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The Sarez Dam, currently recognized as the world's highest natural dam, holds immense economic significance, necessitating the reliable monitoring and early detection of potential deformations. This study utilizes the Beidou high-precision deformation monitoring system for the dam. Employing baseline network solutions, precise point positioning, and real-time kinematic positioning, the monitoring data from October 2021 to March 2023 were meticulously processed and comparatively analyzed. The results reveal varied degrees of displacement deformation at all sites, with horizontal deformation towards the lake center and vertical deformation showing subsidence. The three-dimensional vector average displacement is 29.1 mm, with an average monthly rate of 4.3 mm/month, and the maximum deformation is 41.4 mm. The cause of the horizontal deformation towards the lake center may be a slow collapse of the coastal soil and rock towards the lake center. Additionally, the monitoring detected a 7.2-magnitude earthquake on 23 February 2023, 52 km from the dam, causing an average displacement of 22.5 mm towards the south, which is 20 times the monthly deformation rate. In summary, deformation is present within the dam monitoring area, with a relatively stable deformation rate, warranting continued tracking and monitoring. Furthermore, earthquakes significantly impact dam deformation, necessitating heightened attention to the potential for seismic-induced dam damage in the future. [ABSTRACT FROM AUTHOR]

The Low Earth Orbit (LEO) satellites can be used to effectively speed up Precise Point Positioning (PPP) convergence. In this study, 180 LEO satellites with a global distribution are simulated to evaluate their contribution to the PPP convergence. LEO satellites can give more redundant observations and improve satellite geometric distributions, particularly for a single Global Navigation Satellite System (GNSS). The convergence speed of the PPP float solution using the Global Positioning System (GPS, G) or BeiDou Navigation Satellite System (BDS, C) single system as well as the G/C/Galileo navigation satellite system (Galileo, E)/GLObal NAvigation Satellite System (GLONASS, R) combined system with LEO satellites added is improved by 90.0%, 91.0%, and 90.7%, respectively, with respect to the system without LEO satellites added. We introduced LEO observations to assist GNSS in PPP-AR (Ambiguity Resolution) and PPP-RTK (Real Time Kinematic). The success fix rate of a single system is significantly improved, and the Time-To-First-Fix (TTFF) of G and G/C/E is reduced by 86.4% and 82.8%, respectively, for the PPP-AR solution. We analyzed the positioning performance of LEO satellite assisted G/C/E PPP-RTK in the reference networks of different scales, namely different atmospheric delay interpolation accuracies. The success fix rate of the G/C/E combined system is improved from 86.8 to 94.9%, and the TTFF is reduced by 36.8%, with the addition of LEO satellites in the 57 km reference network. In the 110 km reference network, the success fix rate of the G/C/E combined system is improved from 64.0 to 88.6%, and the TTFF is reduced by 32.1%. GNSS PPP-RTK with adding the LEO satellites in the reference networks of different scales shows obvious improvement because the atmospheric correlation decreases with increasing distance from the reference networks. [ABSTRACT FROM AUTHOR]

In this study, 22 maneuvering events of C59 and C60 geostationary equatorial orbit (GEO) satellites of the BeiDou global navigation satellite system (BDS-3) in 2021 were detected and analyzed based on a time-differenced carrier phase velocity measurement algorithm combined with a broadcast ephemeris and station data. We set different empirical thresholds to analyze the effect of threshold selection on the maneuvering detection sensitivity. The sensitivity and consistency of this algorithm for GEO satellite maneuvering detection were analyzed by combining BDS-3 with other Global navigation satellite systems (GNSS) and selecting different geographic stations. The results demonstrate that changing the threshold significantly affects the maneuvering detection of C60, with the optimal maneuvering thresholds of C59 and C60 being 0.045 and 0.02, respectively. A combination of BDS-3 and GPS with equal weights was identified to be most suitable for maneuvering detection of GEO satellites. For any specific maneuver, the difference between the maneuvering time detection of C59 by stations at different geographical locations was no more than 1 min. During the maneuvering detection of C60, the start time of maneuvering detected by African stations was 4.26–8.61 min earlier than that detected by the Chinese and Australian stations, and the end time of maneuvering detected by the African stations was consistent with that detected by the Chinese and Australian stations. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) technology is one of the core technologies in the field of GNSS high-precision positioning. It is used widely because it can realize centimeter-level positioning in outdoor environments by using only a single receiver. However, its convergence is time-consuming, particularly in urban areas where satellite occlusion is more severe. A combined BeiDou Navigation Satellite System (BDS) and fifth generation mobile communication technology (5G) PPP observation model is proposed, in which the two kinds of observations are combined and solved at the original observation level. The impact of different numbers and geometries of 5G base stations on the convergence time of PPP is analyzed from both static and dynamic perspectives. The results confirm that PPP technology combining BDS and 5G can effectively accelerate convergence while improving the accuracy of positioning. [ABSTRACT FROM AUTHOR]

