ADEOS-II precise orbit determinations with GPS and SLR

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.

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.

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.

With the implementation of the Jason-1 satellite altimeter mission, the goal of reaching the 1-cm level in orbit accuracy was set. To support the Precision Orbit Determination (POD) requirements, the Jason-1 spacecraft carries receivers for DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) and GPS (Global Positioning System), as well as a retroreflector for SLR (Satellite Laser Ranging). The overall orbit accuracy for Jason will depend on the quality and the relative weighting of the available tracking data. In this study, the relative importance of the SLR, DORIS, and GPS tracking data is assessed along with the most effective parameterization for accounting for the unmodeled accelerations through the application of empirical accelerations. The optimal relative weighting for each type of tracking data was examined. It is demonstrated that GPS tracking alone is capable of supporting a radial orbit accuracy for Jason-1 at the 1-cm level, and that including SLR tracking provides additional benefits. It is also shown that the GRACE (Gravity Recovery and Climate Experiment) gravity model GGM01S provides a significant improvement in the orbit accuracy and reduction in the level of geographically correlated orbit errors.

Precise orbit determination for geostationary satellites with multiple tracking techniques

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

Precise orbit determination and rapid orbit recovery supported by time synchronization

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.

Geostationary satellites (GEOs) play a significant role in the regional satellite navigation system. Simulation experiments show that the clock corrections could be mitigated through a single strategy or double differencing strategies for a navigation constellation, but for the mode of individual GEO orbit determination, high precision orbit and clock correction could not be obtained in the orbit determination based on the pseudorange data. A new GEO combined precise orbit determination (POD) strategy is studied in this paper, which combines pseudorange data and C-band transfer ranging data. This strategy overcomes the deficiency of C-band transfer ranging caused by limited stations and tracking time available. With the combination of transfer ranging and pseudorange data, clock corrections between the GEO and the stations can be estimated simultaneously along with orbital parameters, maintaining self-consistency between the satellite ephemeris and clock correction parameters. The error covariance analysis is conducted to illuminate the contributions from the transfer ranging data and the psudoranging data. Using data collected for a Chinese GEO satellite with 3 C-band transfer ranging stations and 4 L-band pseudorange tracking stations, POD experiments indicate that a meter-level accuracy is achievable. The root-mean-square (RMS) of the post-fit C-band ranging data is about 0.203 m, and the RMS of the post-fit pseudorange is 0.408 m. Radial component errors of the POD experiments are independently evaluated with the satellite laser ranging (SLR) data from a station in Beijing, with the residual RMS of 0.076 m. The SLR evaluation also suggests that for 2-h orbital predication, the predicted radial error is about 0.404 m, and the clock correction error is about 1.38 ns. Even for the combination of one C-band transfer ranging station and 4 pseudorange stations, POD is able to achieve a reasonable accuracy with the radial error of 0.280 m and the 2-h predicted radial error of 0.888 m. Clock synchronization between the GEO and tracking stations is achieved with an estimated accuracy of about 1.55 ns, meeting the navigation service requirements.

The Chinese Area Positioning System (CAPS) is a new type of satellite navigation systems. The geostationary satellites for normal communication with 2 or 3 sets of inclined geostationary orbit (GEO) satellites are employed to construct a satellite navigation system. The navigation signals are constructed and disseminated on the ground, and the satellites only transfer the signals to the ground by transponders. Such a system is easy to construct. But for such a positioning system, it needs precise and accurate orbit determination of geostationary satellites. A GEO satellite is placed at an altitude of 36000km above the equator and its movement with respect to the station on the ground is very small, so it is very difficult to determine the orbit precisely. An original method for determination of satellite orbits based on pairs of combined observations is developed at the National Time Service Center, Chinese Academy of Sciences. A special ranging observation with the distance between two stations via a satellite, called pairs of combined observations, is proposed. The satellite behaves with such an observation is not a ball, but an ellipse ball. The Dilution of Precision (DOP) is much less than those methods such as the SLR observation. The advantage of pairs of combined observations is that clock offsets for all observing stations and on-bound are cancelled by the method itself, so, the accuracy and precision of orbit determination is not affected by the clock offsets and the DOP is greatly improved. The ranging signals are generated and measured on the ground, and the instrumentation errors can be determined in real time with a high accuracy. Therefore, such a system is very stable. A very high rate of the PN code is employed, a disseminated power is very low, and it can observe signals from remote stations with a lower power less than 1w. With the spread-spectrum technique, multi-stations can work at the same time and same carrier frequency. It can reach the accuracy of raging about 1 cm. The accuracy and precision of the orbit determination are very high, up to a few centimeters. The observing system with the model proposed above for the GEO satellites including 5 stations (one main station and 4 slave stations) placed in China has been set up. The combined observations were made between the main station and the slave stations. The number of combined observations for the 5 stations is 9. The observations are made per second. The observations for 8 sets of satellites are continuous, lasting for about 5 years. The results for the GEO observations show that the observation residuals of the satellite orbit determination for a 3-day solution are 4.0 cm. With the development of the method to determine the orbit based on the discussion above, it is very easy to correct the orbit with observations nearly in real time. Obviously, the method proposed by the National Time Service Center is suitable for precise orbit determination of GEO satellites in a satellite navigation system, and also it is suitable for satellite management and deep space tracking.

