Galileo orbit determination using combined GNSS and SLR observations

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.

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.

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).

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

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.

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.

<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>

Precise Orbit Determination (POD) is an integral part for analyzing measurements from space geodetic techniques such as Satellite Laser Ranging (SLR) and Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS). In the last two decades, POD based on GPS data has furthermore been established as one of the standard techniques to derive trajectories of satellites in the low Earth orbit (LEO) with highest accuracy. Since the launch of dedicated gravity missions, GPS sensors are not only used as a key tracking system for LEO POD, but also for extracting the long wavelength part of the Earth’s gravity field (together with SLR to spherical satellites). This chapter introduces SLR and GNSS measurements collected by the terrestrial networks of the International Laser Ranging Service (ILRS) and the International GNSS Service (IGS) as the observational basis for the realization of a terrestrial reference frame from satellite data. On this foundation, the basic equations and mathematical methods of orbit determination are introduced and extensively discussed. Pseudo-stochastic orbit modeling techniques are eventually presented as a general and efficient concept to determine satellite trajectories of highest quality even in presence of deficient force models, covering the full range between dynamic and purely kinematic solutions. Selected results from the application of the discussed orbit determination techniques are highlighted for GPS LEO data. Special emphasis is also put to present orbit determination in the context of more general orbit determination problems, where satellite trajectories are simultaneously determined with other parameters encompassing (at maximum) all pillars of geodesy, i.e., the shape, rotation, and gravity field of the Earth.

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.

Abstract. For the azimuth observation to be made at its magnetic observatories routinely, Japan Meteorological Agency (JMA) has adopted a traditional method based on Polaris sighting. Due to its difficulty to implement under overcast weather conditions and to its demand on observers, for overtime work into the evening, we are motivated to seek for an alternative method based on the Global Navigation Satellite Systems (GNSS) observation that might potentially relieve those two disadvantages. An experiment is made at Kakioka to assess the eligibility and effectiveness of the GNSS method for JMA's unmanned observatories, Memambetsu and Kanoya. The GNSS observations themselves achieve as high a precision as approximately 1 arcsec, as far as they are analyzed with Static mode. Derived from the results of GNSS observation and some supplementary horizontal angle measurements, the azimuth of the azimuth mark for the absolute measurement is determined with a precision of a few arcsecond, which is comparable to the azimuth precision achieved by the Polaris sighting. However, we end up with their significant difference by about 10 arcsec. We discuss this discrepancy to be possibly due to a local geoid gradient. The Polaris observation is made with a theodolite tilted in the gravitational direction, also known as the vertical line deviation, whereas the GNSS observations are based on the azimuth of the compliant ellipsoid plane.

The study of climate change is an important field of research. Monitoring of atmospheric variability especially the tropospheric precipitable water vapor (PWV) is a powerful way to investigate climate change. Global navigation satellite systems (GNSS) provide a good tool for studying atmospheric parameters as GNSS signals along its path from the satellites to the ground based receivers suffer a significant delay due to the refractivity of earth’s atmosphere. GNSS signals are not only delayed but also refracted in the neutral atmosphere. The zenith wet delays (ZWD) caused by the troposphere can be estimated during the geodetic processing of GNSS signals. Since the ZWD is tightly correlated to the PWV, GNSS observations can be used to study the changes of PWV. In this study GNSS data from the Egyptian permanent GNSS network (EPGN), International GNSS Service (IGS), EUREF Permanent Network (EPN) and Scripps Orbit and Permanent Array Center (SOPAC), for the years 2013 and 2014, were used. These GNSS stations provided a good geometrical coverage over the respective region. All GNSS data were processed using Bernese V 5.2 software. The needed product from GNSS data processing is the tropospheric zenith total delay (ZTD) over each GNSS site. The ZTD is divided based on physical parameters into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). The ZWD is the basic observable used to calculate PWV. The values of the PWV were calculated and its variation over the study area was investigated. The quality of calculated PWV values from GNSS data evaluated against traditional Radiosonde (RS) measurements. The results of GNSS PWV showed good agreement with RS PWV when the PWV values were low, but this agreement became worse at high PWV values as the differences between the two techniques increased. The correlation coefficient between RS PWV and GNSS PWV varied from 0.31 to 0.84. Standard deviation of the differences between RS PWV and GNSS PWV ranged from 2.369 to 5.973 mm. The PWV estimated from GNSS observations had annual cycle, and its cycle in 2013 was different from that in 2014. The PWV differences between the 2 years clarified that the water vapor content over the east Mediterranean in most of 2014 days was higher than that in 2013. Furthermore, PWV variations were noted on both temporal and spatial scales. The highest temporal variation value was 25.41 mm whereas the maximum value of the spatial variation was 19.67 mm. The present study illustrated the importance of using geodetic networks to provide atmospheric information.

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.

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%.

Recent advances in Satellite Laser Ranging (SLR) allow us to determine an improved value of the geocentric gravitational coefficient (GM) of 398600.4419 +/− .0002 km³/sec² (one sigma). This value is based on recent SLR observations of the LAGEOS I satellite; it is confirmed by observations of LAGEOS II, and is supported by results from Starlette, albeit at a lower level of precision. The information from these other satellites helps to support our claim of a conservative error estimate for GM, which amounts to about one half of a part per billion (ppb). Our determination of GM with the span of LAGEOS I data originally used to determine the current IERS92 standard (398600.4415 +/− .0008 km³/sec²) gives approximately the same value at about the same uncertainty quoted by the authors in 1992. The improved value that we suggest falls well within the two‐ppb error of the current standard, but differs from it by more than the error of the new estimate. The precision of the estimate of GM from SLR observations has improved by an order of magnitude in each of the last two decades.

Global navigation satellite systems (GNSS) products are integral to a wide array of scientific and commercial applications such as pecise orbit determination of low Earth orbit satellites, earthquake monitoring, GNSS reflectomrety, tropospheric and ionospheric research, surveying and much more. These products consisting of GNSS orbit, clock, phase biases and more are generated by the analysis centres of the International GNSS Service (IGS) by processing observations from a global network of ground stations to one or more GNSS constellations. The processing consists of a combined station position and GNSS satellite orbit determination through a least squares approach donated as global multi-GNSS processing.Within global multi-GNSS processing it is assumed that the observation noise is elevation-dependent and any spatial and temporal correlations are disregarded. Within numerous studies it has been shown that this assumption is incorrect while several studies additional pointed out that a sophisticated stochastic modelling has a positiv impact on GNSS processing and resulting products. In past reseach we have shown to exploit the post-fit residuals to derive temporal correlations for a sophisticated stochastic modeling. However, there have not been any large-scale investigations regarding the impact of stochastic modelling of observation noise on global GNSS processing products. Furthermore, to guarantee the quality of the GNSS products global multi-GNSS processing requires a sophisticated cycle slip detection and repairing algorithm. Cycle slips are discontinuities in the phase observations and if not corrected can lead to degrading quality of GNSS products.   We present our advancements in global multi-GNSS processing by exploiting post-fit residuals for stochastic modeling and cycle slip detection. We used several years of observations and a selected IGS network of ground stations to generate GNSS products. Based on this data we analysed the impact our newly integrated approaches have on GNSS products such as orbits, clocks, phase biases and station coordinate time series.