Enhanced Real-Time Onboard Orbit Determination of LEO Satellites Using GPS Navigation Solutions with Signal Transit Time Correction

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

Due to an increasing requirement for high accuracy orbital information for low Earth orbit (LEO) satellites, precise orbit determination (POD) of LEO satellites is a topic of growing interest. To assure the safety and reliability of the applications requiring high accuracy LEO orbits in near-real-time, integrity monitoring (IM) is an essential operation of the POD process. In this contribution, the IM strategy for LEO POD in both the kinematic and reduced-dynamic modes is investigated. The overbounding parameters of the signal-in-space range error are investigated for the GPS products provided by the International GNSS Service’s Real-Time Service and the Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis service. Benefiting from the dynamic models used and the improved model strength, the test results based on the data of the LEO satellite GRACE FO-1 show that the average-case mean protection levels (PLs) can be reduced from about 3–4 m in the kinematic mode to about 1 m in the reduced-dynamic mode in the radial, along-track and cross-track directions. The overbounding mean values of the SISRE play the dominant role in the final PLs. In the reduced-dynamic mode and average-case projection, the IM availabilities reach above 99% in the radial, along-track and cross-track directions with the alert limit (AL) set to 2 m. The values are still above 98% with the AL set to 4 m, when the duty cycle of tracking is reduced to 40%, e.g., in the case of power limits for miniature satellites such as CubeSats.

Real-time orbit determination of Low Earth orbit satellite based on RINEX/DORIS 3.0 phase data and spaceborne GPS data

Global navigation satellite system (GNSS) is currently widely used in fields such as navigation, positioning and timing. High-performance real-time orbit products are the foundation of its applications. To improve the performance of real-time orbit, real-time precise orbit determination (RT-POD) based on filtering has become a popular research area. However, existing research relies solely on ground observations. There are very limited studies have evaluated the potential contribution of LEO satellites to GNSS RT-POD based on filtering, or have the scenarios in which globally distributed stations are unavailable due to financial or politically reasons been considered. The feasibility of RT-POD based on filtering under these scenarios has not been studied. Therefore, the square root information filter is employed by this study for real-time joint orbit determination (RTJOD) of GPS and LEO satellites. Based on observations from eight existing scientific LEO satellites, a detailed study on RTJOD was conducted under two scenarios: one using observations from 100 global stations and the other using observations from 9 regional stations in Australia. The results show that, with 100 global stations, incorporating LEO observations can significantly improve the convergence performance and accuracy for GPS satellites. The convergence times in the along-track, cross-track components are reduced from 3.5, 5.8 h to 0.9, 1.0 h, respectively, while the radial component is kept at 10.3 h. The accuracy improves from 5.8, 3.6, and 2.8–4.0 cm, 2.5 cm, and 2.5 cm. Additionally, the ambiguity resolution (AR) performance is significantly enhanced. The time required to achieve a 90% narrow-lane ambiguity fixing rate is reduced from 4.9 to 0.7 h. After AR, the orbit accuracy further improves to 3.1, 2.3, and 2.4 cm. In the case of the 9 regional stations in Australia, after incorporating LEO, the orbit accuracy of the float solution after convergence is comparable to that of the 100 global stations without LEO, with accuracies of 6.0, 4.8, and 2.9 cm in the three components. It is important to note that, due to insufficient observations in this case, AR does not result in any further improvement in accuracy. In addition, LEO can achieve orbit determination accuracy better than 5 cm within a short time in both station distribution scenarios. This ensures that RTJOD enables LEO and GPS to generate high-precision real-time orbits simultaneously. Finally, the processing time for each epoch in all scenarios is less than 5 s, ensuring that the GPS and LEO RTJOD can provide timely orbit updates.

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.

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

: This paper represents orbit propagation and determination of Low Earth Orbit(LEO) satellites, which is immediate orbit satellite positioning. Beiseds, satellite global positioning system (GPS) configured satellite receiver provides position and velocity measures by navigating the filter to get the coordinates of the orbit propagation (OP), while the satellite orbit coordinates is an important basis for the task operation. The main contradictions in real time orbit which is determined by the problem are: orbit positioning accuracy and the amount of calculating two indicators; how to balance these two indicators. This article is dedicated to solving the problem of tradeoffs. To plan to use a non-linear filtering method for immediate orbit tasks requires more precise satellite orbit state parameters in a short time. Although the traditional extended Kalman filter (Extended Kalman Filter, EKF) method is widely used, its linear approximation of the drawbacks in dealing with nonlinear problems was especially evident, without compromising Kalman filter (Unsented Kalman Filter, UKF). As a new non-linear estimation method, it is measured at the estimated measurements on more and more applications. This paper will be the first study to UKF microsatellites in LEO orbit in real time, trying to explore the real-time precision orbit determination techniques.