GMV is developing FocusPOD, a suite of tools for POD and geodesy, powered by GMV MAORI, a new GMV in-house Flight Dynamics & Geodesy library, written from scratch in modern C++ and python. FocusPOD supports several projects led by GMV, including the operational provision of Precise Orbit Determination (POD) products of the Copernicus Sentinel satellites in the frame of the CPOD Service, the simulation of tracking data for Galileo 2nd Generation (G2G) System Test Bed, and other space debris and flight dynamics activities.FocusPOD is currently capable of processing GNSS data, with a focus on on-board receivers to support POD, and Satellite Laser Ranging (SLR), mostly used in CPOD as an external orbit validation source. Capabilities to process DORIS have been recently added, also targeting POD applications as a first step. GMV’s roadmap for FocusPOD include processing VLBI in addition to these 3 techniques, with the target of becoming a reference software for the geodesy community.This contribution intends to present FocusPOD roadmap to incorporate VLBI processing capabilities, describing the modelling challenges that have been identified and the various steps that will be taken to finally be able to process VLBI and provide VLBI-based ITRF products. As part of this roadmap, other parallel activities to tie together the rest of the techniques will also be undertaken and described, mostly related to the ground-based processing of GNSS, SLR and DORIS data.

Solar radiation pressure (SRP) is an extremely critical perturbative force that affects the GNSS satellites’ precise orbit determination (POD). Its imperfect modelling is one of the main error sources of POD, whose magnitude is even to10−9 m/s2. The shadow factor (i.e., eclipse factor) is one crucial parameter of SRP, generally estimated by the cylindrical model, the conical model, or shadow models considering the Earth’s oblateness and the atmospheric effect, such as the Perspective Projection Method atmosphere (PPMatm) model and Solar radiation pressure with Oblateness and Lower Atmospheric Absorption, Refraction, and Scattering Curve Fit (SOLAARS-CF) model. This paper applies the former four shadow models to determine the corresponding precise orbit using BeiDou satellites’ ground-based observation, and then compared and assessed the orbit accuracy through Satellite Laser Ranging (SLR) validation and Inter-Satellite Link (ISL) check. The results show that the PPMatm model’s accuracy is equivalent to the SOLAARS-CF model. Compared with the conical shadow model, SLR validations show the orbit accuracy from the PPMatm and SOLAARS-CF model can be generally improved by 2–10 mm; ISL range check shows that the Root Mean Square (RMS) can be decreased by 2–7 mm. These results show that the shadow model in GNSS POD should fully consider the Earth’s oblateness and the atmospheric effect, especially for the perturbative acceleration higher than 10–10 m/s2.Graphical

An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning Sys- tem (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Insti- tute of the University of Bern (AIUB) LEO precise or- bit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numeri- cal integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to effi- ciently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circula- tion Explorer (GOCE).

TianQin project, a Chinese initiative in space gravitational wave detection, demands high precision in satellite orbit during both entry and scientific operations. As means of developmental maturation, ground-based measurements play a vital role in ensuring the smooth execution of TianQin satellite’s detection mission. This paper conducts a simulation analysis by utilizing various ground-based measurement data, including the China Deep Space Network (CDSN), S/Ka-band ranging system, and Satellite Laser Ranging (SLR). The main focus is to explore the distinctions in Precise Orbit Determination (POD) capabilities among different methods and to enhance POD accuracy through the integration of multiple techniques for TianQin satellites. The results indicate: (1) Leveraging a strategically positioned station distribution, CDSN stations offer extended observation time, averaging 17.3 h per satellite daily, compared to S/Ka’s 10.5 h. (2) In single-measurement POD scenarios, S/Ka proves superior, achieving accuracy better than 10 m and 0.4 mm s−1 for TianQin satellites with a 7-day orbit arc length. This superiority is attributed to its exceptional observational accuracy, outperforming CDSN’s 40 m and 2.2 mm s−1 for POD accuracy. (3) By integrating high-precision SLR data on the foundation of CDSN or S/Ka observations, the POD accuracy of TianQin satellites is further enhanced, despite the limited SLR data quantity.