The impact of electron precipitation on Earth's thermospheric NO production and the drag of LEO satellites

BDS-3 faces challenges in achieving precision orbit determination (POD) due to the difficulty of establishing a globally uniform distribution of independently operated ground tracking stations. The use of onboard BDS-3 observations collected by low Earth orbit (LEO) satellites can partially mitigate this limitation. However, these observations introduce additional parameters, such as receiver clock offsets and carrier-phase ambiguities, which substantially increase the computational burden. Therefore, the capability of achieving real-time (RT) joint POD for BDS-3 and LEO satellites, relying solely on independently operated tracking stations, is greatly constrained. Currently, the inter-satellite links (ISLs) of BDS-3 have been successfully demonstrated to be effective for POD of BDS-3 satellites. In the future, ISLs of LEO satellites will also be incorporated as a measurement technique. Compared to traditional BDS-3 onboard observations, POD using ISLs involves almost no additional parameters other than the orbital states. Therefore, this paper proposes a method that combines onboard BDS-3 receivers on a subset of LEO satellites with LEO ISL observations to achieve rapid high-precision joint POD for BDS-3 and the full LEO constellation. To validate the proposed approach, measured BDS-3 data from regional ground stations in China are employed, together with simulated onboard BDS-3 data and simulated LEO ISL observations. All datasets were obtained over a three-day period, corresponding to days 131–133 of the year 2025. Firstly, it is demonstrated that, when relying solely on regional ground stations, the 24 MEO and 3 IGSO satellites of BDS-3 cannot achieve high-precision POD, with 1D RMS orbit accuracies of only 11.6 cm and 26.9 cm, respectively. Incorporating onboard BDS-3 data from LEO satellites significantly improves orbit determination accuracy, with 1D RMS accuracies reaching 4.9 cm for MEO and 6.4 cm for IGSO satellites, while LEO satellites themselves achieve orbit accuracy better than 5 cm. Subsequently, the computational burden introduced by onboard BDS-3 data from LEO satellites in joint POD is further assessed. On average, incorporating onboard BDS-3 data from 10 LEO satellites adds approximately 6780 parameters to be estimated, substantially increasing computation time. When onboard BDS-3 data from 20 LEO satellites are included, the achieved BDS-3 orbit accuracy shows negligible degradation compared to using data from all LEO satellites, with 1D RMS accuracies of 4.9 cm and 6.7 cm for MEO and IGSO, respectively. Meanwhile, the processing time for a single batch least squares (BLSQ) solution decreases dramatically from 27.0 min to 5.7 min. Increasing the number of LEO satellites to 30 further improves BDS-3 orbit accuracy, mainly due to the enhanced orbit precision of the LEO satellites. After incorporating LEO ISLs, LEO satellites achieve orbit accuracy in the 1D direction of approximately 1 cm, regardless of whether their onboard BDS-3 data are used. In summary, the proposed approach significantly reduces computational burden while ensuring orbit determination accuracy for both BDS-3 and LEO satellites. This approach is more likely to realize real-time joint POD of BDS-3 and LEO satellites based on large-scale LEO constellations.

Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the satellite laser ranging (SLR)-based ERP products only using SLR observations to Laser Geodynamics Satellite (LAGEOS) and Etalon satellites. Apart from these geodetic satellites, many low Earth orbit (LEO) satellites of Earth observation missions are also equipped with laser retroreflector arrays, and produce a large number of SLR observations, which are only used for orbit validation. In this study, we focus on the contribution of multiple LEO satellites to ERP estimation. The SLR and Global Positioning System (GPS) observations of the current seven LEO satellites (Swarm-A/B/C, Gravity Recovery and Climate Experiment (GRACE)-C/D, and Sentinel-3A/B) are used. Several schemes are designed to investigate the impact of LEO orbit improvement, the ERP quality of the single-LEO solutions, and the contribution of multiple LEO combinations. We find that ERP estimation using an ambiguity-fixed orbit can attain a better result than that using ambiguity-float orbit. The introduction of an ambiguity-fixed orbit contributes to an accuracy improvement of 0.5%, 1.1% and 15% for X pole, Y pole and station coordinates, respectively. In the multiple LEO satellite solutions, the quality of ERP and station coordinates can be improved gradually with the increase in the involved LEO satellites. The accuracy of X pole, Y pole and length-of-day (LOD) is improved by 57.5%, 57.6% and 43.8%, respectively, when the LEO number increases from three to seven. Moreover, the combination of multiple LEO satellites is able to weaken the orbit-related signal existing in the single-LEO solution. We also investigate the combination of LEO satellites and LAGEOS satellites in the ERP estimation. Compared to the LAGEOS solution, the combination leads to an accuracy improvement of 0.6445 ms, 0.6288 ms and 0.0276 ms for X pole, Y pole and LOD, respectively. In addition, we explore the feasibility of a one-step method, in which ERP and the orbit parameters are jointly determined, based on SLR and GPS observations, and present a detailed comparison between the one-step solution and two-step solution.

