Earth scale defined by modern satellite ranging observations

The first two Galileo In-Orbit Validation satellites were launched in October 2011 and started continuous signal transmission on all frequencies in early 2012. Both satellites are equipped with two different types of clocks, namely rubidium clocks and hydrogen masers. Based on two test periods, the quality of the Galileo orbit determination based on Global Navigation Satellite System (GNSS) and Satellite Laser Ranging (SLR) observations is assessed. The estimated satellite clock parameters are used as quality indicator for the orbits: A bump at orbital periods in the Allan deviation indicates systematic errors in the GNSS-only orbit determination. These errors almost vanish if SLR observations are considered in addition. As the internal consistency is degraded by the combination, the offset of the SLR reflector is shifted by +5 cm, resulting in an improved orbit consistency as well as accuracy. Another approach to reduce the systematic errors of the GNSS-only orbit determination employs constraints for the clock estimates with respect to a linear model. In general, one decimeter orbit accuracy could be achieved.

Due to the continued development of the GLONASS satellites, precise orbit determination (POD) still poses a series of challenges. This study examines the impact of introducing the analytical tube-wing model for GLONASS-M and the box-wing model for GLONASS-K in a series of hybrid POD strategies that consider both the analytical model and a series of empirical parameters. We assess the perturbing accelerations acting on GLONASS spacecraft based on the analytical model. All GLONASS satellites are equipped with laser retroreflectors for satellite laser ranging (SLR). We apply the SLR observations for the GLONASS POD in a series of GNSS + SLR combined solutions. The application of the box-wing model significantly improves GLONASS orbits, especially for GLONASS-K, reducing the STD of SLR residuals from 92.6 to 27.6 mm. Although the metadata for all GLONASS-M satellites reveal similar construction characteristics, we found differences in empirical accelerations and SLR offsets not only between GLONASS-M and GLONASS-M+ but also within the GLONASS-M+ series. Moreover, we identify satellites with inferior orbit solutions and check if we can improve them using the analytical model and SLR observations. For GLONASS-M SVN730, the STD of the SLR residuals for orbits determined using the empirical solution is 48.7 mm. The STD diminishes to 41.2 and 37.8 mm when introducing the tube-wing model and SLR observations, respectively. As a result, both the application of the SLR observations and the analytical model significantly improve the orbit solution as well as reduce systematic errors affecting orbits of GLONASS satellites.

In the last decade, we have been witnessing a rapid development of the constellations of Global and Regional Navigation Satellite Systems (GNSS/RNSS). Besides the well-known GPS and GLONASS, newly developed systems such as Galileo, BeiDou, QZSS and NAVIC have become increasingly important. All satellites of new GNSS are equipped with laser retroreflector arrays (LRA) dedicated to Satellite Laser Ranging (SLR). SLR allows, e.g., an independent validation of microwave-based orbit products. Therefore, a fully operational online service called the multi-GNSS Orbit Validation Visualizer Using SLR (GOVUS) has been developed allowing for near real-time analysis of the quality of multi-GNSS orbits. The mean offsets of SLR residuals for Center for Orbit Determination in Europe (CODE) orbits in 2016 are at the level of −8, −38, −14, and −107 mm, for BeiDou, Galileo, GLONASS, and QZSS, respectively, with the standard deviations of 66, 36, 29, and 100 mm. Moreover, GOVUS can be used as a database containing information on equipment used at SLR stations and multi-GNSS satellite parameters. This paper includes a comprehensive description of the functionality and the structure of the developed service with exemplary analyses. The paper points out the most critical issues, limitations and challenges of multi-GNSS and SLR tracking network in the context of the SLR orbit validation. The goal of the paper and GOVUS itself is to determine: (1) what is the current quality of multi-GNSS orbits validated using SLR results; (2) what kinds of systematic errors can affect GNSS orbits and SLR observations; and (3) how to provide the online analysis tools to the broadest possible multi-GNSS community. The service has been officially operating since March 2017 as the Associate Analysis Center of the International Laser Ranging Service (ILRS ACC).

