Genesis satellite.

The combination of advanced technologies for precise orbit determination and timing, as well as the scientific exploitation of GNSS signals, opens major new opportunities for relevant, innovative in-orbit scientific experiments. These opportunities come in the fields of Earth sciences, including geodesy, geophysics and GNSS remote sensing of the atmosphere, land, ocean and ice, fundamental physics, astronomy and time metrology. They could extend some current operational applications such as precise orbit determination for geodesy and altimetry and GNSS radio occultation for meteorology and space weather.

To further enhance the benefits of combining space-based geodetic techniques, the European Space Agency (ESA) has established the Genesis mission. The mission will collocate on board a single well-calibrated satellite, the four space-based geodetic techniques: GNSS, very long baseline interferometry (VLBI), satellite laser ranging (SLR) and Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS). This first-time-ever collocation in space will establish precise and stable ties among these key techniques. The Genesis satellite will be a unique, dynamic space geodetic observatory, whose observations, combined with the measurements using geodetic collocation techniques stations on Earth, will contribute to a significant improvement of the International Terrestrial Reference Frame (ITRF).

The ITRF is recognized as the foundation for all space- and ground-based observations in Earth science and navigation, and therefore this mission will potentially have a major impact on several GNSS and Earth observation applications. It is a particular realization of the terrestrial reference system, and its history goes back to 1984 when the former Bureau International de l’Heure, which was then in charge of maintaining an accessible reference frame, established a frame using space-based geodetic techniques. The tradition was continued by the International Earth Rotation and Reference Systems Service (IERS) when it was established in 1987. The IERS has periodically updated the ITRF incorporating new systems, data sets and analysis procedures. The Genesis mission will help identify any systematic errors in the ITRF and thereby improve the accuracy and stability of the frame, particularly the origin and scale of the frame, which are the most critical parameters for scientific applications.

The Genesis mission was endorsed by the ESA Ministerial Council in November 2022. The mission will be executed under the responsibility of ESA’s Navigation Directorate as an element of the Future Navigation Program in cooperation with ESA’s Operations Directorate.

ESA performed an internal mission feasibility study (a so-called concurrent design facility) in March and April 2022. A team of more than 40 experts reviewed the mission objectives and the possible implementation, derived high-level mission requirements, assessed the necessary mission instruments and their technology readiness level and concluded that the mission is feasible and compatible with the Genesis-defined program boundaries.

GENESIS MISSION OBJECTIVES

The overall mission goal, as defined by the Global Geodetic Observing System (GGOS) initiative of the International Association of Geodesy, is to help achieve an ITRF accuracy of 1 millimeter with long-term stability of 0.1 millimeters per year, to be able to detect the smallest variations in the Earth system solid, fluid and gaseous components.

Figure 1: Genesis mission concept.

The improvements of the ITRF will impact and improve multiple geodetic and geophysical observables, as well as precise navigation and positioning, and strengthen the geodetic infrastructure, including the Galileo constellation, by reducing the systematic biases between different observing techniques.

Furthermore, the Genesis mission will allow us to improve the link between the ITRF and the International Celestial Reference Frame (ICRF) due to improvement in determining the Earth orientation parameters (EOPs). The ICRF is a realization of a quasi-inertial reference system defined by extragalactic radio sources, mostly quasars, billions of light years away. The positions of a set of globally distributed VLBI radio telescopes are determined using the difference in the arrival times of the signals at the different telescopes. The ICRF was established and is maintained through a cooperation between the International Astronomical Union and the IERS.

The ITRF and the ICRF are related through the EOPs, which include pole coordinates, the Earth’s rotation angle typically referred to as Universal Time (and the related length of day), and nutation angles and their rates.

GENESIS MISSION OVERVIEW

Figure 2 Genesis project organization.

The baseline orbit of the Genesis satellite will be circular, will have an altitude of about 6,000 kilometers and an inclination of about 95 degrees. The mass of the satellite will be on the order of 250 kilograms to 300 kilogramsg, and it will have very precise on-board metrology, through a single ultra-stable oscillator. An artist’s conception of the satellite in space is shown in the opening image. The launch is foreseen for 2028, and the baseline duration for operations is two years with an option for extension.

