Galileo POD using optical inter-satellite links: A simulation study

Precise orbit and Earth parameter determination supported by LEO satellites, inter-satellite links and synchronized clocks of a future GNSS

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.

Spacecraft orbit propagator integration with GNSS in a simulated scenario

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.

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.

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.

A novel method, which is based on the triple-frequency combination and Space-Based Telemetry, Tracking, and Command (STT&C) stations, is proposed in this paper. Considering BeiDou Navigation Satellite System (BDS) Geostationary Orbit (GEO) and Inclined Geostationary Orbit (IGSO) satellites as the STT&C facilities, firstly, we presented the BDS Medium Earth Orbit (MEO) satellites’ precise orbit determination scheme based on triple-frequency combination. Then, we gave the sufficient and necessary conditions about the visibility and the coverage rate calculation model of STT&C to BDS MEO satellite. And then we deduced the model of BDS MEO satellites precise orbit determination based on triple-frequency combination observations. At last, we designed the simulation calculation. The simulation results show that orbit determination of BDS MEO satellite based on STT&C station can be realized at all times. And most of the simulation period time, under the condition of the dm level orbit determination for GEO/IGSO satellites, the position accuracy of the relative orbit determination is better than 4 m, the horizontal accuracy of the relative orbit determination is within 2.5 m, and the vertical accuracy of the relative orbit determination is less than 3.5 m.

Owning to some successful applications of RDSS and RNSS, keeping GEO satellites in BeiDou Navigation Constellation becomes one of the key differences between BDS and other Global Navigation Satellite Systems (GNSS). And for the first time, BDS GEO works as a node of Inter-Satellite Links. It makes precise orbit determination (POD) based on Inter Satellite Ranging (ISR) for GEO possible. Orbit, hardware delay and solar radiation pressure parameters are estimated in POD process. Mean value of estimated hardware delay is 1189.18 ns and STD is 0.15. RMS of post-fit residuals of ISR, between 10 of 18 MEO satellites and GEO satellite is less than 45 cm, and that between the other 8 MEO satellites and GEO satellite is less than 56 cm. RMS of GEO 48-h OOD is no greater than 2.4 m in position and no greater than 0.2 m in radial direction.

Extension of the BDS IGSO and MEO satellite antenna patterns with FengYun-3C and LuTan-1 onboard data

Global Navigation Satellite System (GNSS) Radio Occultation measurements can remote sensing Earth's neutral atmosphere and ionosphere. Meanwhile, another GNSS remote sensing technique named GNSS Reflectometry (GNSS-R) has been developed rapidly, which can retrieve sea surface wind speed. The GNSS Occultation Sounder (GNOS) II instrument has been designed to integrate these two GNSS remote sensing techniques in one payload of the third batch FengYun-3 (FY-3) satellites. This paper presents the advancements in research of GNOS II and instrument performance. The qualified module of GNOS II has been manufactured by National Space Science Center (NSSC), Chinese Academy of Sciences. We show that the phase center variety is low enough for the new designed precise orbit determination (POD) antenna to increase the accuracy of precise orbit determination. A wide coverage atmosphere occultation antenna and a 65nm technics ASIC are used in the new generation GNOS instrument. As an important improvement, the GNOS II can generate Delay Doppler Maps (DDMs) of GNSS signals scattered from the ocean surface. The result of test shows that the GNOS II instrument has high performance in precision of code, carrier phase and real-time navigation.

Abstract. Utilizing ground control points (GCPs) to georeference photogrammetry-based point cloud data is a common practice in unmanned aerial system (UAS) mapping. Direct georeferencing or integrated sensor orientation (ISO) can be used to obtain georeferenced point clouds from UAS without relying heavily on GCPs. However, the accuracy of the point cloud may be impacted by the accuracy of the trajectory solution obtained by GNSS. To improve point cloud accuracy, post-processing kinematic (PPK) solutions can be applied to the UAS trajectory, which may provide higher accuracy than low-accuracy trajectory solutions and minimize the reliance on GCPs. This study compares the accuracy and precision of two different point clouds generated using different methods. One point cloud was generated using traditional photogrammetric methods with low accuracy Global Navigation Satellite System (GNSS) observations from the UAS and GCPs that have an average accuracy of one to two centimeters, while the other was generated using PPK trajectory solution for the UAS’s trajectory with two software: open-source Emlid Studio and the widely used Inertial Explorer. The use of PPK techniques in UAS mapping may have several potential benefits over traditional methods. By correcting the errors in the UAS's trajectory, a user may only need to depend on fewer ground control points, which can reduce the time and cost associated with fieldwork. This is particularly useful in areas that are difficult to access or have limited ground control point options, such as in urban or forested areas. To evaluate performance, a GNSS receiver is used to obtain measurements on checkpoints, which are used to assess the accuracies of the point clouds. In our experiments, the accuracy of the point clouds generated using PPK trajectory solution with high accuracy GCPs was found to be higher than those generated with low accuracy GNSS observations while aided with high accuracy ground control points. While the use of PPK with GCPs is generally expected to provide more accurate and reliable data than low-accuracy GNSS observations even after adjusting with GCPs, the number and distribution of GCPs can still significantly impact overall accuracy. Therefore, careful consideration of the number of GCPs and their placement is essential to achieve the desired level of efficiency and effectiveness in UAS mapping.