Atmospheric pressure loading plays a crucial role in precise space geodesy, thus its omission, especially the nontidal loading (ANTL) part, leads to the inconsistency between solutions based on the microwave [Global Navigation Satellite Systems (GNSS)] and optical [satellite laser ranging (SLR)] observations. SLR observations are performed only during the cloudless conditions coincident with high values of air pressure that deforms the earth's crust downward. The systematic shift of the estimated SLR station coordinates, which arises from the ANTL omission, is called the Blue-Sky effect. The offset is related to the long-term averaging of ANTL for SLR observations which are provided in sparse intervals, unlike GNSS, which observes continuously. Based on the ANTL model applied on SLR observations to GNSS, we determined the values of the Blue-Sky effect. The largest values of the Blue-Sky effect are observed for the inland stations, i.e., 2.3, 2.1, 2.0, and 1.9 mm for Svetloe, Potsdam, Baikonur, and Altay, respectively. We also investigate the impact of the omission of ANTL corrections on geodetic parameters, i.e., earth rotation parameters, geocenter motion, precise GNSS orbits, as well as on the global SLR network. The negligence of ANTL causes a systematic effect on geocenter coordinates with the amplitude of the annual signal at the level of 1.9 mm for the Z-component. The omission of ANTL corrections causes also a systematic shift of the multi-GNSS orbit constellation with the amplitude of the annual signal at the level of 2.7 mm for the Z-component.

Variations in Earth’s rotation, encompassing polar motion (PM) and the length-of-day (LOD) changes, result from a variety of factors influencing mass distribution and movement. These factors include the redistribution of air and water masses within the climate system and the solid Earth, and exchanges of angular momentum between the core and mantle. The ability to differentiate between these diverse sources is crucial for comprehending processes occurring at or near the Earth's surface, as well as within its interior.Fluctuations in the low-degree spherical harmonic coefficients of Earth's gravitational potential are linked to the redistribution of mass on a large scale within and on the planet. Observing changes in these coefficients provides a means to investigate the movement of mass within the Earth system. The degree-2 order-0 coefficient (C20) of geopotential holds particular significance for Earth rotation studies since C20 variations (ΔC20) are directly linked to the corresponding excitations of LOD. ΔC20 can be determined from various methods, of which Satellite Laser Ranging (SLR) measurements have the longest tradition. Launching Gravity Recovery and Climate Experiment (GRACE) in 2002 and GRACE Follow-On (GRACE-FO) in 2018 brought new measurements of changes in the Earth's gravitational field, including estimates of the ΔC20. However, estimates of ΔC20 from GRACE/GRACE-FO have limitations due to orbital geometry, the relatively short distance between the two satellites, and tide-like aliases. In practice, GRACE/GRACE-FO computing centres replace ΔC20 with an estimate from SLR measurements. Combining GRACE/GRACE-FO and SLR observations could enhance the accuracy of determining low-degree coefficients of geopotential, including ΔC20, ΔC21, and ΔS21.In this study, we reassess the excitation of LOD over the period 2002–2023, estimated from five different data sources: SLR, GRACE/GRACE-FO, a combination of SLR+GRACE/GRACE-FO, geodetic observations, and geophysical fluid models. To each of the time series we apply the same processing to isolate long-period, seasonal and non-seasonal short-term fluctuations. For every component, we conduct a comparative analysis aiming to evaluate the consistency among various estimates and identify discrepancies between the series. We show that combining GRACE/GRACE-FO with SLR data improves the consistency between ΔC20-derived and observed LOD excitation for the studied oscillations.

The challenge of precise orbit determination for STSAT-2C using extremely sparse SLR data

LAser RElativity Satellite 2 (LARES-2) successfully joined the constellation of geodetic satellites tracked by Satellite Laser Ranging (SLR) stations on July 13, 2022. LARES-2 has a spherical shape and a very favorable area-to-mass ratio that minimizes the non-gravitational orbit perturbations. Due to very small retroreflectors, the spread of center-of-mass corrections for different detectors installed at SLR sites is much smaller than for LAGEOS satellites. LARES-2 orbits at a similar height as LAGEOS-1, however, with a complementary inclination angle of 70° forming a butterfly configuration together with LAGEOS-1.Although the primary objective of LARES-2 is verification of the Lense-Thirring effect emerging from general relativity, the satellite also has a substantial impact on the geodetic parameters derived from SLR observations. We process 18 months of LARES-2 data and compare the LAGEOS-1/2 solutions with the combined LAGEOS-1/2+LARES-2 solutions. We show the impact of LARES-2 on the (1) SLR station coordinates, (2) pole coordinates, (3) length-of-day excess, (4) low-degree gravity field parameters focusing on C20 and C30 coefficients, (5) scale of the reference frame, (6) geocenter motion. We show that LARES-2 can especially improve the Z component of the geocenter coordinates and de-correlate C20 from the length-of-day parameter. The secular drifts of the ascending nodes for LARES-1 and LAGEOS-1 caused by C20 are the same in terms of absolute values but with opposite signs. This allows us to successfully separate the measurements of length-of-day excess (or the UT rate) from the C20-induced changes. We also analyze the empirical accelerations acting on LARES-2 which result from unmodeled non-gravitational orbit perturbations, such as thermal effects, and compare them to those observed for LAGEOS satellites. The observation geometry of LARES-2 is especially beneficial for stations located at high and medium latitudes, which allows it to improve the estimation of station coordinates provided by LAGEOS-1/2. Therefore, LARES-2 substantially contributes not only to general relativity and fundamental physics but also to space geodesy improving the future realizations of the international terrestrial reference frames.