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

Precise relative navigation of spacecraft is required for its critical movement, such as rendezvous and formation flying-key aspects of many current and future space missions. Potential applications of interest include the capabilities to detect and track slowly moving ground vehicles (ground moving target indication (GMTI)) and perform synthetic aperture radar (SAR) imaging, with the requirement to provide GMTI and SAR data to users in a timely manner. Extensive research has been carried out on terrestrial applications of global positioning system (GPS) time transfer. For low earth orbit (LEO) satellites, such missions can use the GPS signals for relative positioning and data time tagging. This paper focuses on linking these two key applications - the use of GPS in LEO for relative navigation and precise formation flying, and time and frequency transfer between LEO satellites. As an example, the research investigates co-orbiting satellites A and B of gravity recovery and climate experiment (GRACE) at a separation of about 200 km. The observations of GPS receivers onboard both GRACE A and B satellites are transferred into receiver independent exchange format (RINEX) format (1 Sept. 2003). The orbit of both satellites is then computed using the zero-difference precise point positioning technique. The RMS orbital difference between the results obtained and the precise orbits from GFZ is below 0.07 m. Two methods are proposed to compute the time difference between GPS receiver onboard satellites A and B respectively. One uses onboard GPS RINEX observations and the GRACE orbit from GeoForschungsZentrum Potsdam (GFZ) which has a large relative latency, the times between A and B in multi-channel common-view mode are compared. Another method computes the clocks of A and B by use of GPS observation onboard and the computed orbit. The times between A and B are then compared. Results indicate that a RMS accuracy of 2-3 nanoseconds (ns) can be achieved. This suggests that GPS has the capabilities of high-precision time transfer between LEO satellites.

Since low earth orbit (LEO) satellite constellations have important advantages over geosynchronous earth orbit (GEO) systems such as low propagation delay, low power requirements, and more efficient spectrum allocation due to frequency reuse between satellites and spotbeams, they are considered to be used to complement the existing terrestrial fixed and wireless networks in the evolving global mobile network. However, one of the major problems with LEO satellites is their higher speed relative to the terrestrial mobile terminals, which move at lower speeds but at more random directions. Therefore, handover management in LEO satellite networks becomes a very challenging task for supporting global mobile communication. Efficient and accurate methods are needed for LEO satellite handovers between the moving footprints. In this paper, we propose a new seamless handover management scheme for LEO satellites (SeaHO-LEO), which utilizes the handover management schemes aiming at decreasing latency, data loss, and handover blocking probability. We also present another interesting handover management model called satellite mobility pattern based handover management in LEO satellites (PatHO-LEO) which takes mobility pattern of both satellites and mobile terminals into account to minimize the handover messaging traffic. This is achieved by the newly introduced billboard manager which is used for location updates of mobile users and satellites. The billboard manager makes the proposed handover model much more flexible and easier than the current solutions, since it is a central server and supports the management of the whole system. To show the performance of the proposed algorithms, we run an extensive set of simulations both for the proposed algorithms and well known handover management methods as a baseline model. The simulation results show that the proposed algorithms are very promising for seamless handover in LEO satellites.

