Integrity monitoring for precise orbit determination of LEO satellites

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

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.

The precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is still not comparable to that of the Global Positioning System because of the unfavorable geometry of the BDS and the uneven distribution of BDS ground monitoring stations. Fortunately, low Earth orbit (LEO) satellites, serving as fast moving stations, can efficiently improve BDS geometry. Nearly all studies on Global Navigation Satellite System POD enhancement using large LEO constellations are based on simulations and their results are usually overly optimistic. The receivers mounted on a spacecraft or an LEO satellite are usually different from geodetic receivers and the observation conditions in space are more challenging than those on the ground. The noise level of spaceborne observations needs to be carefully calibrated. Moreover, spaceborne observational errors caused by space weather events, i.e., solar geomagnetic storms, are usually ignored. Accordingly, in this study, the actual spaceborne observation noises are first analyzed and then used in subsequent observation simulations. Then, the observation residuals from the actual-processed LEO POD during a solar storm on 8 September 2017 are extracted and added to the simulated spaceborne observations. The effect of the observational errors on the BDS POD augmented with different LEO constellation configurations is analyzed. The results indicate that the noise levels from the Swarm-A, GRACE-A, and Sentinel-3A satellites are different and that the carrier-phase measurement noise ranges from 2 mm to 6 mm. Such different noise levels for LEO spaceborne observations cause considerable differences in the BDS POD solutions. Experiments calculating the augmented BDS POD for different LEO constellations considering spaceborne observational errors extracted from the solar storm indicate that these errors have a significant influence on the accuracy of the BDS POD. The 3D root mean squares of the BDS GEO, IGSO, and MEO satellite orbits are 1.30 m, 1.16 m, and 1.02 m, respectively, with a Walker 2/1/0 LEO constellation, and increase to 1.57 m, 1.72 m, and 1.32 m, respectively, with a Walker 12/3/1 constellation. When the number of LEO satellites increases to 60, the precision of the BDS POD improves significantly to 0.89 m, 0.77 m, and 0.69 m for the GEO, IGSO, and MEO satellites, respectively. While 12 satellites are sufficient to enhance the BDS POD to the sub-decimeter level, up to 60 satellites can effectively reduce the influence of large spaceborne observational errors, i.e., from solar storms.

For real-time precise orbit determination (POD) of low earth orbit (LEO) satellites, high-accuracy global navigation satellite system (GNSS) orbit and clock products are necessary in real time. Recently, the Japanese multi-GNSS advanced demonstration of orbit and clock analysis precise point positioning (PPP) service and the new generation of the Australian/New Zealand satellite-based augmentation system (SBAS)-aided PPP service provide free and precise GNSS products that are directly broadcast through the navigation and geostationary earth orbit satellites, respectively. With the high quality of both products shown in this study, a 3D accuracy of centimeters can be achieved in the post-processing mode for the reduced-dynamic orbits of small LEO satellites having a duty cycle down to 40% and at sub-dm to dm level for the kinematic orbits. The results show a promising future for high-accuracy real-time POD onboard LEO satellites benefiting from the precise free-of-charge PPP corrections broadcast by navigation systems or SBAS.

The real-time precise orbit is an essential prerequisite for a real-time precise point positioning service. Focusing on the impact of ambiguity resolution on real-time orbital precision, we propose an efficient approach for real-time ambiguity resolution, which consists of two modules. The first module resolves the double-differenced ambiguities according to their proximity to the nearest integer. The second module sequentially adds the resolved integer ambiguity constraints to the square-root information filter process, after confirming that the same constraints have not been imposed before the current epoch. To validate our method, GPS data collected from 100 globally distributed stations are used to simulate a real-time precise orbit determination. The convergence performance is analyzed, and the accuracy of the orbit is evaluated. The results show that: (1) Almost 90% of the double-differenced ambiguities are fixed correctly in real time for baselines shorter than 1000 km. (2) After application of the proposed approach, the root-mean-square errors of all the satellite orbits are reduced from (5.9, 3.4, 2.3) cm to (4.7, 2.6, 2.2) cm for the along-track, cross-track and radial directions, respectively, with improvements of about 22% for the along-track and cross-track directions, and 6% for the radial direction. (3) Simulated real-time orbits determined with this method can obtain almost the same accuracy as some ultra-rapid products and, particularly, better accuracy can be achieved for eclipsing satellites.

The improvement of BDS Observation Geometry with LEO constellations in Orbit Determination

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

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).

