Search Results (124)

The BeiDou-3 navigation satellite system (BDS-3) has officially provided positioning, navigation, and timing (PNT) services to global users since 31 July 2020. With the application of inter-satellite link technology, global integrity monitoring becomes possible. Nevertheless, the content of integrity monitoring is still limited by the communication capacity of inter-satellite links and the layout of ground monitoring stations. Low earth orbit (LEO) satellites have advantages in information-carrying rate and kinematic velocity and can be used as satellite-based monitoring stations for navigation satellites. Large numbers of LEO satellites can provide more monitoring data than ground monitoring stations and make it easier to obtain full-arc observation data. A new challenge of redundant data also arises. This study constructs multi-source observation links with satellite-to-ground, inter-satellite, and satellite-based observation data, proposes an integrity monitoring method with optimization of observation links, and verifies the performance of integrity monitoring with different observation links. The experimental results show four findings. (1) Based on the integrity status of BDS-3, the proposed system-level integrity mode can realize full-arc anomaly diagnosis in information and signals according to the observation conditions of the target satellite. Apart from basic navigation messages and satellite-based augmentation messages, autonomous messages and inter-satellite ranging data can be used to evaluate the state of the target satellite. (2) For a giant LEO constellation, only a small number of LEO satellites need to be selected to construct a minimum satellite-based observation unit that can realize multiple returns of navigation messages and reduce the redundancy of observation data. With the support of 12 and 30 LEO satellites, the minimum number of satellite-based observation links is 1 and 4, respectively, verifying that a small amount of LEO satellites could be used to construct a minimum satellite-based observation unit. (3) A small number of LEO satellites can effectively improve the observation geometry of the target satellite. An orbit determination observation unit, which consists of chosen satellite-to-ground and/or satellite-based observation links based on observation geometry, is proposed to carry out fast calculations of satellite orbit. If the orbit determination observation unit contains 6 satellite-to-ground monitoring links and 6/12/60 LEO satellites, the value of satellite position dilution of precision (SPDOP) is 38.37, 24.60, and 15.71, respectively, with a 92.95%, 95.49%, and 97.12% improvement than the results using 6 satellite-to-ground monitoring links only. (4) LEO satellites could not only expand the resolution of integrity parameters in real time but also augment the service accuracy of the navigation satellite system. As the number of LEO satellites increases, the area where UDRE parameters can be solved in real time is constantly expanding to a global area. The service accuracy is 0.93 m, 0.88 m, and 0.65 m, respectively, with augmentation of 6, 12, and 60 LEO satellites, which is an 8.9%, 13.7%, and 36.3% improvement compared with the results of regional service. LEO satellites have practical application values by improving the integrity monitoring of navigation satellites. Full article

As the application of the Global Navigation Satellite System (GNSS) continues to expand, its stability and safety issues are receiving more and more attention, especially the interference problem. Interference reduces the signal reception quality of ground terminals and may even lead to the paralysis of GNSS function in severe cases. In recent years, Low Earth Orbit (LEO) satellites have been highly emphasized for their unique advantages in GNSS interference detection, and related commercial and academic activities have increased rapidly. In this context, based on the signal-to-noise ratio (SNR) and radio-frequency interference (RFI) measurements data from COSMIC-2 satellites, this paper explores a method of predicting RFI measurements using SNR correlation variations in different GNSS signal channels for application to the detection and localization of civil terrestrial GNSS interference signals. Research shows that the SNR in different GNSS signal channels shows a correlated change under the influence of RFI. To this end, a CNN-BiLSTM-Attention model combining a convolutional neural network (CNN), bi-directional long and short-term memory network (BiLSTM), and attention mechanism is proposed in this paper, and the model takes the multi-channel SNR time series of the GNSS as the input and outputs the maximum measured value of RFI in the multi-channels. The experimental results show that compared with the traditional band-pass filtering inter-correlation method and other deep learning models, the model in this paper has a root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R²) of 1.0185, 1.8567, and 0.9693, respectively, in RFI prediction, which demonstrates a higher RFI detection accuracy and a wide range of rough localization capabilities, showing significant competitiveness. Since the correlation changes in the SNR can be processed to decouple the signal strength, this model is also suitable for future GNSS-RO missions (such as COSMIC-1, CHAMP, GRACE, and Spire) for which no RFI measurements have yet been made. Full article