Satellite laser ranging (SLR) to the satellites of the global navigation satellite systems (GNSS) provides substantial and valuable information about the accuracy and quality of GNSS orbits and allows for the SLR-GNSS colocation in space. In the framework of the NAVSTAR-SLR experiment two GPS satellites of Block-IIA were equipped with laser retroreflector arrays (LRAs), whereas all satellites of the GLONASS system are equipped with LRAs in an operational mode. We summarize the outcome of the NAVSTAR-SLR experiment by processing 20 years of SLR observations to GPS and 12 years of SLR observations to GLONASS satellites using the reprocessedmicrowave orbits provided by the center for orbit determination in Europe (CODE). The dependency of the SLR residuals on the size, shape, and number of corner cubes in LRAs is studied. We show that the mean SLR residuals and the RMS of residuals
\ndepend on the coating of the LRAs and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including the single-photon and multi-photon detection modes.We also showthat the SLR observations to GNSS satellites are important to validate GNSS orbits and to assess deficiencies in the solar radiation pressure models. We found that the satellite signature effect, which is defined as a spread of optical pulse signals due to reflection from multiple reflectors, causes the variations of mean SLR residuals of up to 15mmbetween the observations at nadir angles of 0◦ and 14◦. in case of multiphoton SLR stations. For single-photon SLR stations this effect does not exceed 1 mm. When using the new empirical
\nCODE orbit model (ECOM), the SLR mean residual falls into the range 0.1–1.8 mm for high-performing singlephoton SLR stations observing GLONASS-M satellites with uncoated corner cubes. For best-performing multi-photon stations the mean SLR residuals are between −12.2 and
\n−25.6 mm due to the satellite signature effect.

Satellite Laser Ranging (SLR) is currently the unique technique to determine station coordinates, Earth Orientation Parameters (EOPs) and Stokes coefficients of the Earth’s gravity field from one observation equation with a high accuracy. These parameters form the so-called ‘three pillars’ (Plag and Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as an official analysis center of the International Laser Ranging Service (ILRS) (Pearlman et al., 2002), DGFI is developing and maintaining software to process SLR observations called ‘DGFI Orbit and Geodetic parameter estimation Software’ (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. In this study, up to 10 satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES and BLITS) with different orbit characteristics (e.g., inclination and altitude) are combined. The relative weighting of the satellites is done using a variance component estimation. The diverse orbits allow to decrease the correlation of parameters such as gravity field coefficients (GFCs) and EOPs. Beside the Earth’s gravity field (weekly GFCs with degree and order ≤ 6 and monthly GFCs with degree and order ≤ 20) and rotation (terrestrial pole coordinates, UT1-UTC extrapolated with LOD), 3-D station coordinates are estimated weekly or monthly. Different combined solutions are compared to LAGEOS-only solutions. If LARES is combined with LAGEOS1/2, a significant improvement in the GFCs, the EOP and the TRF can be achieved. If more satellites are combined, the variation of the pole coordinates w.r.t. the IERS 08 C04 time series can be reduced up to 56%. Furthermore, systematics in LOD are nearly completely eliminated. The variation of the station coordinates w.r.t. SLRF2008 (http://www.ilrs.gsfc.nasa.gov/science/awg/SLRF2008.html, 2013) can be reduced by about 30%.