The Genesis mission architecture will consist of the Genesis satellite, a ground control segment constituted by a mission control center and a (network of) ground station(s), a data processing center (including a global GNSS sensor station network), a data archiving and distribution center, and the required ground infrastructure for the VLBI, SLR and DORIS campaigns (See FIGURE 1). The scope of the procurement for this mission is the Genesis satellite, the ground control segment, the launch service and two years of operations with the option for extension.

As previously mentioned, the satellite will be launched as the first with all four space-based geodetic techniques on board — namely GNSS, VLBI, SLR and DORIS:

• GNSS receiver. This will be a high-quality multi-constellation (Galileo and GPS) and multi-frequency space receiver. The GNSS observations will be of very high quality and will allow multi-GNSS integer ambiguity resolution for the carrier phase with a very high success rate. This instrument is crucial for the very precise orbit determination of the Genesis satellite.
• VLBI. This instrument will transmit radio signals compatible with receivers at each observing VLBI station. To eliminate the ionospheric dispersive delay along the paths to each station, different frequency bands will be used. The signals will also comply with the evolving observation procedures at all VLBI stations. The signals will be observed by all geodetic VLBI antennas, including the new VLBI Global Observing System (VGOS) fast slewing stations, in their standard geodetic receiver setups. The transmitter currently under development is designed to transmit at different frequencies between 2 GHz and 14 GHz, but also higher frequency bands can be considered. The present setup for regular VGOS observations use four 1-GHz-wide bands within the S, C and X frequency bands. The unit is designed to transmit both pseudo-noise and random noise. The random noise signal mimics the broader-band noise emitted by quasar radio sources routinely observed by VLBI, and hence can be processed essentially by the usual station and correlator software. VLBI observations of Genesis will enable VLBI stations to be accurately located within the ITRF consistently with the other geodetic techniques, enable a frame tie between the celestial frame and the dynamic reference frames of satellite orbits as well as a frame tie between the ITRF and the extremely accurate and stable ICRF.
• SLR. A passive SLR retro-reflector (LRR) will be attached to the satellite in such a way to ensure an adequate field of view when the satellite is in Earth-pointing mode. The SLR observable is the round-trip time of flight of a laser pulse between a ground station and the LLR. Currently, the ITRF long-term origin is defined by SLR, and this is the most accurate satellite technique in sensing the Earth’s center of mass.
• DORIS. Genesis will include a DORIS receiver instrument. DORIS is based on the principle of the Doppler effect between a network of transmitting terrestrial beacons and the on-board instrument. DORIS was first featured on the SPOT-2 satellite launched in 1990. Since then, DORIS receivers have been featured on multiple satellites. The integration of the DORIS receiver on Genesis, given the high-precision knowledge of the Genesis orbit, will benefit other space geodetic techniques from the global DORIS network distribution.

All active instruments will rely on a single high-precision compact frequency standard payload, termed the ultra-stable oscillator.

GENESIS PROJECT ORGANIZATION

The Genesis mission is being procured in an end-to-end approach, meaning that the industry prime is responsible for the development of the satellite, including the payload instruments, the launch services and the satellite operations. For this reason, the following approach has been applied: contract signature was in March 2024. Design, development, validation and acceptance will take place between 2024 and 2027, leading up to a planned launch in 2028.

The contract for Genesis amounts to € 76.6 million. A consortium of 14 entities led by OHB Italia S.p.A. has been tasked with developing, manufacturing, qualifying, calibrating, launching and operating the Genesis satellite, including all its payloads. The mission is supported by Italy, Belgium, France, Switzerland, Hungary and the United Kingdom.

Figure 3 Processing, archiving and distribution of Genesis data and products.

The overall project organization is outlined in FIGURE 2. The ESA Genesis project team, led by the project manager, will manage and coordinate the work of all interfaces among i) the industrial consortium, ii) ESA in its role of handling data processing, archiving and operating the distribution center, iii) the scientific community for whatever the necessary interface is required for the preparation of scientific exploitation and coherency between the project development and the scientific mission objectives.

