Extended Integrative Combined Orbit Determination Models Based on Prior Trajectory Information and Optimal Weighting Algorithm

<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 bottleneck of Precise Point Positioning (PPP) is the long convergence time for achieving the centimeter accuracy. Some researchers put forward to improve the diversity of available satellites’ geometric distribution and reduce the correlation of observation data by deploying the Low Earth Orbit (LEO) constellations in addition to the medium and high-orbit satellites. The prerequisite is to get the precise orbit products of all these orbiting satellites. This paper studies the combined precise orbit determination for high-, medium-, and low-orbit navigation satellite systems. In order to investigate the theory and algorithms of the high–medium–low POD and to study the effect of LEO to the POD of high-orbit satellites and the influence of ground data from LEO to its own POD, we simulate all the data, including high orbit to low orbit, medium orbit to low orbit, high orbit to ground stations, medium orbit to ground stations, and low orbit to ground stations. The results show that the combined POD can improve the precision of high-orbit satellites significantly, especially for the along-track component, which can reach to sub-decimeter even centimeter level. Also, the precision of LEO POD can be improved with the data from ground stations.

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.

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.

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.

Being accessible and processible of the raw GNSS data of smartphones has been an innovation for low-cost GNSS positioning studies. With the release of world’s first smartphone with dual frequency GNSS chipset Mi8 by Xiaomi in May 2018, studies on smartphone-based positioning for engineering applications have gained great momentum. Considering these development dynamics, in this study, repeatedly collected Xiaomi Mi8 dual frequency static GNSS observations for two days in two-hour time span were processed using GipsyX and RTKLIB software with epoch by epoch kinematic Precise Point Positioning (PPP) method at different satellite elevation angles, and horizontal positioning accuracies were calculated. The PPP performance of dual frequency GNSS observations collected by Xiaomi Mi8 was investigated at different satellite elevation angles. The process outputs were compared with results analyzed by relative positioning method collected simultaneously with Topcon Hiper SR geodetic receiver by considering as a reference solution. According to the results, it was noted that the horizontal positioning accuracy of RTKLIB outputs has directly inverse relationship with increasing satellite elevation angles whereas GipsyX outputs have differences in this context. In the processing of Xiaomi Mi8 dual frequency observations with PPP method, it was concluded that GipsyX produced higher horizontal positioning accuracy than RTKLIB.

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.

Monitoring the response of engineering structures, such as tall buildings, tower and large-scale bridges, under severe loading conditions, such as strong earthquake or wind storm, is an important requirement to verify their design and construction and to evaluate structural condition and reliability. In the last two decades, high-rate real-time or post-processed kinematic differential Global Positioning System (DGPS) has been widely used in dynamic displacement measurements of civil engineering structures. In recent years, interest has increased for Precise Point Positioning (PPP) due to its capability to generate positioning solutions as accurate as DGPS. In this study, the potential of post-processed kinematic PPP in terms of monitoring dynamic displacement response of a structure has been explored based on free damped oscillation events obtained from a model structure, which is able to vibrate in the fundamental and higher modes of vibration. A number of experiments have been carried out and five events, each of which is different character, have been selected to compare PPP results with DPGS results in the time and frequency domain. The results clearly demonstrate that the PPP method, like the DGPS method, offers great potential for the measurement of horizontal and vertical dynamic movement of structures. The impact of a short period (one minute) of observation length on the result of the kinematic PPP method was also investigated in terms of sensing the dynamic movement of a structure. Twenty selected one-minute data-sets extracted from a one-hour original data-set were processed by Canadian spatial reference system PPP and each one-minute PPP solution was compared with the corresponding segment obtained from the one-hour PPP solution. The results show that the one-minute PPP solution is able to extract the fundamental natural frequency of the oscillation in the horizontal and vertical component just like the one-hour PPP solution after the offset is removed and the lower frequency trend component is filtered out.

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.

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).

The precise point positioning (PPP) is widely used as a typical representative of GNSS. But the main challenge of dual-frequency PPP is that it requires quite a long time to succeed in the ambiguity-fixed so it takes more than 30 min to obtain centimeter-level accuracy. A combination of GPS and low earth orbit (LEO) satellites can improve the diversity of available satellites' geometric distribution and reduce the correlation of observation data between epochs. Then the accuracy of float solution will be promoted and the ambiguity of GPS will take less time to get fixed. The purpose of this paper is to reduce the convergence time of PPP by the contribution of LEO satellites which have low earth orbit and move speedily. We adopt a free-ionosphere PPP model to combine GPS and LEO satellites. Numerous experimental results show that GPS/LEO PPP requires much less convergence time and gets higher positioning accuracy than that of PPP with GPS alone. In addition, an analysis is also made to compare GPS/LEO PPP and GPS/GLONASS PPP. The results indicate that GPS/LEO PPP also requires much less convergence time and gets higher positioning accuracy than that of GPS/GLONASS PPP when increasing the same number of available satellites. This proved that LEO satellites have more contribution to PPP performance than MEO.

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.

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

Precise Point Positioning (PPP) is a stand-alone precise positioning approach. As the quality of satellite orbit and clock products from analysis centers has been improved, PPP can provide more precise positioning accuracy and reliability. A combined use of Global Positioning System (GPS) and Global Orbiting Navigation Satellite System (GLONASS) in PPP is now available. In this paper, we explained about an approach for combined GPS and GLONASS PPP measurement processing, and validated the performance through the comparison with GPS-only PPP results. We also used the measurement obtained from the GRAS reference station for the performance validation. As a result, we found that the combined GPS/GLONASS PPP can yield a more precise positioning than the GPS-only PPP.