Time–frequency analysis of the Galileo satellite clocks: looking for the J2 relativistic effect and other periodic variations

Abstract

When observed from the ground, the frequency of the atomic clocks flying on the satellites of a Global Navigation Satellite System is referred to as apparent frequency, because it is observed through the on-board signal generation chain, the propagation path, the relativistic effects, the measurement system, and the clock estimation algorithm. As a consequence, the apparent clock frequency is affected by periodic variations of different origins such as, for example, the periodic component of the J2 relativistic effect, due to the oblateness of the earth, and the clock estimation errors induced by the orbital estimation errors. We present a detailed characterization of the periodic variations affecting the apparent frequency of the Galileo clocks, obtained by applying time–frequency analysis and other signal processing techniques on space clock data provided by the European Space Agency. In particular, we analyze one year of data from three Galileo Passive Hydrogen Masers, flying on two different orbital planes. Time–frequency analysis reveals how the spectral components of the apparent frequency change with time. For example, it confirms that the amplitude of the periodic signal due to the orbital estimation errors depends on the angle between the sun and the orbital plane. Moreover, it allows to find a more precise estimate of the amplitude of the J2 effect, in agreement with the prediction of the general theory of relativity, and it shows that such amplitude suddenly decreases when the corresponding relativistic correction is applied to the data, thus validating the analytical formula used for the correction.

BDS Satellite Clock Prediction Considering Periodic Variations

“…The Galileo satellite clock offsets have a similar performance. A detailed time-varying analysis of the first two significant periodic terms is carried out for Galileo satellites based on the European Space Agency (ESA) clock products, and confirms that amplitude variations of the first periodic term affected by eclipse seasons, and the amplitude sinusoidal variations of second periodic term related to the J2 relativistic effect [30]. Studies show that the BDS periodic terms have some distinction between the GPS and Galileo, but similar variations of the periodic variations have been found in the BDS satellite clock offsets [31].…”

High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Multi-Source Observations

“…However, since the BDS monitor station are only distributed within China, it is difficult for BDS to realize the above requirements. Under the above circumstances, BDS-3 uses the two-way comparison technology to measure satellite clock offsets [16]. The fundamental principle of the two-way comparison is to subtract two-way measurements to eliminate most of the errors related to spatial information, and obtain their clock offsets.…”

GPS, GLONASS, and Galileo orbit geometry variations caused by general relativity focusing on Galileo in eccentric orbits

“…1) constitute perfect probes for verifying effects emerging from the GR due to high-precision onboard clocks and two techniques for precise orbits determination, broadcasted L-band GNSS signals and Satellite Laser Ranging (Bury et al 2019b;2021;Sośnica et al 2019). So far, only Galileo clocks onboard E14 and E18 have been used to verify GR effects (Delva et al 2018;Herrmann et al 2018;Kouba 2019Kouba , 2021Formichella et al 2021). The onboard clocks require, however, calibration of biases and corrections to the orbit modeling errors.…”