Validation of enhanced orbit determination for GPS satellites with LEO GPS data considering multi ground station networks

Impact of GPS receiver antenna GRAPHIC residual variations on single-frequency orbit determination of LEO satellites

<p>Low Earth orbiting (LEO) satellites require routine maneuvers to maintain the predefined trajectories. However, spaceborne scientific instruments might suffer from data discontinuities or even anomalies due to instantaneous orbit changes caused by the performed maneuvers. With the advances of spaceborne Global Navigation Satellite System (GNSS) technique, the high-low satellite-to-satellite tracking observations enable us to generate high precision satellite orbits for the nominal orbit operation periods, and more importantly, also for the maneuver periods. This research will outline the recent developments of Precise Orbit Determination (POD) for  maneuvering LEO satellites at the Astronomical Institute of the University of Bern (AIUB). The Sentinel-3 mission, an European Space Agency (ESA) Earth observation satellite formation devoted to oceanography and land-vegetation monitoring, is used as test example.</p><p>A prerequisite input for this research is the maneuver information collected by the telemetry measures which clarify the maneuver time span and accelerations. Due to unavoidable in-flight software delays and hardware performance accuracy, the maneuver information may not be perfect and needs to be improved  in the POD process. Essentially two solutions are made in this research: a. estimating the full accelerations or corrections to the known maneuver accelerations, b. estimating instantaneous velocity pulses at the requested epochs. Both algorithms are tested using the Bernese GNSS Software and POD performances for the maneuver days during 2018-2020 will be assessed. Results reveal that the post-fit carrier phase residuals can be significantly reduced, ensuring better internal consistency between the reduced-dynamic and kinematic orbit solutions. Besides, a few institution members from the Copernicus POD Quality Working Group (QWG) have been routinely generating orbit products for the maneuver days, allowing for the direct cross-validations with our new AIUB products. This research implies promising benefits to the Sentinel-3 POD and scientific research community.</p>

<p><span>The motion of a satellite depends on gravitational and non-gravitational accelerations. A major problem in precise orbit determination (POD) of low-Earth orbiting (LEO) satellites is modelling the thermospheric drag. It is the largest non-gravitational acceleration acting on satellites with altitudes lower than 1000 km and decelerates them. In case of the Swarm satellites with an altitude of around 460 km not considering the drag within a POD would cause an error of around 3 meters per revolution in the along-track direction.</span></p><p><span>In this study, we present results of DGFI-TUM in the context of the project TIPOD (Development of High-Precision Thermosphere Models for Improving Precise Orbit Determination of Low-Earth-Orbiting Satellites) funded by DFG in the frame of the SPP 1788 ‘Dynamic Earth’. One aim of this project is the computation of scaling factors for the thermospheric density from different satellite observation techniques, such as SLR, DORIS, GNSS or accelerometry. For a joint estimation of thermospheric model parameters the spatial, temporal and spectral content of the different scaling factors have to be analysed and interpreted. For example, accelerometer measurements along the satellite orbit provide scaling factors as point values. In this study we derive scaling factors from SLR measurements which could be interpreted as quasi-point values. </span></p><p><span>For the POD of LEO satellites, DGFI-TUM’s software package DOGS (DGFI-TUM Orbit and Geodetic parameter estimation Software) is used. It is characterized by the ability to process observations of different space geodetic techniques and to combine their linear parameter estimation systems within a joint Gauss-Markov model. </span></p><p><span>Here, we estimate scaling factors for the thermospheric density with a time resolution much higher than in our previous studies. Therefore, we use information of short passages from selected spherical satellites above SLR ground stations. Different temporal resolutions for the scaling factors varying from 6 hours down to 5 minutes will be tested and discussed in terms of reliability. </span></p>

To get high precise low earth orbiter (LEO) satellite orbit from satellite-borne GPS data, the satellite-borne GPS carrier phase measurements must be used, but there are still remnant cycle-slips after GPS data pre-processing. Least Square is an optimal method to solve parameters if the residual obeys to normal distribution, but it is difficult to process data with systematic error, LP estimation is an effective method to process data with systematic error, LP estimation is applied to estimate satellite-borne GPS data in LEO satellite precise orbit determination in this paper. It is showed that LP estimation is more effective than that of LS to process GPS phase carrier with systematic error, and improve the LEO satellite orbit precision.

Evaluation of Gravitational Field Models Based on the Laser Range Observation of Low Earth Orbit Satellites

Thanks to the high performance of the spaceborne GPS receiver and the availability of precise IGS orbit and clock products, Zero-difference kinematic precise orbit determination (POD) has turned out to be a new method in orbit determination for the LEO satellites. Zero-difference Kinematic POD, which is based on the GPS measurements only from the spaceborne GPS receiver, is independent of force models and orbit design. From that point of view, kinematic POD is well suited for the Earth Observation satellites at very low altitudes, such as CHAMP, GRACE and GOCE et al. This paper reviews the basic zero-difference GPS model, and the corrections in the model are discussed. A block-wise least squares algorithm, which firstly separates the parameters in to groups and then solves the parameter by elimination and back-substitution, is discussed and proposed for the kinematic orbit determination. The orbit solutions for one week of GRACE observations are calculated Comparisons with the published Rapid Science Orbit (RSO) indicate that the accuracy in radial, along-track and cross-track direction can achieve 5.5cm, 5.5cm and 6.6cm respectively, and the RMS in distance is better than 8.6cm.