Recent Developments in CHAMP Orbit Determination at GFZ

Impact of GPS receiver antenna GRAPHIC residual variations on single-frequency 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

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

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.

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.

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.

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).

For multi-LEO combined orbit determination (COD) satellite-network based on space-based tracking telemetry and command (STTC) satellites, kinematic orbit information can be obtained only using the method of precise point positioning (PPP) based on observation models, but the results are not very precise because of observation data precision and GDOP of constellation. If kinematic orbit information of low earth orbit (LEO) can be taken full advantage of participating in dynamic precise orbit determination (POD) and making them achieve best matching, integrative COD models based on kinematic and dynamic information can be constructed to realize dynamic smoothness of kinematic information. Firstly, single LEO difference positioning model and the corresponding algorithm was designed, and integrative COD models were constituted based on kinematic and dynamic trajectory information. Then extended integrative COD models based on prior trajectory information considering nonlinear semi-parametric modeling of observation models errors and sparse parameters modeling of dynamic models were established, and the optimal weighting algorithm of multi-structural nonlinear COD models was designed. Theoretical analysis and simulation computation results show that COD weighting method based on prior trajectory information can realize LEOs dynamic information optimal matching with kinematic prior information, and can restrain nonlinear influence factor including measure models and ephemeris errors to the effects of POD precision by considering models errors modeling and dynamic models sparse parameters denotation.

The need for precise orbit determination (POD) has grown significantly due to the increased amount of space-based activities taking place at an accelerating pace. Accurate POD positively contributes to achieving the requirements of Low-Earth Orbit (LEO) satellite missions, including improved tracking, reliability and continuity. This research aims to systematically analyze the LEO–POD in four aspects: (i) data sources used; (ii) POD technique implemented; (iii) validation method applied; (iv) accuracy level obtained. We also present the most used GNSS systems, satellite missions, processing procedures and ephemeris. The review includes studies on LEO–POD algorithms/methods and software published in the last two decades (2000–2021). To this end, 137 primary studies relevant to achieving the objective of this research were identified. After the investigation of these primary studies, it was found that several types of POD techniques have been employed in the POD of LEO satellites, with a clear trend observed for techniques using reduced-dynamic model, least-squares solvers, dual-frequency signals with undifferenced phase and code observations in post-processing mode. This review provides an understanding of the various POD techniques, dataset utilized, validation techniques, and accuracy level of LEO satellites, which have interest to developers of small satellites, new researchers and practitioners.

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.

<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>

Enhanced real-time onboard orbit determination for low-Earth-orbit satellites is essential for autonomous spacecraft operations. However, the accuracy of such systems is often limited by signal propagation delays between GPS satellites and the user spacecraft. These delays, primarily due to Earth’s rotation and ionospheric effects become particularly significant in high-dynamic LEO environments, leading to considerable errors in range and range rate measurements, and consequently, in position and velocity estimation. To mitigate these issues, this paper proposes a real-time orbit determination algorithm that applies Earth rotation correction and dual-frequency (L1 and L2) ionospheric compensation to raw GPS measurements. The enhanced orbit determination method is processed directly in the Earth-centered Earth-fixed frame, eliminating repeated coordinate transformations and improving integration with ground-based systems. The proposed method employs a reduced-dynamic orbit determination strategy to balance model fidelity and computational efficiency. A predictive correction model is also incorporated to compensate for GPS signal delays under dynamic motion, thereby enhancing positional accuracy. The overall algorithm is embedded within an extended Kalman filter framework, which assimilates the corrected GPS observations with a stochastic process noise model to account for dynamic modeling uncertainties. Simulation results using synthetic GPS measurements, including pseudoranges and pseudorange rates from a dual-frequency spaceborne receiver, demonstrate that the proposed method provides a significant improvement in orbit determination accuracy compared to conventional techniques that neglect signal propagation effects. These findings highlight the importance of performing orbit estimation directly in the Earth-centered, Earth-fixed reference frame, utilizing pseudoranges that are corrected for ionospheric errors, applying reduced-dynamic filtering methods, and compensating for signal delays. Together, these enhancements contribute to more reliable and precise satellite orbit determination for missions operating in low Earth orbit.

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

<p><span>The neutral mass density of the upper atmosphere (thermosphere) can be determined by orbit and accelerometer data from Low Earth Orbit (LEO) satellites. Especially the accelerometers of geodetic satellites, measuring the non-gravitational accelerations acting on the satellites, are a very useful observation for precise density determination also on very short time scales. </span></p><p><span>Nevertheless, the accelerometers of geodetic satellites are affected by bias and drift. Therefore a calibration of the data is indispensable. A time dependent bias and scale factor are to be determined. Usually calibration parameters are estimated by dynamic Precise Orbit Determination (POD) or Gravity Gield Recovery (GFR), together with all other parameters of interest. In both cases, the estimated accelerometer calibration parameters are not the major interest. With the used parametrizations and weighting of the observations, good gravitational field and orbit solutions, do not necessarily give good or physical accelerometer calibration solutions. This is unsatisfying, especially for the anticipated use in density determination and the direct comparison to modeled non-gravitational accelerations. </span></p><p><span>In this contribution we use dynamic POD and investigate different parametrization strategies tailored for an accurate and physical accelerometer calibration for thermospheric density determination. For example we investigate the effect of constraining the accelerometer calibration parameters in that way, that a continuous calibration over all arcs is achieved, where normally each arc is treated locally separated from all other arcs, leading to jumps in the calibration. The scale factor, which is highly correlated to the estimated bias, is concurrently estimated but over a longer batch of arcs. We compare different bias parametrizations, arc lengths, as well as different observation data and weighting strategies. </span></p><p><span>Finally we show some preliminary density estimation results with our approach and the influence of the accelerometer calibration. </span></p>

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