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.

Many sophisticated Global Navigation Satellite System (GNSS ) applications require high-precision satellite orbit and clock products. The GNSS orbits and clocks are usually derived from the analysis of tracking data collected by a globally distributed GNSS receiver network. The estimation process adjusts parameters for the satellite orbits, transmitter and receiver clocks, station positions, tropospheric delays, Earth orientation, intersystem and interfrequency biases, and carrier-phase ambiguities. The estimation requires detailed modeling of geophysical processes, atmospheric and relativistic effects, receiver tracking modes, antenna phase centers, spacecraft properties, and attitude control algorithms. This chapter describes precise orbit and clock determination of the GNSS constellations as performed by the analysis centers of the International GNSS Service, including models, estimation strategies, products, and the combination of orbit and clock solutions.

Global Navigation Satellite Systems (GNSS) rely on one-way signal travel time measurements from satellites to receivers. To ensure accurate ranging, GNSS must estimate and compensate for clock offsets on at least one end of the transmitter-receiver system. Consequently, clock offsets are highly correlated with GNSS-derived parameters such as station coordinates, tropospheric delay estimates, satellite radial orbit parameters, and apparent geocenter coordinates. Improper handling of clock offsets can lead to their absorption into these parameters, degrading geodetic product accuracy. Traditionally, clocks have been handled within individual techniques without being specially addressed. However, some research efforts and experimental trials have explored using VLBI to synchronize clocks for GNSS and refining clock models to reduce correlations with other estimated parameters in GNSS, thereby improving overall precision.With recent advancements, high-precision optical clocks and fiber-optic time transfer technologies provide new possibilities for enhancing clock synchronization in GNSS. Optical fiber offers a stable, interference-free medium for time and frequency transfer, eliminating atmospheric effects such as ionospheric and tropospheric delays that impact GNSS-based synchronization. Moreover, fiber-optic time transfer is inherently two-way, removing the need for external clock offset estimation. Thus, fiber-optic clock synchronization represents the most precise timing technique currently available. Establishing a common clock by connecting multiple GNSS receivers via optical fiber could significantly reduce the number of estimated clock parameters in GNSS solutions, leading to improved geodetic measurement precision and a more accurate geodetic reference frame.Despite its potential, the approach of implementing a common clock with optical fiber for GNSS receivers remains largely untested. Although optical fiber links have been successfully used in clock synchronization, their integration into GNSS receiver clocking is still in an experimental stage. Notable existing efforts include: (1) the Geodetic Observatory Wettzell, where multiple receivers are connected to a single clock via optical fiber, representing a local baseline setup, and (2) the GFZ experiment, where a receiver is linked to the ultra-stable clock of PTB, representing a regional baseline approach.This study characterizes existing fiber-optic connections among GNSS receivers to identify practical challenges and evaluate their impact on GNSS parameter estimation. We process data from receivers sharing a common clock using Bernese GNSS Software. Initially, PPP will be performed to compare GNSS-derived clock parameters across receivers sharing a common clock, verifying the effectiveness of fiber-optic clock synchronization. Following this validation, we will leverage GNSS-derived clock parameters to evaluate inter-receiver clock differences measured via optical fiber. Subsequently, we will implement a strategy in which only one receiver’s clock parameters are estimated, using fiber-measured clock differences as a priori constraints for other receivers in the PPP solution. This approach reduces the number of estimated clock parameters and serves as a preliminary test of the feasibility of a GNSS common clock framework.Future developments will focus on refining our analysis framework to enable simultaneous estimation of GNSS receivers operating under a common clock. This research contributes to the broader goal of integrating ultra-stable clocks into global GNSS networks, ultimately enhancing the stability of geodetic reference frames and improving GNSS-derived geodetic products.

Abstract. Tropospheric delay has always been an important issue in Global Navigation Satellite System (GNSS) processing. Empirical tropospheric delay models are difficult to simulate complex and volatile atmospheric environments, resulting in poor accuracy of the empirical model and difficulty in meeting precise positioning demand. In recent years, some scholars proposed to establish real-time tropospheric product by using real-time or near-real-time GNSS observations in a small region, and achieved some good results. This paper uses real-time observing data of 210 Chinese national GNSS reference stations to estimate the tropospheric delay, and establishes ZWD grid model in the country wide. In order to analyze the influence of tropospheric grid product on wide-area real-time PPP, this paper compares the method of taking ZWD grid product as a constraint with the model correction method. The results show that the ZWD grid product estimated based on the national reference stations can improve PPP accuracy and convergence speed. The accuracy in the north (N), east (E) and up (U) direction increase by 31.8 %,15.6 % and 38.3 %, respectively. As with the convergence speed, the accuracy of U direction experiences the most improvement.