The rapid movement of low Earth orbit (LEO) satellite can improve geometric diversity, which contributes to the rapid convergence of Global Navigation Satellite System (GNSS) precise point positioning (PPP). However, the LEO onboard receiver clock cannot be used directly by PPP users as the LEO satellite clock because the LEO onboard receiver clock and LEO satellite clock absorb different code delays when receiving and transmitting signals. In this study, a real-time estimation approach for the LEO satellite clock based on ground tracking stations was proposed for the first time. The feasibility for the rapid convergence of the LEO satellite clock was analyzed using the satellite time dilution of precision (TDOP) that one satellite is relative to multiple ground tracking stations. The LEO constellation of 168 satellites and observations for 15 ground tracking stations were simulated to verify the proposed method. The experiment results showed that the average convergence time was 31.21 min for the Global Positioning System (GPS) satellite clock, whereas the value for the LEO satellite clock was only 2.86 min. The average root mean square (RMS) and standard deviation (STD) values after convergence were 0.71 and 0.39 ns for the LEO satellite clock, whereas the values were 0.31 and 0.13 ns for the GPS satellite clock. The average weekly satellite TDOP for the LEO satellite was much smaller than that for the GPS satellite. The average satellite TDOPs for all LEO and GPS satellites were 19.13 and 1294.70, respectively. However, the average delta TDOPs caused by satellite motion for all LEO and GPS satellites were both 0.10. Therefore, the rapid convergence of the LEO satellite clock resulted from the better geometric distribution of the LEO satellite relative to ground stations. Despite errors and the convergence time of the LEO satellite clock, the convergence time and positioning accuracy for LEO-augmented GPS and BeiDou Navigation Satellite System (BDS) PPP with the real-time estimated LEO satellite clock can still reach 10.63 min, 1.94 cm, 1.44 cm, and 4.18 cm in the east, north, and up components, respectively. The improvements caused by LEO satellite for GPS/BDS PPP were 59%, 30%, 31%, and 33%, respectively.

Communication via satellite begins when the satellite is positioned in the desired orbital position. Ground stations can communicate with LEO (Low Earth Orbiting) satellites only when the satellite is in their visibility region. The ground station’s ideal horizon plane is in fact the visibility region under 0o of elevation angle. Because of natural barriers or too high buildings in urban areas, practical (visible) horizon plane differs from the ideal one. The duration of the visibility and so the communication duration varies for each LEO satellite pass at the ground station, since LEO satellites move too fast over the Earth. The range between the ground station and the LEO satellite depends on maximal elevation of satellite’s path above the ground station. The dimension of the horizon plane depends on satellite’s orbital attitude. The range variations between the ground station and the satellite, and then ground station horizon plane simulation for low Earth orbiting satellites as a function of orbital attitude is presented. The range impact and horizon plane variations on communication duration between the ground station and LEO satellites are given.

High-precision real-time satellite orbit products are prerequisite for achieving high-performance navigation and positioning services. This study develops an integrated precise orbit determination approach that combines GPS and low Earth orbit (LEO) satellites using the Square Root Information Filtering (SRIF) algorithm to improve the convergence time and accuracy of GPS real-time satellite orbits. By collecting data from varying numbers of global ground stations and LEO satellites (Sentinel-3A/B, GRACE-C/D, Swarm-A/B/C), GPS and LEO satellite orbits were determined synchronously. Orbit convergence time and accuracy were evaluated against the official reference products. Results show, with 9 ground stations, adding 7 LEO satellites decreases the GPS orbit convergence time in along-track, cross-track, and radial directions from 28.0, 28.3, and 21.8 h to 1.9, 3.9, and 14.3 h, respectively, achieving remarkable improvements of 93%, 86%, and 34%. Increasing the number of ground stations to 79 further reduces the convergence time to 0.7, 1.4, and 10.9 h in three directions. For LEO satellites, increasing ground stations from 9 to 79 decreases the average convergence time across all three directions by 44-70%. In terms of GPS orbit accuracy after convergence, the configuration of 7 LEO satellites with 9 ground stations reaches accuracies of 6.5, 3.8, and 3.0 cm in the along-track, cross-track, and radial directions, which is improved by 64%, 66%, and 48%, respectively, compared to the results without LEO satellites. When 79 ground stations are used, the GPS orbit accuracy is further improved to 5.0, 2.5, and 2.6 cm in the three directions. Notably, the three-dimensional GPS orbit accuracy reaches 6.8 cm with 19 ground stations and 7 LEO satellites, which outperforms the accuracy level of 7.4 cm obtained utilizing only 79 ground stations. These results indicate the optimal deployment of LEO satellites can effectively compensate for ground network limitations while maintaining high-precision real-time orbit determination.

