory.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:47582
Publisher:American Physical Society

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