The design of a modern Global Navigation Satellite System (GNSS) has been exceptionally valued by the military and civilians of various countries. The inclusion of the pilot channel in addition to the navigation data channel is considered one of the major changes in GNSS modernization. Schemes of an equal weight combination (1:1 combination) and power ratio combination for data and pilot are primarily adopted by traditional receivers. With the emergence of the new data and pilot modulation signals with unequal power, such as L1C at Global Positioning System (GPS) L1 frequency and B1C at BeiDou Navigation Satellite System (BDS) B1 frequency, the traditional combination coefficient cannot achieve optimal reception performance. Considering the influence of the combination coefficient on the reception performance, the optimal coefficient of the correlator joint is estimated in this paper. The entire architecture of the data/pilot correlator joint tracking and positioning with unequal power is given. Based on the equivalence principle of the correlator joint and the discriminator joint, the optimal coefficient of the carrier loop is determined. A mathematical model of joint code tracking accuracy is established, and the optimal coefficient of the code loop is determined. The real-life satellite signal and simulation results show that the amplitude–ratio combined scheme is the best for receiving of correlator joints, followed by the power–ratio combination scheme and, finally, the 1:1 combination scheme. It is worth mentioning that the positioning accuracy of the amplitude–ratio combination is improved by 2% compared to the 1:1 combination, and by 1.3% compared to the power–ratio combination for B1C signal. The positioning accuracy of the amplitude–ratio combination is improved by 2.37% compared to the 1:1 combination, and by 1.6% compared to the power–ratio combination for L1C signal. The conclusions of this paper are validated for the traditional data/pilot with an equal power allocation. The techniques and test results provide technical support for GNSS high-precision-user receivers. [ABSTRACT FROM AUTHOR]

With the development of the Chinese BeiDou Navigation Satellite System (BDS), from a regional system BDS-2 to a global system BDS-3, more satellites can now be employed in the domain of globally precise time and frequency transfer. However, if the current BDS-3 and BDS-2, Global Positioning System (GPS), Galileo and GLObal NAvigation satellite system (GLONASS) are combined for multi-global navigation satellite system (multi-GNSS) time transfer, the characteristics of inter-system biases (ISBs) remain unclear. In this study, we analyzed the characteristics of ISBs between BDS-3 and BDS-2, GPS, Galileo and GLONASS, and revealed that their ISB series is not constant and that all the daily ISB series of the multi-GNSS show some systematic characteristics among different stations. Therefore, three stochastic models for ISBs of white noise process, random constant process and random walk process expressed as 'White', 'Hour' and 'Walk', respectively, were employed to assess the performance of the time and frequency transfer using the time link accuracy and frequency stability indicators. The results show that the models for the 'Hour' and 'Walk' schemes are notably better than that for the 'White' scheme by 10.4% and 16.8%, respectively, for the least noisy time link of WTZZ-BRCH. Furthermore, the improvements in the 'Hour' and 'Walk' schemes are 2.1% and 3.5%, respectively, for the TP01-BRCH time link, when compared with that of the 'White' scheme. With respect to frequency stability, the 'Hour' and 'Walk' schemes also perform better in terms of frequency stability than the 'White' scheme at different time intervals. Similarly, the improvements over the 'White' scheme are 5.05% and 4.97% for the TP01-BRCH time link and are 24.01% and 32.48% for the WTZZ-BRCH time link. [ABSTRACT FROM AUTHOR]