The rapid increase of the number of low Earth orbit (LEO) satellites brings up the possibility of LEO satellite missions transmitting dedicated signals for positioning, navigation, and timing (PNT). Although great attention has been paid in recent years to understand the benefits of LEO satellites for PNT, dense LEO constellations will also provide unique measurements of the Earth's upper atmosphere. The benefits of the highly dense LEO-PNT systems are explored in this work to analyze the potential gains of using total electron content (TEC) measurements derived from LEO-PNT systems for 3-D ionospheric imaging. As a result, we have found obvious improvement in the ionospheric imaging system by including LEO satellites to the system geometry. Furthermore, our investigation has discovered that accurate electron density representations can be obtained even when no horizontal viewing angles are included in the imaging system, which is a unique point to imaging systems. In addition, we propose a method to derive accurate 3-D electron density representation based on ranging measurements from intersatellite links. The method provides accurate electron density estimations with no evident bias, but it still depends on the accuracy of background representations. The results indicate that improvements of over 80% can be achieved for both vertical and horizontal distributions of the ionosphere in comparison to the background.

Many low Earth orbit (LEO) satellite constellations have been designed in recent years to provide global broadband Internet services. These constellations provide opportunities for LEO satellites to serve as navigation satellites by launching navigation signals while also being equipped with an onboard global navigation satellite system (GNSS) receiver. We propose a kinematic precise orbit determination (KPOD) and precise clock estimation (PCE) approach for LEO satellites by integrating regional ground observations and onboard observations of LEO satellites. By taking into account the LEO satellite clock bias, this approach can demonstrate the contributions of the ground and onboard observations of LEO satellites to the orbit and clock results, respectively. A composite LEO satellite constellation consisting of 168 satellites and observations from regional ground stations and LEO satellite onboard receivers are simulated considering the LEO satellite clock bias to verify the proposed approach. The results indicate that the convergence time of LEO satellite orbit determination can reach 9.38 min with the integrated KPOD (IKPOD) method, which is a reduction of 24.0% compared with the traditional KPOD method. However, the additional improvement in the LEO satellite orbit accuracy after convergence is very limited. The average root mean square (RMS) and standard deviation (STD) values of all LEO satellite clocks using the integrated PCE (IPCE) method with the participation of LEO satellite onboard observations can reach 0.27 ns and 0.15 ns, respectively. The improvements in the average RMS and STD are 42.6% and 60.5%, respectively, compared with the ground LEO PCE method. The convergence time and accuracy of LEO/GNSS precise point positioning can be improved by 44.6%, 48.3%, 26.7%, and 20.4% in the east, north, and up directions, respectively, using LEO satellite orbits and clocks from the IKPOD and IPCE methods compared with KPOD and PCE.

A simplified GNSS/LEO joint orbit determination method

There are only a few ways that a low Earth orbit (LEO) satellite can communicate with Earth without a ground station network. A LEO satellite can link with other LEO satellites establishing a mesh network that connects with Earth, or LEO satellites can relay their traffic through one of only a few specialized existing or planned geostationary Earth orbit (GEO) or medium Earth orbit (MEO) relay satellites such as the Tracking and Data Relay Satellite System (TDRSS) and Audacy. Unfortunately, there is a real possibility that these limited choices for satellite communications will not accommodate all of the anticipated growth in LEO satellite deployments that are forecast for the next 10 years. The less efficient direct LEO to Earth communications link method will be used unless another solution can be found. A new option may be to leverage the on-orbit commercial GEO satellites that already support the fixed satellite services (FSSs) market. In this scenario, a LEO satellite would relay its communications through the GEO satellite and down to an Earth station, much the same way terrestrial very small aperture terminals, cruise ships, or jet airliners do today. Utilizing several of these commercial GEO satellites, a LEO satellite could communicate with Earth during a large portion of each orbit. There are some challenges with such a scheme, including regulatory hurdles, but if they could be overcome a significant resource of satellite communication services could be engaged to support the future growth of the satellite industry. Several new LEO to GEO relay methods have been proposed or are in development, requiring the deployment of new GEO relay satellites, but this article discusses the idea of utilizing the hundreds of existing FSS GEO satellites operating in C, Ku, and Ka band to leverage an existing resource for satellite communications with LEO satellites.

Mobility models for low Earth orbit (LEO) satellite networks have been researched and reported on in depth. However, most of the analyses discounted the significance of Earth rotation with respect to the LEO satellite speed of rotation and trajectory. In this paper, an approach to the problem of LEO satellite mobility model that takes into consideration the Earth rotation for LEO satellite networks is put forward. The proposed novel mobility model is based on realistic and accurate facts, and involves the use of elementary vector calculus. Analysis of the impact of Earth rotation on LEO satellite networks is provided using simulation results and arguments. The importance for such a model in the study and analysis of LEO satellite systems is also discussed.