The rapid development of Low Earth Orbit (LEO) satellite navigation systems requires modulation schemes with strong anti-jamming capabilities, high spectral efficiency, and the ability to achieve precise tracking in high-dynamic environments. Traditional Binary Offset Carrier (BOC) modulation suffers from multi-peak ambiguity, leading to false lock issues. To address this, FH-BOC modulation, which integrates BOC modulationand frequency hopping, significantly improves both anti-jamming performance and spectral efficiency. Against this background, this paper proposes a comprehensive high-dynamic tracking algorithm for FH-BOC signals. (1) Based on the adaptive Kalman filter algorithm, high-precision carrier tracking was achieved in high-dynamic environments. (2) By leveraging the correlation between the ranging code and frequency-hopping offset carrier, a composite pseudo-code is generated through the XOR operation, and a corresponding composite code-tracking loop is introduced. (3) Based on code loop tracking results, the frequency-hopping moments of the subcarrier are detected, and a phase-locked loop for the frequency-hopping subcarrier is established. Simulation results indicate that the algorithm achieves centimeter-level pseudorange measurement accuracy for FH-BOC navigation signals under the JPL high-dynamic model. Full article

The recent rapid development of low Earth orbit (LEO) constellation-based navigation techniques has enhanced the ability of position, navigation, and timing (PNT) services in deep attenuation and interference environments. However, existing navigation modulations face the challenges of high acquisition complexity and do not improve measurement precision at the same signal strength. We propose a pulsed orthogonal time frequency space (Pulse-OTFS) signal, which naturally converts continuous signals into pulses through a special delay-Doppler domain pseudorandom noise (PRN) code sequence arrangement. The performance evaluation indicates that the proposed signal reduces at least 89.4% of the acquisition complexity. The delay measurement accuracy is about 8 dB better than that of the traditional binary phase shift keying (BPSK) signals with the same bandwidth. It also provides superior compatibility and anti-multipath performance. The advantages of fast acquisition and high-precision measurement are verified by processing the real signal in the developed software receiver. As Pulse-OTFS occupies only one time slot of a signal period, it can be easily integrated with OTFS-modulated communication signals and used as a navigation signal from broadband LEO satellites as an effective complement to the global navigation satellite system (GNSS). Full article

It is essential to provide high-integrity navigation information for safety-critical applications. Global navigation satellite systems (GNSSs) play an important role in these applications because they can provide global, high-accuracy, all-weather navigation services. Therefore, it has been a hot topic to improve GNSS integrity performance. This paper focuses on an initial proposal of the next-generation BeiDou Navigation Satellite System (BDS) integrity subsystem, with the aim of providing high-quality and global integrity services for the BDS. This paper first reviews the current status of the third-generation BDS integrity service. Following this, this paper proposes a space–ground integrated integrity monitoring design for the BDS that integrates the traditional ground-based integrity monitoring method, the advanced satellite autonomous integrity monitoring (A-SAIM) method, and the augmentation from low-earth-orbit (LEO) satellites. Specifically, this work offers an initial design of the A-SAIM method, which considers both single-satellite autonomous integrity monitoring and multi-satellite joint integrity monitoring. In addition, this work describes two different ways to augment BDS integrity with LEO satellites, i.e., (a) LEO satellites act as space monitoring stations and (b) LEO satellites act as navigation satellites. Simulations are carried out to validate the proposed design using CAT-I operation in civil aviation as an example. Simulation results indicate the effectiveness of the proposed design. In addition, simulation results suggest that if the fault probability of LEO satellites is worse than 1 × 10⁻⁴, LEO satellites can contribute more to BDS integrity performance improvement by acting as space monitoring stations; otherwise, it would be better to employ LEO satellites to broadcast navigation signals. The results also suggest that after taking LEO satellites into account, the global coverage of CAT-I can be potentially improved from 67% to 99%. This work is beneficial to the design of the next-generation BDS integrity subsystem. Full article

