Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS was found in the geocenter x- and y-coordinate series. Our tests, however, clearly reveal artifacts in the z-component determined with the GLONASS data. Large periodic excursions in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system and thus have a period of about 4 months (third of a year). A detailed analysis revealed that the artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). A simple formula is derived, describing the relation between the geocenter z-coordinate and the corresponding parameter of the SRP. The effect can be explained by first-order perturbation theory of celestial mechanics. The theory also predicts a heavy impact on the GNSS-derived geocenter if once-per-revolution SRP parameters are estimated in the direction of the satellite’s solar panel axis. Specific experiments using GPS observations revealed that this is indeed the case. Although the main focus of this article is on GNSS, the theory developed is applicable to all satellite observing techniques. We applied the theory to satellite laser ranging (SLR) solutions using LAGEOS. It turns out that the correlation between geocenter and SRP parameters is not a critical issue for the SLR solutions. The reasons are threefold: The direct SRP is about a factor of 30–40 smaller for typical geodetic SLR satellites than for GNSS satellites, allowing it in most cases to not solve for SRP parameters (ruling out the correlation between these parameters and the geocenter coordinates); the orbital arc length of 7 days (which is typically used in SLR analysis) contains more than 50 revolutions of the LAGEOS satellites as compared to about two revolutions of GNSS satellites for the daily arcs used in GNSS analysis; the orbit geometry is not as critical for LAGEOS as for GNSS satellites, because the elevation angle of the Sun w.r.t. the orbital plane is usually significantly changing over 7 days.

Impact of loading displacements on SLR-derived parameters and on the consistency between GNSS and SLR results

Displacements of the Earth’s surface caused by tidal and non-tidal loading forces are relevant in high-precision space geodesy. Some of the corrections are recommended by the international scientific community to be applied at the observation level, e.g., ocean tidal loading (OTL) and atmospheric tidal loading (ATL). Non-tidal displacement corrections are in general recommended not to be applied in the products of the International Earth Rotation and Reference Systems Service, in particular atmospheric non-tidal loading (ANTL), oceanic and hydrological non-tidal corrections. We assess and compare the impact of OTL, ATL and ANTL on SLR-derived parameters by reprocessing 12 years of SLR data considering and ignoring individual corrections. We show that loading displacements have an influence not only on station long-term stability, but also on geocenter coordinates, Earth Rotation Parameters, and satellite orbits. Applying the loading corrections reduces the amplitudes of annual signals in the time series of geocenter and station coordinates. The general improvement of the SLR station 3D coordinate repeatability when applying OTL, ATL and ANTL corrections are 19.5 %, 0.2 % and 3.3 % respectively, w.r.t. the solutions without loading corrections. ANTL corrections play a crucial role in the combination of optical (SLR) and microwave (GNSS, VLBI, DORIS) space geodetic observation techniques, because of the so-called Blue-Sky effect: SLR measurements can be carried out only under cloudless sky conditions—typically during high air pressure conditions, when the Earth’s crust is deformed, whereas microwave observations are weather-independent. Thus, applying the loading corrections at the observation level improves SLR-derived products as well as the consistency with microwave-based results. We assess the Blue-Sky effect on SLR stations and the consistency improvement between GNSS and SLR solutions when ANTL corrections are included. The omission of ANTL corrections may lead to inconsistencies between SLR and GNSS solutions of up to 2.5 mm for inland stations. As a result, the estimated GNSS–SLR coordinate differences correspond better to the local ties at the co-located stations when applying ANTL corrections.