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We analyse the weekly time series of position residuals of to GPS-DORIS (Global Positioning System-Doppler Orbitography and Radiopositioning Integrated by Satellite) co-located stations in order to evaluate the spectral content of the observed nonlinear station motion. We have used the discrete wavelet transform to extract trends and seasonal signals, and the Allan variance to characterise the residual noise which allows to evaluate the positioning stability of stations.

The GPS-DORIS co-located time series were produced using the GIPSY/OASIS II software, referred to ITRF2005 and expressed in the local geodetic reference frame. The wavelet analysis has revealed useful nonlinear trends, annual and semi-annual signals contained in the studied time series. For GPS time series, the amplitude of the annual signal is around 1.5 and 2.9 mm in the horizontal (North and East) and Vertical components respectively, and the semi-annual signal shows amplitude around 0.8, 1.3 and 2.3 mm in the North. East and Vertical components, respectively. For DORIS time series, the annual and semi-annual signals show amplitudes of around 4-6 mm in the three components.

However, after having removed the trends, annual and semi-annual signals, the slope of the Allan variance graph shows for GPS position time series, a combination of a low flicker noise and dominant white noise in the all three components, while for DORIS time series, the white noise is more frequent in the three components. The noise level, defined by the Allan deviation for the one-year sampling time, is smaller than 3 and 5 mm in the three components for GPS and DORIS time series, respectively. (C) 2011 Elsevier B.V. All rights reserved.