Signal-in-space (SIS) continuity and availability are important indicators of performance assessment for Global Navigation Satellite Systems (GNSSs). The BeiDou Navigation Satellite System (BDS) Open Service Performance Standard (BDS-OS-PS-1.0) has been released, and the corresponding public performance indicators have been provided, but the actual SIS performance is uncertain to users. SIS continuity and availability are primarily related to unscheduled outages (failures). Therefore, based on the existing failure classification system and actual operation modes, four types of failure modes are first analysed: long-term failure related to satellite service period, maintenance failure related to satellite manoeuvring, short-term failure associated with random repairable anomalies and equivalent failure corresponding to a combination of the above three types of failures. Second, based on the failure classification and selected precise and broadcast ephemerides from 2015–2016, the Mean Time Between Failure (MTBF) and Mean Time To Repair (MTTR) of each failure type are obtained using appropriate detection methods. Finally, using a corresponding assessment model, the SIS continuity and availability of BeiDou are calculated for individual and equivalent failure cases, and these are compared with the provided index in the BDS Open Service Performance Standard. [ABSTRACT FROM AUTHOR]

The signal-in-space (SIS) anomalies caused by satellites and control segments can greatly affect the reliability and safety of navigation and positioning users. The prior information associated with the failure of the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm were obtained by the evaluation of SIS failure rates broadcasted with navigation ephemeris to investigate the integrity of navigation and positioning. For the existing ARAIM algorithm, the failure rate of satellites in the BeiDou Navigation Satellite System (BDS) is a conservative estimate, which is inconsistent with the actual SIS performance of BDS. Only the accurate detection of the SIS anomalies of BDS satellites can provide an effective reference to associate with failure. Therefore, to improve the accuracy of SIS anomaly detection for BDS satellites, and to provide higher integrity services for users, this study presents an improved method of SIS anomaly detection with precise ephemeris. The median method was used to detect a gross error in clock data before the calculation of clock datum, and the combination of an experience threshold and trimmed mean was used to determine the anomaly detection threshold. The feasibility and efficiency of the proposed method were also analyzed using data collected between 2015 and 2016. The detection results show that the constellation fault caused by erroneous clock data can be avoided, and the SIS anomalies can also be detected using the proposed method. Additionally, through the comprehensive tests performed in this study, it was found that from 2015 to 2016, the average accumulated duration of anomalies for BDS satellites was 10 h for geostationary orbit (GEO) and incline geosynchronous orbit (IGSO) and 55 h for medium earth orbit (MEO), respectively. These anomalies were primarily caused by the satellite clock. [ABSTRACT FROM AUTHOR]

In this study, a model of precise time transfer is developed based on the triple-frequency un-combined observations of the BeiDou navigation satellite system, known as UC-PPP. In this model, except for the traditional position, troposphere delay and receiver clock parameters, ionosphere delays are estimated as unknown parameters by adding the prior, spatial and temporal constraints. In addition, receiver differential code biases (DCB) are also estimated as unknown parameters. The standard triple-frequency ionosphere-free model is also introduced, named as IF-PPP. To assess the performance of the model, datasets with short baseline and common external time frequency are used. The results show that the triple-frequency UC-PPP model can be used for precise time transfer, with accuracy and stability identical to those of the IF-PPP model. The model can also provide the receiver DCB and ionosphere total electron content products. [ABSTRACT FROM AUTHOR]

This paper proposes a model for combined Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) Real-Time Kinematic (RTK) positioning. The approach uses only one common reference ambiguity, for example, that of GPS L1, and estimates the pseudo-range and carrier phase system and frequency biases. The validations show that these biases are stable during a continuous reference ambiguity period and can be easily estimated, and the other estimated double-differenced ambiguities, such as those of GPS L2, BDS L1, and BDS L2, are not affected. Therefore, our approach solves the problems of a frequently changing reference satellite. In addition, because all the carrier phase observations use the same reference ambiguity, a relationship is established between the different systems and frequencies, and the strength of the combined model is thus increased. [ABSTRACT FROM AUTHOR]

China is promoting the construction of an integrated positioning, navigation, and timing (PNT) systems with the BeiDou Navigation Satellite System (BDS) as its core. To expand the positioning coverage area and improve the positioning performance by taking advantage of device-to-device (D2D) and self-organizing network (SON) technology, a BDS/SON integrated positioning system is proposed for the fifth-generation (5G) networking environment. This system relies on a combination of time-of-arrival (TOA) and BeiDou pseudo-range measurements to effectively supplement BeiDou signal blind spots, expand the positioning coverage area, and realize higher precision in continuous navigation and positioning. By establishing the system state model, and addressing the single-system positioning divergence and insufficient accuracy, a robust adaptive fading filtering (RAF) algorithm based on the prediction residual is proposed to suppress gross errors and filtering divergence in order to improve the stability and accuracy of the positioning results. Subsequently, a federated Kalman filtering (FKF) algorithm operating in fusion-feedback mode is developed to centrally process the positioning information of the combined system. Considering that the prediction error can reflect the magnitude of the model error, an adaptive information distribution coefficient is introduced to further improve the filtering performance. Actual measurement and significance test results show that by integrating BDS and SON positioning data, the proposed algorithm realizes robust, reliable, and continuous high precision location services with anti-interference capabilities and good universality. It is applicable in scenarios involving unmanned aerial vehicles (UAVs), autonomous driving, military, public safety and other contexts and can even realize indoor positioning and other regional positioning tasks. [ABSTRACT FROM AUTHOR]

