GLONASS precise orbit determination with identification of malfunctioning spacecraft

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

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.

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.

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 inter-satellite link (ISL) equipment of the third-generation BeiDou Navigation Satellite System (BDS-3) can enhance the accuracy of precise orbit determination (POD) for BDS-3 satellites. However, the hardware delays within ISL observations can impact the measurement accuracy of ISL observations. This study evaluates the characteristics of hardware delays in ISL observations for BDS-3 medium Earth orbit (MEO) satellites and investigates their effects on POD. Analysis shows that most links exhibit slow variations in hardware delays, with standard deviations (STD) of 6.4 cm and 3.6 cm over 45 days for the C19-C25 and C20-C21 links, respectively. Conversely, some links like C30-C23 and C30-C33 show more pronounced variations, with STD values reaching 17.7 cm and 14.1 cm within three days. Links involving satellites C23 and C30 display higher variability and significant jumps in hardware delays compared with other links. The larger variations in hardware delays of these links can be absorbed by other parameters, thereby affecting the accuracy of parameter estimation. To mitigate their impact on POD, a segmented estimation strategy for hardware delays is proposed. This strategy divides a single link into multiple segments based on a set interval length and estimates the hardware delay parameters for each segment separately, thereby absorbing the variations in hardware delays or unmodeled errors. The effectiveness of this strategy is demonstrated through ISL POD residual analysis, comparison with L-band orbit determination results, and validation using Satellite Laser Ranging (SLR) residuals. The root mean square (RMS) of ISL observation residuals decreased by approximately 44.3%, from 6.1 cm to 3.4 cm. Comparisons with L-band orbits confirmed an approximate 28.2% reduction in the 3D RMS of orbit discrepancies, from 26.5 cm to 19.0 cm. Additionally, the RMS of the overall SLR residuals showed a slight decrease. Overall, the improved segmented estimation strategy effectively reduces the influence of hardware delay variations on BDS-3 orbit determination, notably enhancing the orbit determination accuracy of BDS-3 satellites, especially for C23 and C30, which experience larger hardware delay fluctuations.

The Russian Global Navigation Satellite System (GLONASS) satellites have a stretched body shape and take a specific attitude mode inside the eclipse. Based on previous studies, the new Empirical CODE orbit model (ECOM2) performs better than the classical ECOM model if a satellite has elongated shape or does not maintain yaw-steering mode, and the use of an a priori box-wing (BW) model improves the orbits significantly when employing the ECOM model. However, we find that the ECOM model performs better than the ECOM2 model for GLONASS satellites outside eclipse seasons, while it performs two times worse in eclipse seasons. The use of the conventional box-wing model results in very little improvement. By assessing the ECOM Y _{0} estimates, we conclude that there are potential radiators on the -x surface of GLONASS satellites causing orbit perturbations also inside the eclipse. The higher-order Fourier terms of the ECOM2 model can compensate for such effects better than the ECOM model. Based on this finding, we first confirm that GLONASS-K satellites take a similar attitude mode as GLONASS-M satellites inside the eclipse. Then, we adjust optical parameters of GLONASS satellites as part of precise orbit determination (POD) considering the potential radiator and thermal radiation effects. Finally, the adjusted parameters are introduced into a new box-wing model and jointly used with the ECOM and ECOM2 model, respectively. Results show that the amplitude and the dependency of the empirical parameters on the beta angle are greatly reduced for both ECOM and ECOM2 models. Rather than the conventional box-wing model, the new box-wing model reduces the orbit misclosure between two consecutive arcs for both GLONASS-M and GLONASS-K satellites. In particular, the improvement in GLONASS-M satellites is more than 30% for the ECOM model during eclipse seasons. Further evaluation from 24-h predicted orbits demonstrates that the improvement during eclipse seasons is mainly in along- and cross-track directions. Finally, we validate GLONASS satellite orbits using Satellite Laser Ranging (SLR) observations. The use of the new box-wing model reduces the spurious pattern of the SLR residuals as a function of beta and Delta u significantly, and the linear dependency of the SLR residuals on the elongation drops from as large as -0.760 mm/deg to almost zero for both ECOM and ECOM2 models. In general, GLONASS-M satellites benefit more from the new a priori box-wing model and the BW+ECOM model results in the best SLR residuals, with an improvement of about 50% and 20%, respectively, for the mean and standard deviation (STD) values with respect to the orbit products without a priori model.

Precise orbit determination for geostationary satellites with multiple tracking techniques

Since the beginning of satellite altimetry missions, the ocean surface topography community requires precise and accurate satellite orbits. With start of the satellite Sentinel-3A on February 16, 2016, two radio- and one altimeter onboard the satellite accomplish the Copernicus program with a ocean- and land monitoring mission, planned for a nominal mission lifetime of 7 years. The satellite is orbiting the Earth on a polar, Sun-synchronous trajectory at an altitude of 815 km. For the purpose of precise orbit determination, the satellite is equipped with a geodetic-grade dual-frequency Global Positioning System (GPS) receiver. The GPS measurements are employed together with a set of gravitational and non-gravitational models in a Reduced-Dynamic Orbit Determination (RDOD) approach, which combines the advantages of a dynamic and a kinematic positioning for deriving precise satellite orbits. However, especially the non-gravitational force models require sophisticated modeling techniques. Therefore, a satellite macro model is introduced, which allows a proper modeling of accelerations due to Solar Radiation Pressure (SRP), Earth Radiation Pressure (ERP), and atmospheric drag. Especially the Sun-synchronous orbit, and the huge solar array, which is loosely coupled to the satellite body, makes the precise orbit determination challenging. As members of the Copernicus Quality Working Group, the Astronomical Institute of the University of Bern (AIUB), and the German Aerospace Center (DLR) are, among others, responsible for the orbit validation of Sentinel-3A. Both groups make use of a satellite macro model within a reduced-dynamic approach but differ in the employed software solutions and the pseudo-stochastic modeling. Basically, the pseudo-stochastic parameters allow to compensate potential deficits in the employed force models. Within this poster, the modeling aspects are briefly introduced, followed by comparing the results of both groups. The results include the estimated empirical accelerations, and the estimated satellite orbits of Sentinel-3A. Furthermore, the orbit quality is assessed by Satellite Laser Ranging (SLR), an external and independent tool for orbit validation.

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.

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.

The precise orbit determination (POD) for BeiDou satellites mainly relies on a regional tracking network distributed in China area at the present time. The multi-satellite POD for BeiDou regional navigation satellite system via double-difference observations is presented. First, the double-difference phase measurements are modeled on ionosphere-free combination of B1 and B2 signals. The POD strategies are detailed, followed by a brief data-processing flow. Then, the POD tests based on regional network of domestic monitoring stations are developed, and the orbit quality assessed by arc overlaps and Satellite Laser Ranging (SLR) residuals shows an accuracy of about 20 cm in radial direction. Finally, contributions of the overseas monitoring stations to the POD accuracy of BeiDou satellites are investigated by introducing several IGS Multi-GNSS Experiment (IGS M-GEX) monitoring stations with BeiDou tracking capability into the multi-satellite POD test. The improved orbit accuracy indicates that more BeiDou observing sites should be established worldwide in future.

ADEOS-II precise orbit determinations with GPS and SLR

Precise orbit determination and rapid orbit recovery supported by time synchronization

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.