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| Titel |
Verification of ARMA identification for modelling temporal correlation of GPS observations using the toolbox ARMASA |
| VerfasserIn |
Xiaoguang Luo, Michael Mayer, Bernhard Heck |
| 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 |
250032947
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| Zusammenfassung |
| One essential deficiency of the stochastic model used in many GNSS (Global Navigation
Satellite Systems) software products consists in neglecting temporal correlation of GNSS
observations. Analysing appropriately detrended time series of observation residuals resulting
from GPS (Global Positioning System) data processing, the temporal correlation behaviour of
GPS observations can be sufficiently described by means of so-called autoregressive moving
average (ARMA) processes. Using the toolbox ARMASA which is available free of
charge in MATLAB® Central (open exchange platform for the MATLAB® and
SIMULINK® user community), a well-fitting time series model can be identified
automatically in three steps. Firstly, AR, MA, and ARMA models are computed up to some
user-specified maximum order. Subsequently, for each model type, the best-fitting model is
selected using the combined (for AR processes) resp. generalised (for MA and ARMA
processes) information criterion. The final model identification among the best-fitting
AR, MA, and ARMA models is performed based on the minimum prediction error
characterising the discrepancies between the given data and the fitted model. The ARMA
coefficients are computed using Burg’s maximum entropy algorithm (for AR processes),
Durbin’s first (for MA processes) and second (for ARMA processes) methods,
respectively.
This paper verifies the performance of the automated ARMA identification using the
toolbox ARMASA. For this purpose, a representative data base is generated by means of
ARMA simulation with respect to sample size, correlation level, and model complexity. The
model error defined as a transform of the prediction error is used as measure for the deviation
between the true and the estimated model. The results of the study show that the recognition
rates of underlying true processes increase with increasing sample sizes and decrease with
rising model complexity. Considering large sample sizes, the true underlying processes can
be correctly recognised for nearly 80% of the analysed data sets. Additionally, the
model errors of first-order AR resp. MA processes converge clearly more rapidly to
the corresponding asymptotical values than those of high-order ARMA processes. |
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