Filling gaps in time series of space-geodetic positioning

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.