The modernized GPS, Galileo, and BeiDou global navigation satellite system (BDS3) offers new potential for time transfer using overlap-frequency (L1/E1/B1, L5/E5a/B2a) observations. To assess the performance of time and frequency transfer with overlap-frequency observations for GPS, Galileo, and BDS3, the mathematical models of single- and dual-frequency using the carrier-phase (CP) technique are discussed and presented. For the single-frequency CP model, the three-day average RMS values of the L5/E5a/B2a clock difference series were 0.218 ns for Galileo and 0.263 ns for BDS3, of which the improvements were 36.2% for Galileo and 43.9% for BDS3 when compared with the L1/E1/B1 solution at BRUX–PTBB. For the hydrogen–cesium time link BRUX–KIRU, the RMS values of the L5/E5a/B2a solution were 0.490 ns for Galileo and 0.608 ns for BDS3, improving Galileo by 6.4% and BDS3 by 12.5% when compared with the L1/E1/B1 solution. For the dual-frequency CP model, the average stability values of the L5/E5a/B2a solution at the BRUX–PTBB time link were 3.54 × 10−12 for GPS, 2.20 × 10−12 for Galileo, and 2.69 × 10−12 for BDS3, of which the improvements were 21.0%, 45.1%, and 52.3%, respectively, when compared with the L1/E1/B1 solution. For the BRUX–KIRU time link, the improvements were 4.2%, 30.5%, and 36.1%, respectively. [ABSTRACT FROM AUTHOR]

The orbital maneuvers of the global navigation satellite system (GNSSs) have a significant influence on the performance of the precise positioning, navigation, and timing (PNT) services. Because the Chinese BeiDou Navigation Satellite System (BDS) has three types of satellites in the geostationary orbit (GEO), inclined geosynchronous orbit (IGSO), and medium earth orbit (MEO) maneuvers occur more frequently. Thus, it is essential to determine an effective approach for the detection of orbital maneuvers. This study proposes a method for the detection of orbital maneuvers using epoch-differenced carrier phase observations and broadcast ephemeris data. When using the epoch-differenced velocity estimation as a basic data solution model, the time discrimination and satellite identification factors are defined and used for the real-time detection of the beginning and the pseudorandom noise code (PRN) of satellites. The datasets from four GNSS stations (WUH1, BJF1, POHN, CUT0) from the year 2016 were collected and analyzed. The validations showed that the beginning, the PRN of the orbital maneuver of the satellite can be precisely detected in real time for all GEO, IGSO, and MEO satellites, and the detected results also showed good consistency, with the beginning time at a difference of 1–2 min across different stations. The proposed approach was observed to be more sensitive, and the detected beginning time was about 30 min earlier than the single point positioning approach when the high-precision carrier phase observation was used. Thus, orbital maneuvering can be accurately detected by the proposed method. It not only improves the utilization of the collected data but also improves the performance of PNT services. [ABSTRACT FROM AUTHOR]

