Prediction of GNSS satellite clocks

This thesis deals with the characterisation and prediction of GNSS-satellite-clocks. A prerequisite to develop powerful algorithms for the prediction of clock-corrections is the thorough study of the behaviour of the different clock-types of the satellites. In this context the predicted part of the IGU-clock-corrections provided by the Analysis Centers (ACs) of the IGS was compared to the IGS-Rapid-clock solutions to determine reasonable estimates of the quality of already existing well performing predictions. For the shortest investigated interval (three hours) all ACs obtain almost the same accuracy of 0,1 to 0,4 ns. For longer intervals the individual predictions results start to diverge. Thus, for a 12-hours- interval the differences range from nearly 10 ns (GFZ, CODE) until up to some 'tens of ns'. Based on the estimated clock corrections provided via the IGS Rapid products a simple quadratic polynomial turns out to be sufficient to describe the time series of Rubidium-clocks. On the other hand Cesium-clocks show a periodical behaviour (revolution period) with an amplitude of up to 6 ns. A clear correlation between these amplitudes and the Sun elevation angle above the orbital planes can be demonstrated. The variability of the amplitudes is supposed to be caused by temperature-variations affecting the oscillator. To account for this periodical behaviour a quadratic polynomial with an additional sinus-term was finally chosen as prediction model both for the Cesium as well as for the Rubidium clocks. The three polynomial-parameters as well as amplitude and phase shift of the periodic term are estimated within a least-square-adjustment by means of program GNSS-VC/static. Input-data are time series of the observed part of the IGU clock corrections. With the estimated parameters clock-corrections are predicted for various durations. The mean error of the prediction of Rubidium-clock-corrections for an interval of six hours reaches up to 1,5 ns. For the 12-hours interval 2-3 ns are obtained. This represents a distance-error of 60-90 cm. A comparison of the results from GNSS-VC/static to the predicted Ultra-Rapid-clocks of the ACs of the IGS confirms the very good quality of our clock solution which is at the level of the best AC solutions. The use of GNSS-VC/static for GLONASS-satellite-clocks is problematic. The GLONASS satellite clocks show a hard to characterize behaviour covering a number of jumps and breaks in the time-series within just a few hours. Therefore the prediction of GLONASS-satellite-clocks seems not reasonable at this time. In view of more stable clocks upcoming with the new GLONASS satellite generation K a similar model as used to characterize the GPS Rubidium clock might be applicable. The results of GNSS-VC/static are affected by a three-hours-delay. Thus an almost real-time solution to obtain high quality clock predictions has been established in parallel. The programme GNSS-VC/kalman enables to evaluate the parameters of the prediction-model by a Kalman-filter approach. Because of the short prediction-interval of just six hours the model is reduced to a simple quadratic polynomial. Input-data are RT-clock-corrections evaluated with the programme RTR-Control [Opitz, 2010] based on the observation data provided by the IGS-RT project. The clock correction polynomial coefficients are estimated every minute. After an initialization period of the filter (about 30 minutes) the mean error of the polynomial parameters as well as the evaluated clock corrections is below 2 ns for most of the satellite clock (author)