High-precision Low Earth Orbit (LEO) satellite clocks are essential for LEO-augmented Positioning, Navigation, and Timing (PNT) services. Nowadays, high-precision LEO satellite clocks can be determined in real-time using a Kalman filter either onboard or on the ground, as long as the GNSS observations collected onboard LEO satellites can be transmitted to the ground in real-time. While various real-time and high-precision GNSS products are available nowadays in the latter case, their continuity and latencies in engineering reality are not as perfect as expected and will lead to unignorable impacts on the precision of the real-time LEO satellite clocks. In this study, based on real observations of Sentinel-3B, the impacts of different latencies and continuity of the real-time GNSS products on LEO real-time clocks are determined and discussed for two scenarios, namely the “epoch estimation” and “arc estimation” scenarios. The former case refers to the traditional filter-based processing epoch-by-epoch, and the latter case connects LEO satellite clocks from different rounds of filter-based processing under a certain arc length. The two scenarios lead to the “end-loss” and “mid-gap” situations. Latencies of the real-time GNSS products are discussed for the cases of orbit-only latency, clock-only latency, and combined forms, and different handling methods for the missing GNSS satellite clocks are discussed and compared. Results show that the real-time LEO satellite clock precision is very sensitive to the precision of real-time GNSS satellite clocks, and prediction of the latter becomes essential in case of their latencies. For the “end-loss” situation, with a latency of 30 to 120 s for the GNSS real-time clocks, the LEO satellite clock precision is reduced from about 0.2 to 0.28–0.57 ns. Waiting for the GNSS products in case of their short latencies and predicting the LEO satellite clocks instead could be a better option. For “arc-estimation”, when the gap of GNSS real-time products increases from 5 to 60 min, the real-time LEO clock precision decreases from 0.26 to 0.32 ns. Full article

The moving sofa problem, introduced by Leo Moser in 1966, seeks to determine the maximal area of a 2D shape that can navigate an L-shaped corridor of unit width. Joseph Gerver’s 1992 solution, providing a lower bound of approximately 2.2195, is the best known, though its global optimality remains unproven. This paper leverages neural networks’ approximation power and recent advances in invexity optimization to explore global optimality. We propose two approaches supporting Gerver’s conjecture that his sofa is the unique global maximum. The first approach uses continuous function learning, discarding assumptions about the monotonicity, symmetry, and differentiability of sofa movements. The sofa area is computed as a differentiable function using our “waterfall” algorithm, with the loss function incorporating both differential terms and initial conditions based on physics-informed machine learning. Extensive training with diverse network initialization consistently converges to Gerver’s solution. The second approach applies discrete optimization to the Kallus–Romik upper bound, improving it from 2.37 to 2.3337 for five rotation angles. As the number of angles increases, our model asymptotically converges to Gerver’s area from above, indicating that no larger sofa exists. Full article

Research on augmentation and supplement systems for navigation systems has become a significant aspect in comprehensive positioning, navigation and timing (PNT) studies. The BeiDou-3 navigation satellite system (BDS-3) has constructed a dynamic inter-satellite network to gain more observation data than ground monitoring stations. Low Earth orbit (LEO) satellites have advantages in their kinematic velocity and information carrying rate and can be used as satellite-based monitoring stations for navigation satellites to make up for the distribution limitation of ground monitoring stations. This study constructs multi-source observation links with satellite-to-ground, inter-satellite and satellite-based observation data, proposes an orbit synchronization method for navigation satellites and LEO satellites and verifies the influence thereof on orbit accuracy with different observation data. The experimental results under conditions of real and simulated observation data showed the following: (1) With the support of satellite-based observation links, the orbit accuracy of the BDS-3 MEO satellites could be improved significantly, with a 78% improvement with the simulation data and a 76% improvement with the real data. When the navigation satellites leave the monitoring area of the ground monitoring stations, the accuracy reduction tendency of the orbit prediction could also be slowed down with the support of the LEO satellites and the accuracy could be maintained within centimeters. (2) Comparing the orbit accuracy with the support of the satellite-to-ground observation links, the orbit accuracy of the MEO satellites could be improved by 65.5%, 73.7% and 79.4% with the support of the 6, 12 and 60 LEO satellites, respectively. When the observation geometry and the covering multiplicity meet the basic requirement of orbit determination, the improvements to the orbit accuracy decrease with the growth of LEO satellite numbers. (3) The accuracy of orbit determination with the support of the LEO satellites or the inter-satellite links was at the centimeter level for both, verifying that inter-satellite links and satellite-based links can be used as each other’s backups for navigation satellites. (4) The accuracy of orbit determination with the multi-source observation links was also at the centimeter level, which was not better than the results with the support of the satellite-to-ground and inter-satellite links or the satellite-to-ground and satellite-based links. Full article

Low Earth orbit (LEO) satellites have unique advantages in navigation because of their high signal intensity and rapid geometric changes in a short period. In order to solve the problem of constellation performance degradation after a potential failure pertaining one or more medium Earth orbit (MEO) navigation satellites, this paper designs the LEO navigation constellation and considers the task requirements of different stages of constellation deployment. Firstly, the LEO navigation constellation is designed by a non-dominated sorting genetic algorithm II (NSGA-II). The average position dilution of precision (PDOP) is 1.676, which is an improvement compared to the average PDOP offered by the four traditional GNSS. Secondly, the staged deployment of constellation takes into account the degradation of constellation performance caused by the failure of MEO navigation satellites, and the Monte Carlo method is used to analyze the case of three simultaneous satellite failures. The results show that a single satellite failure within each orbital plane and adjacent satellites with close phase separation has a great impact on the performance of the MEO navigation constellation. On this basis, a staged deployment strategy was adopted in order to balance cost, risk, and performance. The three phases deploy 66, 156, and 288 satellites, respectively; as a make-up constellation under contingencies, a navigation enhancement constellation, and an independent navigation constellation, the deployment of the staged sub-constellations meets the mission requirements. The constellation design and staged deployment method proposed in this paper can provide reference for the future study of LEO navigation constellations. Full article