The satellite-induced code bias variation of geostationary satellite orbit satellites and medium earth orbit satellites of the second-generation BeiDou Navigation Satellite System (BDS-2) exceeds 1 m, which severely affects the accuracy and stability of the ambiguity resolution and high-precision positioning. With the development of the third-generation BDS (BDS-3) with a new system design and new technology, analysis of the satellite-induced code variation characteristics of BDS-3 has become increasingly important. At present, many scholars have explored the satellite-induced code bias of BDS-3, but most of them focus on BDS-3 experimental satellites via normal geodetic antenna. Compared to normal geodetic antenna, the 40-m dish antenna from the National Time Service Center can accurately detect satellite-induced code variations with low noise and high gain. Thus, observational data from fifteen BDS-3 medium earth orbit satellites are collected with the B1I/B2b/B3I/B1C/B2a frequency bands on the day of year (DOY) 199–206 in 2019, the PRN numbers of which are C19/C20/C21/C22/C23/C24/C25/C26/C27/C28/C30/C32/C33 /C35/C37, via the 40 m dish antenna to analyze the code bias variation characteristics. The results show that the obvious satellite-induced elevation‑dependent code bias variations exist in the B1I/B2b/B3I/B1C/B2a frequency bands of C28, compared with other satellites. Similarly, the multipath (MP) combination of B3I has an obvious elevation‑dependent variation within a range of 0.1 m for C21/C24/C27/C28/C37 and elevation‑dependent variation of the B2a and B2b frequency bands also exists in most satellites with a range of 0.1 m. However, the MP combination values of some satellites are asymmetric with respect to elevation, which is different from BDS-2 satellites and especially obvious for BDS-3 satellites B1I and BIC frequency bands with elevation‑dependent variations of 0.2 m, indicating that the code bias variation is not uniquely related to elevation, especially for the B1I/BIC frequency bands. What's more, the satellite-induced code bias variation of the BDS-3 satellites is greatly reduced compared with that of the BDS-2 satellites. In addition, the similar code bias variation appears at the Xia1 station with a normal geodetic antenna of B1I/B1C/B3I/B2a/B2b of C21, B3I/B2a/B2b of C24 and B2b of C28 among B1I/B1C/B3I/B2a/B2b of C21/C24/C27/C28/C37. The influence of the BDS-3 satellite-induced elevation‑dependent code bias on precision positioning and ambiguity fixing is worth further study using different antennas or receivers. [ABSTRACT FROM AUTHOR]

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver. [ABSTRACT FROM AUTHOR]

• GTS distribution of orbit determination can be optimized by the proposed algorithm. • GTS saturated number for orbit determination can be got by the proposed algorithm. • ISL can weaken the influence of GTS distribution and number on orbit determination. A precise satellite orbit is the basis for high-precision services for users, and the determination of high-precision satellite orbits depends on the reasonable distribution and volume of ground tracking stations (GTSs). In July 2020, the BeiDou global navigation satellite system (BDS-3) was completed and began to be operated globally. Based on the principle of dynamic orbit determination, we first developed an algorithm to determine the optimal distribution and number of GTSs for accurate satellite orbit determination. Subsequently, based on 10 GTSs located in China, the optimal distribution and number of GTSs with and without inter-satellite link (ISL) ranging observations were determined. Finally, real measurements of GTS and ISL ranging observation data were used to validate the GTS results yielded by the algorithm. Using 18 BDS-3 satellites, and based on non-ISL observations and 10 Chinese regional GTSs, we found that GTSs distributed near the equator contributed significantly to the accuracy of orbit determination for these satellites compared to other GTSs. Orbit determination results obtained from the measured data of the optimal GTSs were more accurate than those obtained from the measured data of uniformly distributed global GTSs. Upon the addition of 55 uniformly distributed GTSs worldwide, the orbit determination accuracy for BDS-3 satellites tended to plateau. Moreover, following the addition of ISL, although the distribution and number of GTSs was optimized using the proposed algorithm, the orbit determination results from the measured data revealed that a change in the distribution and number of GTSs had a limited effect on the BDS-3 orbit determination results. [ABSTRACT FROM AUTHOR]

• Under regional GTS, ISL significantly improves BDS-3 orbit determination accuracy. • The initial weight ratio has little effect on the result when VCE algorithm is used. • VCE algorithm has contribute to fusion data processing of L-band and Ka-band. The BeiDou global navigation satellite system (BDS-3) has established the Ka-band inter-satellite link (ISL) to realize a two-way ranging function between satellites, which provides a new observation technology for the orbit determination of BDS-3 satellites. Therefore, this study presents a BDS satellite orbit determination model based on ground tracking station (GTS) observations and ISL ranging observations firstly to analyze the impact of the ISL ranging observations on the orbit determination of BDS-3 satellites. Subsequently, considering the data fusion processing, the variance component estimation (VCE) algorithm is applied to the parameter estimation process of the satellite orbit determination. Finally, using the measured data from China's regional GTS observations and BDS-3 ISL ranging observations, the effects of ISL ranging observations on the orbit determination accuracy of BDS-3 satellites are analyzed. Moreover, the impact of the VCE algorithm on the fusion data processing is evaluated from the aspects of orbit determination accuracy, Ka-band hardware delay parameter stability, and ISL ranging observation residuals. The results show that for China's regional GTSs, the addition of BDS-3 ISL ranging observations can significantly improve the orbit determination accuracy of BDS-3 satellites. The observed orbit determination accuracy of satellite radial component is improved from 48 cm to 4.1 cm. In addition, when the initial weight ratio between GTS observations and ISL ranging observations is not appropriate, the various indicators which include orbit determination accuracy, ISL hardware delay, and ISL observation residuals were observed to have improved after the adjustment of the VCE algorithm. These results validate the effectiveness of the VCE algorithm for the fusion data processing of the GTS observations and ISL ranging observations. [ABSTRACT FROM AUTHOR]