For the data processing, exploitation, archiving and dissemination of data to the scientific community, the PROcessing, Archiving, exploitation and Dissemination Centre (PROAD) has been set up, (See FIGURE 3), using the European Space Operations Centre (ESOC) Navigation Support Office facilities and the GNSS Science Support Centre (GSSC) of the European Space Astronomy Centre (ESAC).

For the data processing required in advance of scientific exploitation of the data, the ESOC Navigation Support Office facilities will be used. The data processing includes the precise orbit determination for the GENESIS satellite.

Figure 4 Genesis science team.

Furthermore, after the processing performed by ESOC, ESAC’s GSSC will be used for data archiving and data distribution for scientific exploitation. The PROAD will be set up and coordinated internally in ESA.

The setup and coordination of the required ground infrastructure, VLBI and SLR campaigns, the DORIS network and so on, will be managed by ESA’s Genesis project team together with a Genesis science team (See FIGURE 4).

The science team will also support ESA’s Genesis project team as required in the reviews and follow-up activities, especially with respect to compliance with the mission objectives.

SUMMARY

The Genesis mission is a very challenging one, which has been made possible by the combined effort from the scientific community, ESA member states, industry and ESA itself. The success of Genesis will strongly depend on the interaction, cooperation and support of the international scientific community. The mission objectives of Genesis address core scientific as well as societal aspects. Above all, the Genesis mission is at the foundation level of all positioning and navigation.

ACKNOWLEDGEMENTS

This article has drawn, in part, on the multi-author paper “GENESIS: co-location of geodetic techniques in space,” Earth, Planets and Space (2023), Vol. 75, No. 5, https://doi.org/10.1186/s40623-022-01752-w

<p>The post Innovation: ESA’s multi-modal space mission to improve geodetic applications first appeared on GPS World.</p>

Photo: Government of Japan

In early 2015, the Navigation Support Office of the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA) began a collaboration. At its core, the ESA-JAXA collaboration is designed to cross-validate Japan’s Quasi-Zenith Satellite System (QZSS) Precise Orbit Determination (POD) results and share expertise to improve the POD accuracy of QZSS.

The cross-validation of the QZSS POD performance was implemented by jointly analyzing QZSS observations and validating the POD results of the QZSS satellites. As a result of this joint activity, ESA and JAXA have significantly improved the robustness and accuracy of their respective POD products. This collaborative approach not only ensures the continuous improvement of QZSS force modeling and precise orbit determination performance but also demonstrates the effectiveness of international cooperation in advancing the field of space navigation, especially as the benefits of GNSS interoperability become very evident.

An important milestone in this collaboration was ESA’s role in supporting the In-Orbit Testing (IOT) activities for QZS-1R towards the end of 2021. The successful execution of these tests demonstrated the practical results of the ESA-JAXA partnership and further solidified the commitment of both agencies to enhance their capabilities for QZSS POD and associated products.

FIGURE 1 ESA’s Solar Radiation Pressure (SRP) model output in satellite-Sun frame.

The benefits of this collaboration extend beyond the agencies to the entire scientific community. Notable achievements include the revision of metadata for the QZSS constellation, such as the optical properties of the QZS-1 solar arrays, which have been refined and improved through shared expertise, while simultaneously releasing the satellite mass and attitude mode history in a machine-readable file format for easy access and adoption by the users.

To evaluate the spacecraft models and metadata for QZS-1R prior to their public release, ESA and JAXA conducted several comparative tests. Since both organizations use different software packages for satellite POD — ESA uses NAPEOS (Dow, Springer 2009, Enderle et al., 2019 and 2022) and JAXA uses MADOCA (Kawate et al., 2023) — their results can be considered as largely independent. One comparison involved the Solar Radiation Pressure (SRP) model results produced by both organizations. FIGURE 1 shows the accelerations in satellite-Sun frame computed by ESA’s SRP model. The comparison of the computed SRP accelerations in different reference frames, spacecraft-fixed and inertial, showed excellent agreement with differences of less than 0.1 nm/s².

FIGURE 2 One-way Satellite Laser Ranging (SLR) range residuals calculated with respect to QZS- 1R orbits generated with (green) and without (blue) a-priori radiation force models and displayed as function of the Earth-Probe-Sun angle.

