Filling gaps in time series of space-geodetic positioning
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ORIGINAL PAPER
Filling gaps in time series of space-geodetic positioning Sofiane Khelifa 1 & Bachir Gourine 1 & Habib Taibi 1 & Hicham Dekkiche 1 Received: 8 April 2018 / Accepted: 8 June 2018 # Saudi Society for Geosciences 2018
Abstract Several methods of time series analysis and forecasting require data at regular time intervals. But in space geodesy, most datasets are often full of gaps, resulting for example from hardware issue, modification of models, change of analysis strategy, and local geophysical phenomenon. The purpose of this paper is to fill the gaps in time series of space-geodetic station positions, by the use of two different approaches: the iterative singular spectrum analysis (ISSA) and the generalized regression neural network (GRNN). In order to test the efficiency of the proposed methods to properly process missing data, we created synthetic gaps at random points in regular time series (i.e., time series without gaps) of Global Positioning System (GPS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) station positions with data span longer than 4 years. For each analyzed time series, we created gaps (by removing successive points) of different lengths ranging from 1 to 52 gaps, and then, we filled these gaps by ISSA, GRNN, and other classical methods of interpolation such as nearest neighbor, linear, and cubic interpolations. The interpolation precision was evaluated by the technique of cross-validation which compares the estimated values with the original data. After several simulations on position time series with different lengths, we found that the ISSA technique provides better results in terms of root mean square error. Keywords Time series analysis . Geodetic station positions . Data gap filling . Iterative singular spectrum analysis . Generalized regression neural network
Introduction A time series is a sequential set of numerical observations performed over time. Since, the data are measurements taken through time, presence of gaps (a sequence of missing data) in time series data is very common. In space geodesy, this may occur due to local geophysical phenomena (earthquake, landslides, etc.), material problem (change of antenna or other instruments of the station, etc.), modification of the models used (atmosphere, gravity field, etc.), or the change of analysis strategies. The analysis of time series with gaps may distort the results. Therefore, when gaps are present in the time series, it may be necessary to estimate the missing values. In literature, different methods and mathematical models for filling gaps
* Sofiane Khelifa [email protected] 1
Centre of Space Techniques, PO Box 13, 31200 Arzew, Algeria
are applied. Often, for small gaps (a short sequence of missing values), the classical interpolation methods (linear interpolation, nearest neighbor, or cubic interpolation) are enough. On the other hand, for slightly larger gaps (a long sequence of missing values), the method used to fill gaps needs to be chosen very carefully due to its
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