In order to analyse the contribution of inter-satellite ranging observation to the BeiDou regional navigation satellite system (BDS-2) satellite orbit determination under the condition of regional ground tracking stations, first, the methods of using the observation model, the dynamic parameters dilution of precision (DPDOP), and the satellite position dilution of precision (SPDOP) to describe the contribution of inter-satellite ranging observation to orbit determination accuracy are proposed. Then, based on the measured observation data of the regional ground tracking stations located in China, as well as simulated inter-satellite ranging observation data, the contribution of inter-satellite ranging observation to orbit determination accuracy for the three types of satellites used by BDS-2 is analysed. The results show that the inter-satellite ranging observation improves the solution strength of the dynamic parameters by adding redundant observations without adding new parameters to be estimated, which effectively improves the orbit determination accuracy of the along-track component of Geostationary Earth Orbit (GEO) satellite and the cross-track and radial components of Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. In addition, under the condition of the regional tracking stations, the inter-satellite ranging observation compensates for the disadvantage that the satellite cannot be tracked by the whole arc segment. The accuracy and continuous stability of the orbit determination solution and the geometry structure of satellites that can be observed by stations and other satellites are significant improved, for which the average DPDOP values of GEO, IGSO, and MEO satellites are improved 50.2%, 73.0%, and 72.1%, respectively. • Simulated ISL observations improves the orbit determination accuracy of BDS-2. • Simulated ISL observations compensates for the observed arc of satellites. • Simulated ISL observations improves the observed structure of satellites. [ABSTRACT FROM AUTHOR]

• We analyze the time synchronization performance within the BDS-3 ISL system using real data (one month) • A two-way time synchronization method with error correction models is utilized. • The one-way ranging accuracy of BDS-3 ISLs is consistently better than 7 cm, and the calculated clock-free observables better than 5 cm. • Correcting various errors is crucial for improving synchronization to sub-ns levels. • The overall time synchronization accuracy between satellites achieved is better than 0.4 ns, with most BDS-3 satellites showing comprehensive synchronization accuracy of better than 0.3 ns. • The results verify the effectiveness of the BDS-3 ISL system for high-precision timekeeping. Time synchronization through inter-satellite link (ISL) observations is crucial for enabling autonomous navigation in global navigation satellite systems. This study investigates the time synchronization performance within China's BeiDou Navigation Satellite System (BDS) using ISL measurements from 29 BDS-3 constellation satellites. A dedicated two-way time synchronization method is detailed, emphasizing its uniqueness and precision in ensuring accurate time synchronization. The study also delves into the application of various error corrections, encompassing time delay induced by motion, relativistic effects, and hardware delays. Ranging results show accuracies around 7 cm for one-way ISLs. The impact of error corrections is quantified, with the time delay error caused by motion exhibiting the most significant influence on synchronization accuracy. Using one month of BDS-3 ISL data, time synchronization accuracies better than 0.4 ns are consistently achieved between all satellites after implementing comprehensive error mitigation. The results indicate the robust performance of the BDS-3 ISL system for high-precision timekeeping, supporting autonomous orbit determination and navigation without relying on ground monitoring. These findings demonstrate the effectiveness of using ISLs for GNSS satellites and provide valuable insights for advancing satellite navigation capabilities. [ABSTRACT FROM AUTHOR]

Abstract A new BeiDou Navigation Satellite System (BDS) Real Time Kinematic (RTK) algorithm based on zero-combined observations and ionosphere constraints is developed in this study. When applying the zero-combined observations, the Double-Differenced (DD) ionospheric residuals are estimated as unknown parameters by adding the a priori information, i.e., the spatial and temporal ionosphere constraints. An experimental dataset was used to perform the validation and analysis. The results show that the proposed algorithm can precisely correct the DD atmosphere residuals, not only for the short baselines but also for the long baselines. Besides, the positioning results reveal much smaller noise and are more stable than the method of utilizing ionosphere-free combinations. A positioning accuracy of about 1–2 cm can be achieved with the BDS RTK for the baseline of 100 km. [ABSTRACT FROM AUTHOR]