In addition, pseudo-range and carrier phase dual-frequency measurement data from 200 tracking stations of the International GNSS Service (IGS) network were used to generate precise QZS-1R satellite orbits and clock offsets on a day-to-day basis over a 12-month period spanning from January to December 2022. Comparison between ESA and JAXA solutions yielded a root-mean-square (RMS) agreement of 8.6 centimeters (orbit) and 0.21 nanoseconds (clock), respectively. Analysis of Satellite Laser Ranging (SLR) data from seven stations of the International Laser Ranging Service (ILRS) suggests a radial RMS accuracy of the generated orbital trajectories of about 4 cm. Without applying the analytical models for SRP and other non-gravitational perturbation forces, such as antenna thrust (AT), the RMS accuracy decreases by a factor of five (FIGURE 2).

In conclusion, the ESA-JAXA collaboration on Japanese Quasi-Zenith Satellite System POD has been a resounding success. Through this continuous and mutual support, performance cross-validation and knowledge sharing, significant improvements related to modeling and subsequently to POD accuracy could be achieved for ESA as well as for JAXA. Additionally, the global scientific community benefitted from this ESA/JAXA collaboration via improved QZSS POD products and validated metadata.

Figure 1 and 2 courtesy of the authors

<p>The post Research Report: Advancing precision in navigation first appeared on GPS World.</p>

To produce GNSS satellite orbit ephemerides and clock data with high precision and for all constellations, the Navigation Support Office of the European Space Agency’s European Space Operations Centre (ESA/ESOC) continually strives to keep up and improve its precise orbit determination (POD) strategies. As a result of these longstanding efforts, satellite dynamics modeling and GNSS measurement procedures have progressed significantly over the last few years, especially those developed for the European Galileo satellites. Because the accuracy of ESA/ESOC’s GNSS orbits has reached such a high level (about 1 to 3 centimeters), introducing a completely new type of GNSS satellite into the processing is not as easy as it used to be. New spacecraft models – the first and foremost being a model for a satellite’s response to solar radiation pressure (SRP) – are needed for the “newcomer” so that the quality of the overall multi-GNSS solution does not suffer. Just as important are spacecraft system parameters, or metadata, such as the location of the satellite antenna’s electrical phase center and the satellite attitude law.

In this article, we show the efforts we have made at ESA to bring the quality of our orbit estimates for the GPS Block III satellites up to par with those for Galileo and the earlier GPS satellite blocks. We report on the results from on-ground and in-flight determinations of the Block III transmit antenna phase center characteristics up to 17 degrees from the antenna boresight direction. Moreover, we take advantage of the non-zero horizontal offsets of the transmit antenna from the spacecraft’s yaw axis to estimate the satellite yaw angle during Earth eclipse season and present a simple analytical formula for its calculation. Finally, we describe the development and validation of improved radiation force models for the Block III satellites.

We start, however, by giving a brief overview of the GPS Block III program.

GPS BLOCK III

The U.S. Space Force GPS Block III (previously referred to as Block IIIA) is a series of 10 satellites being procured by the United States to bring new future capabilities to both military and civil positioning, navigation, and timing (PNT) users across the globe. Designed and manufactured by defense contractor Lockheed Martin (LM), the satellites are reported to deliver three times better accuracy, 500 times greater transmission power, and an eightfold enhancement in anti-jamming functionality over previous GPS satellite blocks. At ESA/ESOC, we are paying particular attention to this new tranche of satellites as they are the first to broadcast L1C, a new common signal interoperable with other GNSS, including Galileo.

At the time of this writing, there are six GPS III space vehicles (SVs) in orbit. The first one – nicknamed “Vespucci,” in honor of Italian explorer Amerigo Vespucci – lifted off atop a SpaceX Falcon 9 rocket from Cape Canaveral Air Force Station, Florida, in December 2018, and entered service on January 13, 2020. An additional four SVs are expected to be launched soon, before moving on to an updated version called GPS IIIF (“F” for Follow On). The first Block IIIF satellite is projected to be available for launch in 2026.

In view of the growing number of GPS III SVs in orbit, and soon to be joined by IIIFs, accurate spacecraft models and metadata information are becoming more and more important in order to maximize PNT accuracy.

