Uncertainties of drift coefficients and extrapolation errors: application to clock error prediction

In Global Navigation Satellite Systems (GNSS), the on-board time has to be modelled and predicted in order to broadcast the time parameters to final users. As a consequence, the time prediction performance of the on-board clocks has to be characterized. In order to estimate the time uncertainty of the on-board oscillator, a linear or parabolic fit is performed over the sequence of observed time differences and extrapolated over the prediction period. In 1998, the French Centre National d'Etudes Spatiales (CNES) proposed specifications of orbit determination and time synchronization for GNSS-2. The synchronization requirements were stated as the maximum acceptable error between the real time deviation of the on-board oscillator and its estimation predicted by extrapolating the fit. The purpose of this paper is to estimate this error for different types of noise. This is achieved by the theoretical calculation of the variances of the drift coefficients, of the residuals and of the extrapolation errors, in the case of quadratic and linear drift models affected by different types of noise. The method and its results are described using real data examples, and the predicted extrapolation uncertainties are compared with the real extrapolation errors.