• Proposed a combined positioning algorithm with BDS and 5G that is based on raw observations. • It is suitable for the environment with the geometric distribution of satellites was uneven or the number of visible satellites was insufficient. • Positioning algorithm of TDOA based on 5G millimeter wave. In environments such as urban canyons and indoor environments, an insufficient number of visible satellites can degrade the positioning performance of the BeiDou Navigation Satellite System (BDS). Thus, a positioning algorithm that combines the BDS and 5G technology was developed based on raw observation data. Three different satellite occlusion environments were simulated to compare the effects of factors such as the number of base stations and geometric configurations on the positioning performance. The experimental results revealed that the introduction of 5G base stations effectively increased the positioning accuracy and reliability under different occlusion conditions. Additionally, increasing the number of base stations and optimizing the geometric configuration further improved the accuracy and reliability of fusion localization. Moreover, the positive effects of the introduction of 5G base stations were stronger under more severe satellite occlusion conditions. In the future, this fusion positioning algorithm is expected to facilitate the realization of seamless indoor and outdoor positioning. [ABSTRACT FROM AUTHOR]

• The SEID model is used to efficiently correct the ionospheric delay of single frequency stations. • The SEID model to BDS-2 and BDS-3 new signals single frequency PPP are evaluated. • The performance between single- and dual-frequency PPP is compared for GPS and BDS. The Satellite-specific Epoch-differenced Ionospheric delay (SEID) model can effectively correct ionospheric errors, which is of great significance in the application of entailing low-cost global positioning system (GPS) single-frequency (SF) receivers for retrieving tropospheric delays and deformation monitoring. This study aims to explore the impact of the SEID model on SF and dual-frequency (DF) precise point positioning (PPP) based on the GPS–, BeiDou Navigation Satellite System (BDS) –only and the GPS–BDS dual-system. Two sets of data were collected, corresponding to three test networks with DF stations separated by 34, 139, and 172 km, respectively. The GPS, BDS, and GPS–BDS dual-system observations in the networks were utilized to test positioning results, tropospheric delay and the impact of satellite-induced code bias variations existing in BDS on the positioning of DF PPP with ionosphere-free combinations, ionosphere-constrained SF PPP, and SF PPP based on SEID model transformation (STSF). The results show that the positioning results of STSF PPP became slightly inaccurate with increasing reference station separation distances. However, the SF PPP based on the SEID model exhibited substantially improved positioning accuracy and coordinate repeatability of SF PPP especially with regard to BDS, and obtain similar positioning results of DF PPP. The difference in the Standard Deviation (STD) and Root Mean Square (RMS) of the positioning bias of the GPS-only and GPS-BDS dual systems between DF PPP and STSF PPP was similar within 1 cm, but the difference in the case of BDS was as large as 2 cm in the E and U directions in the networks with separations of 139 and 172 km. Furthermore, the improvement of the STD and RMS of the STSF PPP positioning result was the greatest more than 67% for GPS–, BDS–only, and GPS–BDS dual- system in the networks separated by 34 km compared to SF PPP. [ABSTRACT FROM AUTHOR]

• Real-time monitoring the dynamic variation of satellite orbital maneuvers. • Extending the usable observations for improving the user service. • Useful for precise orbit control and satellite healthy monitoring. The BeiDou Navigation Satellite System (BDS) frequently experiences orbital maneuvers. This study proposed a method for the real-time monitoring of the dynamic variation of satellite orbital maneuvers. Based on the epoch-differenced velocity estimation model, the epoch variation of the receiver clock error can be calculated for each station. The dynamic variation of the orbital maneuver can then be estimated real-time by the monitoring model, using observations from three or more BDS tracking stations. The feasibility and effectiveness of this method is validated by different datasets. The results show that the method can precisely detect orbital maneuvers, thereby extending the usable observations for about three hours. Thus, it is useful for improving the positioning, navigation, and timing service. The dynamic variations of orbital maneuvers can be monitored in real-time, which is useful for precise orbit control, and is helpful for keeping the satellite healthy and monitoring the navigation system operation. [ABSTRACT FROM AUTHOR]