SATELLITE ANTENNA PHASE CENTER PARAMETERS

GNSS signal measurements refer to the electrical phase center of the satellite transmitting antenna, which is neither a physical nor a stable point in space. The variation of the phase center location as a function of the direction of the emitted signal on a specific frequency is what we call the phase center variation (PCV). The mean phase center is usually defined as the point for which the phase of the signal shows the smallest (in a “least-squares” sense) PCV.

Figure 1: Ground-calibrated GPS Block III transmit antenna phase center variations (PCVs). (All figures provided by the authors).

The point of reference for describing the motion of a satellite, however, is typically the spacecraft center of mass (CoM). The difference between the position of the mean phase center and the CoM is what we typically refer to as the satellite’s antenna phase center offset (PCO). Both PCO and PCV parameters must be precisely known — from either a dedicated on-ground calibration or one performed in flight — so that we can tie our GNSS carrier-phase measurements consistently to the satellites’ CoM.

On-Ground Calibrations. Like for previous GPS vehicles, the Block IIR and Block IIR-M satellites, LM has fully calibrated the GPS III transmit antennas prior to launch at their ground test facilities. Antenna offset parameters for all three carrier signals (L1, L2 and L5) were posted on the U.S. Coast Guard Navigation Center (NAVCEN) website (www.navcen.uscg.gov) shortly after each satellite launch. In December 2021, NAVCEN released the PCOs for SV number (SVN) 78, along with updates to the first four satellites (see Table 1). About ten months later, in October 2022, the antenna pattern for each satellite and signal frequency were published (see Figure 1).

Table 1: Ground-calibrated GPS Block III transmit antenna PCOs in millimeters. (Image: GPS World staff)

The December 2021 offsets are referred to as predicted values at the end of year one on orbit. They differ from the previous ones by several centimeters in both vertical (Z) and horizontal (X and Y) directions. Particularly surprising are the X- and Y-PCOs, which were initially reported to be close to zero. The differences in the horizontal PCOs have generated uncertainty and debate, especially within the International GNSS Service (IGS) about which values to adopt for the new antenna model release (igs20.atx). Testing of the two different PCO datasets in our software demonstrated that the non-zero values as given in Table 1 are the significantly more accurate ones. We will return to this later in this article.

Combined Ground- and Space-Based Tracking. In this part of this article, we discuss the combination of dual-frequency tracking data from geodetic-quality GPS receivers in low Earth orbit (LEO) with those from a global receiver network on the ground to determine the phase center parameters of the GPS Block III transmit antennas. The LEO-based measurements were taken by the GNSS receivers on board the ocean altimetry satellites Sentinel-6 Michael Freilich and Jason-3. The 1,336-km altitude of both of these missions enables the estimation of the GPS satellite antenna PCVs from 0 up to 17 degrees from boresight while GPS receivers on Earth can only see the satellites up to a maximum angle of 14 degrees. The 14-degree limit is also referred to as the GPS satellites’ edge of Earth (EoE) angle.

For the modeling of the PCVs we follow the approach of the IGS using piece-wise linear functions of the boresight angle and constraining the PCV values to between 0 and 14 degrees to have zero mean. Furthermore, we employ fully normalized spherical harmonic expansions of degree 8 and order 5 to solve for the azimuth- and elevation-angle-dependent PCVs of the orbiting receiver antennas. The IGS standard antenna phase center corrections from igs20.atx are applied to all terrestrial receiver and GPS Block II transmit antennas.

Figure 2: GPS Block III transmit antenna PCVs as a function of boresight angle. The gray shaded area indicates the angular range that is inaccessible from the ground but relevant to high altitude LEO missions such as Sentinel-6 Michael Freilich or Jason-3.

The estimated Block III antenna PCVs are depicted in Figure 2. The estimates for the five individual antennas match each other to within 0.4 millimeters root-mean-square (RMS) (see Figure 2, top). The agreement among the PCVs that we get when processing the tracking data from each LEO receiver’s antenna separately is at the sub-millimeter level, too (see Figure 2, middle). Overall, the level of consistency suggests that the PCVs are of very good quality and that a block-specific representation is sufficient for precise applications. Comparison of the final block-specific PCV estimates against the values from the current IGS antenna model and from the ground calibrations shows strong agreement (RMS = 0.7 millimeters) between 0 and 14 degrees from boresight (see Figure 2, bottom). Beyond the 14-degree limit, the differences compared to the IGS standard are up to three centimeters, underlying the urgent need for an update of the igs20.atx file.