Low Earth orbit (LEO) satellites can be used to augment global navigation satellite system (GNSS) precise point positioning (PPP) for rapid convergence, which has been demonstrated by an abundance of simulation studies. In this contribution, we analyze the performance of LEO augmented GNSS PPP using real data from two in-orbit CENTISPACETM experimental satellites launched by Beijing Future Navigation Tech Co., Ltd. The onboard GNSS observations are used to determine the precise orbits and the initial clock offsets of LEO satellites, and the clock corrections are estimated using the observations from a ground network. The RMS values of measurement residuals for dual-frequency ionosphere-free combination of LEO downlink pseudorange and phase observations are about 0.8 m and 2 cm. We select three ground tracking stations for the PPP experiment and the performance of GPS, BeiDou Navigation Satellite System (BDS)-3, GPS + BDS-3, GPS + BDS-3 + Galileo PPP with the augmentation of 1 and 2 LEO satellites is evaluated and analyzed. The results indicate that the observations from LEO satellites can significantly improve the GNSS convergence performance. Compared with GNSS-only PPP, the convergence time is shortened by more than 50% with the addition of 1 LEO satellite, while the two LEO satellites achieve an improvement of 68%–73%. In particular, to achieve a horizontal accuracy of better than 10 cm, the convergence time for the GPS + BDS-3 + Galileo PPP solutions is reduced from 10.8 min to 3–5 min with the augmentation of 1–2 LEO satellites, which reveals the excellent potential of LEO satellites for rapid PPP convergence. The correlation analysis between ambiguity parameters and other related parameters during the PPP processing also demonstrates the superior performance of the LEO satellites in accelerating the PPP convergence. Furthermore, the GNSS/LEO combined PPP improves the 3D positioning accuracy by 10%–20%.

The navigation performance with low Earth orbit (LEO) satellite signals is evaluated. The navigation framework used to perform this evaluation tightly integrates a vehicle’s inertial navigation system (INS) with Doppler and pseudorange measurements from LEO satellites. The following scenario is considered. A vehicle has access to global navigation satellite system (GNSS) signals and a priori, uncertain information about LEO satellite states. The vehicle navigates by tightly integrating GNSS pseudorange measurements with its onboard INS. During the period when GNSS signals are available, the vehicle tracks the LEO satellites from pseudorange and Doppler measurements, refining estimates about their states. Next, GNSS signals are assumed to be unavailable. The vehicle transitions to a simultaneous tracking and navigation (STAN) mode where it simultaneously tracks the LEO satellites and navigates by integrating pseudorange and Doppler measurements made on the LEO satellites with its onboard INS. The performance of this navigation framework is evaluated for two cases: when the LEO satellites periodically transmit their position and when the do not transmit such information. Simulation results with existing LEO satellite constellations pertaining to Orbcomm and Globalstar as well as the future satellite constellation pertaining to Starlink are presented. It was assumed that the LEO satellites are periodically transmitting their positions. These simulation results consider an unmanned aerial vehicle (UAV) equipped with a tactical-grade inertial measurement unit (IMU) navigating for 81.6 km in 600 seconds, in which GNSS signals were only available for the first 100 seconds. It is demonstrated that the final position error of the INS-Orbcomm-Globalstar system was 93.01 m while the INS-Starlink system was 9.81 m. The position root mean squared error (RMSE) of the INS-Orbcomm-Globalstar system was 58.59 m while the INS-Starlink system was 10.13 m. Experimental results with existing Orbcomm LEO satellites are presented in which only Doppler measurements were made on two available satellites. The experimental results were conducted on a ground vehicle equipped with a tactical-grade IMU that traversed 7.5 km in 258 seconds, in which GNSS signals were only available for the first 30 seconds. It is demonstrated that the final position error of the INS without GNSS signals was 3.73 km and the position RMSE was 1.42 km. On the other hand, the final position error of the INS-Orbcomm system was 233.3 m and the position RMSE was 188.6 m when the position of the satellite was decoded from its transmitted message. If such position was not decoded and was estimated only from the STAN framework, the final position error was 476.3 m and the position RMSE was 195.6 m.