It is valuable for ground users to realize centimeter-level positioning based on PPP. However, the initialization of PPP algorithm costs a long time, which limits its application. In order to achieve the near-real-time PPP positioning for users, an augmentation scheme by utilizing LEO satellite is proposed so as to improve the initialization speed of PPP solver. And then, the real-time orbit determination method with high-precision by utilizing a PPP pre-processing procedure is investigated to achieve the real-time orbit determination for LEO satellites at centimeter-level, and the orbit determination model and processing algorithm are designed. STK, GPS simulator, high dynamical GPS receiver, navigation augmentation equipment and the processing software are utilized to carry out the experimental verification. The experimental results show that, the real-time orbit determination software works correctly, the accuracy of orbit determination is better than 0.05m, and the position and velocity prediction errors are less than 0.15 m and 0.018cm/s in 15 minutes.

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

DIODE (Doris Immediate On-board orbit DEtermination) is a series of real-time orbit determination software, which process one-way up-link Doppler measurements performed by a DORIS receiver on a satellite. The DIODE software are embedded within the DORIS receivers, and they provide orbit and time determination to the user as well as technical parameters to adjust the tracking loop within the instrument. After a first successful flight on-board SPOT4, the second generation of the family operates on-board Jason-1, with more efficient and more accurate algorithms. Similar versions have been embarked onboard SPOT5 and ENVISAT. The accuracy is between 10 and 30 centimeters RMS for the radial component, and about 50 centimeters RMS in 3D. With several Failure Detection and Incident Recovery (FDIR) enhancements implemented in the software, DIODE/Jason-1 has experienced only one anomaly in July 2004; its availability is 99.7%, after two years and a half in-orbit. This article describes the DORIS/DIODE element of the Jason-1 system. It summarizes the main results obtained from the various verification activities that concerned all parts of this navigation and time-tagging Jason-1 subsystem.

The GeoForschungsZentrum Potsdam (GFZ) operationally provides CHAMP orbit products for various purposes. Here the rapid and ultra-rapid orbits are highlighted. Significant developments in Precise Orbit Determination (POD) for Low Earth Orbiters (LEOs), in particular SAC-C and GRACE besides CHAMP, are described. GFZ also started to generate CHAMP-like rapid orbits for SAC-C with good accuracy. Furtheron improved LEO orbit accuracies are demonstrated by simultaneous orbit solutions of the GPS satellites and one or more LEOs in an integrated approach.

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).

Orbit determination (OD) is a fundamental problem in space surveillance and tracking, crucial for ensuring the safety of space assets. Real-world ground-based optical tracking scenarios often involve challenges such as limited measurement time, short visible arcs, and the presence of outliers, leading to sparse and non-Gaussian observational data. Additionally, the highly perturbative and nonlinear orbit dynamics of resident space objects (RSOs) in low Earth orbit (LEO) add further complexity to the OD problem. This article introduces a variant of the higher order unscented Kalman estimator (HOUSE) called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$w$</tex-math></inline-formula>-HOUSE, which employs a square-root formulation and addresses the challenges posed by nonlinear and non-Gaussian OD problems. The effectiveness of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$w$</tex-math></inline-formula>-HOUSE was demonstrated through synthetic and real-world measurements, specifically outlier-contaminated angle-only measurements collected for the Sentinel 6 A satellite flying in LEO. Comparative analyzes are conducted with the original HOUSE (referred to as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula>-HOUSE), unscented Kalman filters (UKF), conjugate unscented transformation (CUT) filters, and precise OD solutions estimated via onboard global navigation satellite system measurements. The results reveal that the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$w$</tex-math></inline-formula>-HOUSE filter exhibits greater robustness when dealing with varying values of the dependent parameter compared to the original <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula>-HOUSE. Moreover, it surpasses all other filters in terms of positioning accuracy, achieving 3-D root-mean-square errors of less than 60 m in a three-day scenario. This research suggests that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$w$</tex-math></inline-formula>-HOUSE filter represents a viable alternative to UKF and CUT filters, offering improved positioning performance in handling the nonlinear and non-Gaussian OD problems associated with LEO RSOs.

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

Some Orbit Determination (OD) of Low Earth Orbiters (LEOs) based on undifferenced spaceborne GPS data were discussed firstly in this paper. Then the principle and mathematical models of two different types of reduced-dynamic were present. After that, dual-frequency spaceborne GPS data of doy 89, 2004 from CHAMP and GRACE satellite were computed using two types of reduced-dynamic POD and the OD results were analyzed. Our CHAMP orbiting results of one day using two different reduced dynamic POD methods are within 7 centimeters compared with GFZ Post processed Science Orbits (PSO) and the GRACE orbiting results are with 3 centimeters compared with JPL OD results.