Applying the extended PCV corrections as part of the POD process to the GPS LEO receiver data shows significant improvement in the post-fit carrier-phase residuals when compared to the PCV corrections from the IGS legacy model. It removes a previously existing boresight angle-dependent trend and leads to a more than 20% reduction in the computed residual RMS (see Figure 3).

Figure 3: Post-fit residuals of GPS III carrier-phase data from Sentinel-6 Michael Freilich when using igs20.atx (top) and esa22.atx (bottom), respectively.

YAW MODELING

Figure 4: Yaw turn maneuver of GPS Block III satellite SVN 78 near orbit noon (top) and orbit midnight (bottom), respectively.

GNSS satellites cannot follow an ideal yaw-steering whenever the Sun elevation angle relative to the orbital plane (the so-called beta angle) gets too low and the yaw rate required to keep the satellite solar panels pointing towards the Sun exceeds the maximum satellite yaw rate. The strategies on how GNSS satellites perform rate-limited yaw-steering are different for each type of spacecraft and only partly documented for public users. Continuous knowledge of GNSS spacecraft yaw attitude, however, is important for kinematic and dynamic reasons. Errors in yaw are known to affect the modeling of transmit antenna phase center’s position, carrier-phase wind-up, and radiation pressure forces. On the other hand, when the mean antenna phase center location is offset from the spacecraft’s Z-axis, the satellite yaw state can be estimated instantaneously from the tracking data of a global receiver network. The approach behind this is commonly referred to as “upside down” or “reverse kinematic precise point positioning” (RPP). The horizontal antenna offset vector can be viewed here as a kind of rotating lever arm whose length determines the accuracy of the yaw angle estimates. Since the Block III X-offset is just 7 centimeters, one should not expect the same RPP accuracy as for other GNSS satellites like those of the GPS IIF or GLONASS-M series, which have an X-offset that is six (GPS IIF) or even eight (GLONASS-M) times larger.

Nonetheless, with more than three hundred ground stations, kinematic RPP works reasonably well even for GPS III as we can see from Figure 4, which shows the estimated yaw angle of SVN 78 while passing orbit noon and orbit midnight with a Sun elevation angle of almost zero degrees. The plots suggests that Block III satellites — unlike previous Block IIA and IIF SVs — perform their yaw slews near noon and near midnight in the same way and at the same yaw rate. In this respect, the yaw turn behavior is similar to that of the IIR/IIR-M satellites. However, with a maximum yaw rate of 0.10 degrees per second, the Block III satellites rotate only half as fast as those of the IIR/IIR-M family. What is also different is the start time of the yaw maneuver. As can be seen from Figure 4, the maneuver does not start when the required yaw rate exceeds the physical limit but already a couple of minutes before.

The RPP analysis has led to the development of a simple yaw model for the Block III satellites. For a Sun elevation angle β below β₀ = 4.780 degrees, the yaw angle can be approximated with an RMS accuracy of about 8 degrees by the following formula:
whereas

is a modified Sun elevation angle, SIGN(β₀, β) a FORTRAN function returning the value of β₀ with the sign of β, and η is the satellite’s argument of latitude with respect to orbit midnight. The agreement between estimated and modelled yaw angles is illustrated in Figure 5.

Figure 5: Differences between yaw angle estimates and yaw angle models.

Fourier Series for Radiation Force Modeling. The most critical component determining the shape of a GNSS satellite’s trajectory is SRP – the force caused by the impact of solar photons hitting the satellite’s surfaces. A satellite’s sensitivity to SRP can be characterized by the variation of the cross-sectional area to mass ratio (A/M) of the satellite body as it orbits Earth and the Sun. The greater the change in A/M, the higher the sensitivity. From this perspective, the Block III spacecraft can be considered the most sensitive in GPS history.

