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| Titel |
Handling nonlinearity in two nonlinear Kalman filters with symmetric analysis ensembles |
| VerfasserIn |
Xiaodong Luo, Irene Moroz, Ibrahim Hoteit |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250038945
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| Zusammenfassung |
| The Kalman filter (KF) is a sequential data assimilation scheme that achieves the optimal
performance in linear Gaussian systems. In the presence of nonlinearity, several methods
have been developed to allow the implementation of the KF. We refer to the resulting filters as
nonlinear Kalman filters, which include, for example, the extended Kalman filter (EKF), the
ensemble Kalman filter (EnKF), and the filters discussed below. Roughly speaking, it is
the ways in handling nonlinearity that make the nonlinear KFs distinct from each
other.
Here we focus on two nonlinear KFs, called the unscented Kalman filter (UKF) and the
divided difference filter (DDF), respectively. Although these two filters are developed based
on different philosophies, they share the same analysis scheme. More concretely, each
filter generates as the analysis ensemble some special system states (called sigma
points), which are symmetric about the analysis mean and preserve the analysis
covariance.
The UKF is an EnKF-type filter, which adopts Monte Carlo approximations to estimate
the mean and covariance of the system states. The main feature of the UKF is that its
analysis ensemble is symmetric about the analysis mean. It can be shown that, with
the symmetry, the UKF can avoid some of the sampling errors and biases in the
EnKF.
The idea of the DDF is similar to that of the EKF. Like Taylor series expansion used in
the EKF, Stirling’s interpolation formula is adopted in the DDF to expand a nonlinear
function locally. Through the formula, there is no need for the DDF to evaluate the
derivative(s) of a nonlinear function. Here the analysis ensemble serves as interpolation
points, which are required to be symmetric about the local point (e.g., the analysis mean)
where the nonlinear function is expanded.
In this contribution we discuss the benefits of symmetric sampling and compare the
theoretical and practical aspects of the UKF and DDF. We suggest strategies to reduce the
computational costs of both filters in applications. Numerical results will be presented and
discussed. |
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