The laser station (BORL) owned by the Space Research Centre of the Polish Academy of Sciences and situated at the Astrogeodynamic Observatory in Borowiec near Poznań regularly observes more than 100 different objects in low Earth orbit (LEO) and medium Earth orbit (MEO). The BORL sensor’s laser observation range is from 400 km to 24,500 km. The laser measurements taken by the BORL sensor are utilized to create various products, including the geocentric positions and movements of ground stations, satellite orbits, the components of the Earth’s gravitational field and their changes over time, Earth’s orientation parameters (EOPs), and the validation of the precise Galileo orbits derived using microwave measurements, among others. These products are essential for supporting local and global geodetic and geophysics research related to time. They are crucial for the International Terrestrial Reference Frame (ITRF), which is managed by the International Earth Rotation and Reference Systems Service (IERS). In 2023, the BORL laser station expanded its list of tracked objects to include all satellites of the European satellite navigation system GALILEO, totaling 28 satellites. During that year, the BORL laser station recorded 77 successful passes of GALILEO satellites, covering a total of 21 objects. The measurements taken allowed for the registration of 7419 returns, resulting in 342 normal points. The average RMS for all successful GALILEO observations in 2023 was 13.5 mm. Full article

Navigation resource allocation for low-earth-orbit (LEO) constellations refers to the optimal allocation of navigational assets when the number and allocation of satellites in the LEO constellation have been determined. LEO constellations can not only transmit navigation enhancement signals but also enable space-based monitoring (SBM) for real-time assessment of GNSS signal quality. However, proximity in the frequencies of LEO navigation signals and SBM can lead to significant interference, necessitating isolated transmission and reception. This separation requires that SBM and navigation signal transmission be carried out by different satellites within the constellation, thus demanding a strategic allocation of satellite resources. Given the vast number of satellites and their rapid movement, the visibility among LEO, medium-earth-orbit (MEO), and geostationary orbit (GEO) satellites is highly dynamic, presenting substantial challenges in resource allocation due to the computational intensity involved. Therefore, this paper proposes an optimal allocation algorithm for LEO constellation navigation resources based on dynamic programming. In this algorithm, a network model for the allocation of navigation resources in LEO constellations is initially established. Under the constraints of visibility time windows and onboard transmission and reception isolation, the objective is set to minimize the number of LEO satellites used while achieving effective navigation signal transmission and SBM. The constraints of resource allocation and the mathematical expression of the optimization objective are derived. A dynamic programming approach is then employed to determine the optimal resource allocation scheme. Analytical results demonstrate that compared to Greedy and Divide-and-Conquer algorithms, this algorithm achieves the highest resource utilization rate and the lowest computational complexity, making it highly valuable for future resource allocation in LEO constellations. Full article

The Global Navigation Satellite System (GNSS) can be utilized for long-distance and high-precision time transmission. With the ongoing development of low Earth orbit (LEO) satellites and the rapidly changing geometric relationships between them, the convergence rate of ambiguity parameters in Precise Point Positioning (PPP) algorithms has increased, enabling fast and reliable time transfer. In this paper, GPS is used as an experimental case, the LEO satellite constellation is designed, and simulated LEO observation data are generated. Then, using the GPS observation data provided by IGS, a LEO-enhanced PPP model is established. The LEO-augmented PPP model is employed to facilitate faster and more reliable high-precision time transfer. The application of the LEO-augmented PPP model to time transfer is examined and discussed through experimental examples. These examples show multiple types of time transfer links, and the experimental outcomes are uniform. GPS + LEO is compared with exclusive GPS time transfer schemes. The clock offset of the time transfer link for the GPS + LEO scheme converges more swiftly, meaning that the time required for the clock offset to reach a stable level is the briefest. In this paper, standard deviation is employed to assess stability, and Allan deviation is utilized to assess frequency stability. The results show that the clock offset stability and frequency stability achieved by the GPS + LEO scheme are superior within the convergence time range. Controlled experiments with different numbers of satellites for LEO enhancement indicate that time transfer performance can be improved by increasing the number of satellites. As a result, augmenting GPS tracking data with LEO observations enhances the time transfer service compared to GPS alone. Full article