Based upon LM’s tried-and-true A2100 bus, the satellite is much more elongated than previous generations. With an estimated size of 7.5 meters squared, the X-side is almost twice as large as the Z-side. Depending on the elevation angle of the Sun relative to the orbital plane, the body’s cross-sectional area exposed to sunlight varies between 4.0 and 8.5 meters squared (See Figure 6). With a nominal on-orbit weight of approximately 2,160 kilograms, this results in a change of A/M of 0.0021 meters squared per kilogram. For comparison, the corresponding values for the previous GPS SVs are 0.0015 (IIF), 0.0017 (IIR), and 0.0013 (IIA) meters squared per kilogram.

Figure 6: Size of GPS satellite body’s cross-sectional area exposed to sunlight.

Given the size and shape of Block III spacecraft, an appropriate radiation force model is considered mandatory to achieve the highest orbit accuracy possible. With that said, we empirically derived a set of background force models for the first five GPS III satellites. Our approach rests on dynamical long-arc (9-day) fitting to precise orbit data spanning up to three years and the following low-order Fourier functions of the Earth-spacecraft-Sun angle ε to represent the radiation force in the satellite body-fixed system:

The Fourier coefficients (XS1, XS2, XS3, YC2, ZC1, ZS2 and ZS4) are iteratively adjusted together with initial epoch state, a constant Y-axis bias, and 1‐cycle per revolution along‐track parameters to best fit the orbit data in a least-squares sense. All individual 9-day arc solutions are rigorously combined on a normal equations level to form a robust set of Fourier model coefficients for each satellite or group of satellites.

ORBIT OVERLAP TESTS

Figure 7: Impact of horizontal antenna PCOs and Fourier force model on day-boundary orbit overlap errors.

To investigate the effect of the transmit antenna PCOs and the Fourier force models on the satellite orbits, we use our ESA/IGS processing strategy to generate dynamic 24-hour-arc solutions spanning January 2020 to December 2022, first with zero PCO and the non-zero horizontal offsets from Table 1 and no a-priori radiation force model, then with the non-zero offsets and the additional Fourier model in the background. The direct comparison of the generated orbits reveals significant differences for the Block III satellites of about 0.1 meters (3D).

To demonstrate the improved performance of the non-zero offsets and the Fourier model, we take the orbits for successive days and look at the midnight epoch where they overlap. The difference in the orbit position, subsequently referred to as “overlap error,” gives us a worst case estimate of the satellite orbit accuracy. Comparison of the overlap errors provides evidence that the Block III orbits are much more accurate when using the non-zero rather than the zero X and Y PCOs. The overall 3D overlap RMS reduces from 49.5 millimeters (with zero PCOs) down to 32.3 millimeters (with non-zero PCOs). Results for the Sun elevation regions below 45 degrees, in particular, show significant improvement (see Figure 7).

Use of the Fourier model has additional positive impact on the overlaps. Comparing the orbits produced with and without the a-priori radiation force model, we see a decrease in the 3D overlap error RMS from 32.3 to 29.7 millimeters averaged over all satellites. The orbit component that benefits most from both the improved antenna phase and the advanced force modeling is the one normal to the satellite orbital plane (across track). The SVs improving the most are SVN 75 and SVN 78, though significant improvements can be seen for all other satellites too (see Table 2).

Table 2: Day-boundary overlap RMS errors of GPS III spacecraft orbits in millimeters.

EMPIRICAL PARAMETER ESTIMATES

Another means of assessing the quality of spacecraft models is the size and variability of the five-plus-three empirical dynamic radiation pressure parameters that we still estimate on a daily basis for each GNSS satellite in addition to its a-priori force model. Introducing the non-zero PCO and Fourier models into the POD turned out to reduce the size of the empirical parameters and their dependency on the satellite-Sun geometry to a great extent as the example in Figure 8 demonstrates.

Figure 8: Impact of horizontal antenna PCOs and Fourier force model on empirical once-per-revolution acceleration term BC.