The meteorological parameters such as the temperature and the pressure are crucial for tropospheric delay correction of Satellite Laser Ranging (SLR). Considering that the meteorological data of the SLR observations may be missing, this paper selects two common global meteorological models, GPT2 and GPT2w, to evaluate the accuracy of the meteorological model and apply them to SLR-based satellite orbit validation. In this study, we validated the accuracy of the empirical models with the observed meteorological data collected from the SLR stations. The results show that the RMSE of the pressure and temperature generated by GPT2 model is 5.61 hPa and 4.90 K, respectively. The RMSE of the pressure and temperature derived from the GPT2w is 5.58 hPa and 4.83 K, respectively. Then the SLR residuals are compared by applying the empirical meteorological models and the real observations. The results indicate that the RMS of the SLR residuals with the real meteorological data is 3.22 cm, and the RMS of the SLR residuals calculated with the GPT2 and GPT2w models are 3.45 cm and 3.42 cm, respectively. The GPT2w model performs slightly better than the GPT2 model in SLR data processing. It concludes that replacing the real meteorological data by the empirical models is feasible for SLR data processing.

Satellite laser ranging (SLR) constitutes a fundamental space geodetic technique providing global geodetic parameters, such as geocenter coordinates, Earth rotation parameters, and low-degree gravity field coefficients. The tropospheric delay correction is one of the crucial corrections that have to be taken into account when processing SLR data. Current conventional models of the troposphere delays assume a full symmetry of the atmosphere above SLR stations. Neglecting horizontal gradients in SLR solutions introduces a systematic error in SLR products, especially for the observations at low elevation angles, and leads to a deterioration of the consistency between SLR and other space geodetic techniques, such as global navigational satellite systems and very-long-baseline interferometry. We derive new mapping function coefficients, as well as first- and second-order horizontal gradients, all of which are based on numerical weather models, in order to properly consider the azimuthal asymmetry in SLR solutions. We test the enhanced mapping function and horizontal gradients on the solutions based on 11 years of SLR observations to LAGEOS-1/2 satellites and 1 year of SLR observations to Sentinel-3A. The consideration of azimuthal asymmetry of the atmosphere above the SLR stations has a systematic effect on SLR-derived products, such as station and geocenter coordinates and pole coordinates. Horizontal gradients in SLR solutions improve the consistency between SLR-derived pole coordinates and the combined IERS-C04 series by means of reducing the offset for the X and Y pole coordinates by 20 {upmu }mathrm{as}. The second-order horizontal gradients are negligible in SLR solutions; thus, including first-order gradients is sufficient for SLR solutions.

Determining precise multi-satellite orbits and geodetic parameters using satellite laser ranging (SLR) observations of spherical laser geodetic satellites is essential for high-accuracy geodetic scientific applications. Weekly multi-satellite combined solutions for satellite orbits, station coordinates and earth rotation parameters (ERPs) using SLR observations from LAGEOS, Etalon and newly launched LARES-2 satellites are achieved using a self-developed software function based on a new processing strategy. We present an in-depth accuracy analysis of the satellite orbits and geodetic parameters determined from the combined solution of LAGEOS-Etalon and LAGEOS-Etalon-LARES-2, in which the impact of two years of LARES-2 SLR observations is mainly studied. The root mean square (RMS) value of post-fit residuals is 0.81 cm for LARES-2, which is comparable to or slightly smaller than that of the LAGEOS and Etalon satellites. The statistics of the differences in overlapping orbit and external orbit comparison are performed for orbit accuracy assessment. For LAGEOS and Etalon, the results of overlapping orbit and external orbit comparison present similar conclusions. The mean of the RMS values of orbit difference for LAGEOS is about 3 cm in the three-dimensional (3D) direction, and less than 1 cm in the radial (R) direction. The mean RMS value of orbit difference for Etalon is about 15 cm in the 3D direction, and less than 3 cm in the R direction. The inclusion of LARES-2 SLR observations can slightly improve the orbit accuracy of Etalon. For LARES-2, the mean RMS values of overlapping orbit difference are 1.79 cm and 0.29 cm in the 3D and R directions, respectively, which are smaller than those for LAGEOS. Moreover, the stability and accuracy of the estimated station coordinates and ERPs are improved after adding LARES-2 SLR observations to multi-satellite combined solutions.