A fast time synchronization method for large-scale LEO satellite networks based on a bionic algorithm is proposed. Because the inter-satellite links are continuously established and interrupted due to the relative motion of the satellites, the topology of the LEO satellite networks is time varying. Firstly, according to the ephemeris information in navigation messages, a connection table which records the connections between satellites is generated. Then, based on the connection table, the current satellite network topology is calculated and generated. Furthermore, a bionic algorithm is used to select some satellites as time source nodes and calculate the hierarchy of the clock transmission tree. By taking the minimum level of the time transmission tree as the optimization objective, the time source nodes and the clock stratums of the whole satellite networks are obtained. Finally, the onboard computational center broadcasts the time layer table to all the satellites in the LEO satellite networks and the time synchronization links can be established or recovered fast. Full article

Precision point positioning (PPP) utilizing the Global Navigation Satellite System (GNSS) is a traditional and widely employed technology. Its performance is susceptible to observation discontinuities and unfavorable geometric configurations. Consequently, the integration of the Inertial Navigation System (INS) and GNSS makes full use of their respective advantages and effectively mitigates the limitations of GNSS positioning. However, the GNSS/INS integration faces significant challenges in complex and harsh urban environments. In recent years, the geometry between the user and the satellite has been effectively improved with the advent of lower-orbits and faster-speed Low Earth Orbit (LEO) satellites. This enhancement provides more observation data, opening up new possibilities and opportunities for high-precision positioning. Meanwhile, in contrast to the traditional extended Kalman filter (EKF) approach, the performance of the LEO-enhanced GNSS/INS tightly coupled integration (TCI) can be significantly improved by employing the factor graph optimization (FGO) method with multiple iterations to achieve stable estimation. In this study, LEO data and the FGO method were employed to enhance the GNSS/INS TCI. To validate the effectiveness of the method, vehicle data and simulated LEO observations were subjected to thorough analysis. The results suggest that the integration of LEO data significantly enhances the positioning accuracy and convergence speed of the GNSS/INS TCI. In contrast to the FGO GNSS/INS TCI without LEO enhancement, the average enhancement effect of the LEO is 22.16%, 7.58%, and 10.13% in the north, east, and vertical directions, respectively. Furthermore, the average root mean square error (RMSE) of the LEO-enhanced FGO GNSS/INS TCI is 0.63 m, 1.21 m, and 0.85 m in the north, east, and vertical directions, respectively, representing an average improvement of 41.91%, 13.66%, and 2.52% over the traditional EKF method. Meanwhile, the simulation results demonstrate that LEO data and the FGO method effectively enhance the positioning and convergence performance of GNSS/INS TCI in GNSS-challenged environments (tall buildings, viaducts, underground tunnels, and wooded areas). Full article

Low-Earth-Orbit (LEO) satellite Signal-of-Opportunity (SOP) positioning technology has gradually matured to meet the accuracy requirements for unmanned aerial vehicle (UAV) positioning in daily scenarios. Advancements in miniaturization technology for positioning terminals have also made this technology’s application to UAV positioning crucial for UAV development. However, in the increasingly complex electromagnetic environment, there remains a significant risk of degradation in positioning performance for UAVs in LEO satellite SOP positioning due to unintentional or malicious jamming. Furthermore, there is a lack of in-depth research from scholars both domestically and internationally on the anti-jamming capabilities of LEO satellite SOP positioning technology. Due to significant differences in the downlink signal characteristics between LEO satellites and Global Navigation Satellite System (GNSS) signals based on Medium Earth Orbit (MEO) or Geostationary Earth Orbit (GEO) satellites, the anti-jamming research results of traditional satellite navigation systems cannot be directly applied. This study addresses the narrow bandwidth and high signal-to-noise ratio (SNR) characteristics of signals from LEO satellite constellations. We propose a Consecutive Iteration based on Signal Cancellation (SCCI) algorithm, which significantly reduces errors during the model fitting process. Additionally, an adaptive variable convergence factor was designed to simultaneously balance convergence speed and steady-state error during the iteration process. Compared to traditional algorithms, simulation and experimental results demonstrated that the proposed algorithm enhances the effectiveness of jamming threshold settings under narrow bandwidth and high-power conditions. In the context of LEO satellite jamming scenarios, it improves the frequency-domain anti-jamming performance significantly and holds high application value for drone positioning. Full article