NARROW-LANE AMBIGUITY FRACTIONALS

Integer ambiguity resolution — that is, resolving the unknown cycle ambiguities of double-differenced carrier-phase data to integer values — is considered indispensable to GNSS satellite POD and commonly results in a factor of two improvement in orbit precision. Of particular importance is the narrow-lane ambiguity that results from combining the carrier-phase measurements from a pair of GNSS frequencies. One of the intermediate steps in the ambiguity resolution algorithm is the fixing of the double-differenced narrow-lane ambiguities to integer values. For reliable fixing, the fractional part of the difference between the integer and decimal (float) values should be as close as possible to zero and follow a symmetrical distribution. The “tailedness” of the distribution curve may be characterized by its kurtosis — the larger the kurtosis, the fewer values are in the tails of the distribution and the more peaked is the distribution. In other words, the larger the kurtosis, the closer the “fractionals” cluster around zero, the more ambiguities can be resolved with higher confidence, and the more accurate the resolved solution. Moreover, as satellite orbit and antenna phase center errors do not cancel out completely through double-differencing, the narrow-lane kurtosis may also be considered as an indicator for the accuracy of the satellite force and phase center models that were used. The results in Figure 9 show that the non-zero horizontal PCOs bring a major improvement and that the Fourier force model does give some additional benefit.

Figure 9: Impact of horizontal antenna PCOs and Fourier force model on fractional part of double-differenced narrow-lane ambiguities.

CONCLUSIONS

Adding a new GNSS satellite type to high-precision multi-GNSS solutions requires detailed knowledge and understanding of the satellite type. Key issues are the transmit antenna phase center parameters, the satellite’s attitude, and the radiation pressure forces acting on its surfaces.

In this article, improved antenna phase center, attitude, and radiation pressure models for the current series of GPS Block III spacecraft have been developed using multiple years of in-flight orbit and tracking data. A number of internal metrics such as post-fit carrier-phase residuals, day-boundary orbit differences (overlaps), empirical acceleration parameters, and carrier phase ambiguity statistics have been used to gauge the models’ performances. Overall, the results underscore the importance of the models for GPS III orbit determination. This applies primarily to the radiation force and the antenna phase center model, or more precisely, the horizontal (X and Y) offsets of the phase center model whose existence has been neglected for years in the analysis of GPS III data.

Comparison of the overlap statistics suggest that orbits generated based upon updated (non-zero) phase center corrections and ESA/ESOC’s new (Fourier-based) radiation pressure model in the background are better by almost a factor of two. The average overlap RMS errors calculated across all current Block III SVs and for each orbital component (radial, along track and across track) dropped from 21 , 28 and 35 millimeters down to 14, 21 and 16 millimeters, respectively.

More relevant when it comes to processing GPS data recorded on board low-flying satellites such as Sentinel-6 Michael Freilich or Jason-3, is the extension of the current IGS Block III antenna PCV model beyond a 14-degree boresight angle. After applying the extended PCV corrections, we reduced Block III carrier-phase residuals by 20% with no or few systematic signatures remaining, unlike the residuals produced with the current IGS antenna model. The IGS is strongly encouraged to adopt the Block III PCV extension into their antenna model to continue to support GPS-based POD of low-Earth-orbiting satellites.

For further details on ESA/ESOC’s solar radiation pressure modeling approach, see our paper “GPS III Radiation Force Modeling” presented at the IGS 2022 Virtual Workshop: click here.

FLORIAN DILSSNER is a satellite navigation engineer in the Navigation Support Office at the European Space Operations Centre (ESOC) of the European Space Agency (ESA), Darmstadt, Germany. He earned his Dipl.-Ing. and Dr.- Ing. degrees in geodesy from the University of Hannover, Germany.

TIM SPRINGER has been working for the Navigation Support Office at ESA/ESOC since 2004. He received his Ph.D. in physics from the Astronomical Institute of the University of Bern in 1999.

FRANCESCO GINI is a satellite navigation engineer in the Navigation Support Office at ESA/ESOC. He received his Ph.D. in astronautics and space sciences from the Centro di Ateneo di Studi e Attività Spaziali at the University of Padova in 2014.

ERIK SCHÖNEMANN is a satellite navigation engineer in the Navigation Support Office at ESA/ESOC. He earned his Dipl.-Ing. and Dr.- Ing. degrees in geodesy from the University of Darmstadt, Germany.

WERNER ENDERLE is head of the Navigation Support Office at ESA/ESOC. He holds a doctoral degree in aerospace engineering from the Technical University of Berlin, Germany.

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