<p>Numerous active low Earth orbiters (LEOs) and Global Navigation Satellite System (GNSS) satellites, including the Galileo constellation, are equipped with laser retroreflectors used for Satellite Laser Ranging (SLR). Moreover, most of LEOs are equipped with GNSS receivers for precise orbit determination. SLR measurements to LEOs, GNSS, and geodetic satellites vary in terms of the number of registered normal points (NPs) or registered satellite passes. In 2016-2018, SLR measurements to LEOs constituted 81% of all NPs and 59% of all registered satellite passes, whereas 10% of NPs and 30% of satellite passes, respectively, were assigned to GNSS. The remaining SLR measurements were completed by geodetic satellites, including LAGEOS-1/2, and LARES-1.</p><p>In this study, we show that the SLR observations to Galileo, passive geodetic and active LEO satellites together with precise GNSS-based orbits of LEOs and Galileo, can be used for the determination of global geodetic parameters, such as geocenter coordinates (GCC) and Earth rotation parameters (ERPs), i.e. pole coordinates, and length-of-day parameter.</p><p>GCC are typically determined using SLR observations to passive geodetic satellites, such as LAGEOS-1/2. Also, the SLR observations to LAGEOS-1/2 together with GNSS and Very Long Baseline Interferometry data are used for the determination of ERPs. Here, we use SLR observations to Galileo, LAGEOS-1/2, LARES-1, Sentinel-3A, SWARM-A/B/C, TerraSAR-X, Jason-2, GRACE-A/B satellites to investigate whether they can be applied for the reference frame realization and for deriving high-quality global geodetic parameters.</p><p>We present various types of solutions to investigate the best solution set-up. The studied solutions differ in terms of solution lengths, the combination of different sets of satellites and the relative weights for the variance scaling factors of technique and satellite-specific normal equations. We compare our results with the standard LAGEOS-based solutions, the combined EOP-14-C04 products and show the consistency of the results.</p>

Satellite laser ranging (SLR) has proven a very efficient method for contributing to the tracking of altimetric satellites and determining accurately their orbit although hampered by the non-worldwide coverage and the meteorological conditions. Indeed, in some cases it is the only method available to determine the satellite orbit (e.g., the orbits of the ERS-1 and Geosat-Follow-On missions). Moreover, any operational and non-weather dependent techniques, like GPS, DORIS, PRARE, can exhibit systematic errors in positioning and orbitography. A comparison with SLR results allows to evidence such errors and vice versa. For doing that, two different approaches for determining precise orbits can be considered: one based on global orbit determination, the other on a short-arc technique used to locally improve a global orbit determined by another tracking techniques, such as DORIS or GPS. We can thus validate a global orbit and achieve orbit quality control to a level of 2 to 3 centimeters at present and expect to achieve a level of 1 to 2 centimeters in the near future. Errors induced by station coordinates or by the gravity field (geographically correlated errors, for example) can be estimated from SLR tracking data. Colocation experiments with different techniques in the same geodetic site play also a key role to ensure precise relationships between the geodetic reference frames linked to each technique. In particular, the role of the SLR technique is to strengthen the vertical component (including velocity) of the positioning, which is crucial for altimetry missions. The role of SLR data in the modelling of the first terms of the gravity field has finally to be emphasized, which is of primary importance in orbitography, whatever the tracking technique used. Another application of SLR technology is the satellite altimeter calibration. Examples of past calibration and future experiments are given, including the accuracy we can expect from the Jason-1 and EnviSat space oceanography missions.

The recovery of Earth’s time variable gravity field from satellite data relied heavily on Satellite Laser Ranging (SLR) before the recent GRACE and GRACE Follow-On satellite gravity missions. Currently, the monthly gravity solutions from GRACE/GRACE-FO provide important global information about the temporal variations of gravity field. However, there are a few low-degree coefficients derived from GRACE/GRACE-FO that are not well determined, because of the satellite gravity mission configuration and issues with the accelerometer data. These low-degree coefficients can be determined reasonably well using SLR data from the dedicated SLR satellite configuration and can be used to replace the less well-determined values from GRACE/GRACE-FO. A more rigorous and consistent approach is to directly combine SLR and GRACE/GRACE-FO gravity solutions in a simultaneous solution. This paper presents a combination strategy for gravity field recovery from combined SLR and GRACE/GRACE-FO mission data. To correctly account for all correlations, the combination is performed at the information (normal) equation level. The coefficients C20 and C30 are determined mainly from SLR by renaming C20 and C30 parameters in GRACE/GRACE-FO information equations. The results show that the combined products are improved in comparison with the nominal GRACE/GRACE-FO gravity solutions. The gravity field products are evaluated by comparing different gravity solutions through coefficient-wise comparison, equivalent water height variations and mass changes over selected areas.