GNSS Research Articles

Infrastructures of globalisation. Shifts in global order and Europe’s strategic choices

In the emerging triad competition between the US, China and the EU, the control over infrastructures is increasingly contested. This paper asks how this conflict of connectivity influences the EU’s infrastructure policy and what specific factors play a role when translating these global shifts into strategies. We develop a political-economic perspective that highlights the relevance of infrastructures for capitalist production and the pattern of dependencies between actors. Viewing the triad competition in infrastructural terms, we argue that the EU is in the process of becoming a geopolitically and geoeconomically oriented infrastructural policy actor. Two cases in the field of high-tech infrastructure are studied more deeply: the EU’s development of the satellite navigation system Galileo and its strategy on 5G. They show that – despite the EU’s geoeconomic approach – the particular mode of global competition in combination with internal political factors can hinder the translation of geoeconomic ambitions into specific policies.

A Novel Design of Flat-Top Beamforming Anti-Multipath Antenna

This article discusses a novel design method of wide-beam circular polarization array antenna for satellite navigation. For special applications such as satellite navigation guiding aircraft landing, high-performance ground reference station antennas are required. In the system of satellite navigation guiding aircraft landing, the antenna of satellite navigation receiver needs to have the following radiation characteristics: the shape of antenna pattern is close to an ideal hemisphere, the upper half of space has uniform right-hand circular polarization gain, and the beam has the characteristic of sharp cutoff below 5 degrees of elevation. Whether the GNSS reference station antenna can have a wider beam circular polarization characteristic to receive more navigation satellites signal; whether it can suppress the multipath effect to a greater extent to reduce the multipath error; and whether it can work in a wider frequency band, so that several major satellite navigation systems work together, the above factors directly affect the satellite navigation and positioning accuracy of the entire system. The beam of this antenna has the following feature: sharp cutoff near the horizon for multipath mitigation at low elevation angles. Comprehensive design thereby accelerates system design. It owns wide beam, good circular polarization characteristics, low elevation angle sharp cutoff, and ultralow sidelobe radiation characteristics that achieve the purpose of receiving satellite navigation signal and multipath. The low sidelobe characteristic of the antenna is beneficial to suppress multipath effect. According to the theoretical knowledge of the symmetrical dipole and the four-arm helical antenna, the simple structure of the symmetrical element is fully utilized, and the printed balun easily realizes the dual-frequency operation of the antenna. Combined with the wide-beam circular polarization characteristic of the four-arm helical antenna structure, the shaped beam array antenna is designed. The wide-beam circularly polarized antenna unit not only covers the frequency band of the satellite navigation system but also satisfies the system performance and key feature requirements of the array antenna for the unit; that is, it satisfies the wide-beam circular polarization characteristics of the upper half space. According to the linear array basic theory and array antenna synthesis theory, Woodward Lawson sampling synthesis algorithm is used to synthesize the array amplitude and phase weights corresponding to the specific antenna pattern required for the Ground-Based Augmentation System (GBAS) engineering. The shaped beam array antenna consists of 21 units, of which 11 antenna units are directly fed, and the feeding ports of the rest are dummy ports. It is an equally spaced array antenna. The spacing between antenna units is close to half wavelength. They are fed according to the value corresponding to the excitation function. The array antenna is simulated by HFSS (High-Frequency Structure Simulator). Compared with traditional satellite navigation antennas, the antenna in this paper has excellent front-to-rear ratio and flat-top beam pattern. The results show that the wide-beam circularly polarized array antenna meets the engineering requirements of GBAS applications and lays the solid foundation for GBAS engineering applications.

Performance assessment of real-time orbit determination for the Haiyang-2D using onboard BDS-3/GPS observations

The Global Navigation Satellite System (GNSS) receivers equipped on the Haiyang-2D (HY-2D) satellite is capable of tracking the signals of both the third generation of BeiDou satellite navigation System (BDS-3) and the Global Positioning System (GPS), which make it feasible to assess the performance of real-time orbit determination (RTOD) for the HY-2D using onboard GNSS observations. In this study, the achievable accuracy and convergence time of RTOD for the HY-2D using onboard BDS-3 and GPS observations are analyzed. Benefiting from the binary-offset-carrier (BOC) modulation, the BDS-3 C1X signal includes less noise than the GPS C1C signal, which has the same signal frequency and chipping rate. The root mean squares (RMS) of the noises of C1X and C1C code measurements are 0.579 m and 1.636 m, respectively. Thanks to a ten-times higher chipping rate, the code measurements of BDS-3 C5P, GPS C1W and C2W are less noisy. The RMS of code noises of BDS-3 C5P, GPS C1W, and C2W are 0.044 m, 0.386 m, and 0.272 m, respectively. For the HY-2D orbit, the three-dimensional (3D) and radial accuracies can reach 31.8 cm and 7.5 cm with only BDS-3 observations, around 50 % better than the corresponding accuracies with GPS. Better performance of the BDS-3 in RTOD for the HY-2D is attributed to the high quality of its broadcast ephemeris. When random parameters are used to absorb ephemeris errors, substantial improvement is seen in the accuracy of HY-2D orbit with either BDS-3 or GPS. The 3D RMS of HY-2D orbit errors with BDS-3 and GPS are enhanced to 23.1 cm and 33.6 cm, and the RMS of the radial components are improved to 6.1 cm and 13.3 cm, respectively. The convergence time is 41.6 and 75.5 min for the RTOD with BDS-3 and GPS, while it is reduced to 39.2 and 27.4 min after the broadcast ephemeris errors are absorbed by random parameters. Overall, the achievable accuracy of RTOD with BDS-3 reaches decimeter level, which is even better than that with GPS, making real-time navigation using onboard BDS-3 observations a feasible choice for future remote sensing missions.

A Survey of GNSS Spoofing and Anti-Spoofing Technology

With the development of satellite navigation technology, the research focus of GNSS has shifted from improving positioning accuracy to expanding system application and improving system performance. At the same time, improving the survivability of satellite navigation systems has become a research hotspot in the field of navigation, especially with regard to anti-spoofing. This paper first briefly analyzes the common interference types of satellite navigation and then focuses on spoofing. We analyze the characteristics and technical mechanism of satellite navigation and the positioning signal. Spoofing modes are classified and introduced separately according to signal generation, implementation stage and deployment strategy. After an introduction of GNSS spoofing technology, we summarize the research progress of GNSS anti-spoofing technology over the last decade. For anti-spoofing technology, we propose a new classification standard and analyze and compare the implementation difficulty, effect and adaptability of the current main spoofing detection technologies. Finally, we summarize with considerations, prospective challenges and development trends of GNSS spoofing and anti-spoofing technology in order to provide a reference for future research.

Damped Micromechanical Hyrovertical

The article considers the methods for vertical gyro construction on rough microelectromechanical elements, such as: angular velocity sensors and accelerometers. It is proposed to improve the accuracy of the microelectromechanical vertical gyro by combining it with a satellite navigation system. The solutions proposed in the article make it possible to improve the accuracy of the integrated vertical gyro based on micromechanical technologies, by the means of complex data processing that uses a compensation scheme with the latest dynamic filter, which practically does not distort the errors of the strapdown inertial microelectromechanical vertical gyro, and thus obtain an estimate of the ground speed as close to the true speed as possible. Based on the obtained estimate, it is proposed to construct a scheme of the vertical gyro speed correction (damping scheme), which would significantly improve the accuracy of estimation of the angular orientation’s parameters.

Performance Evaluation of Near Real-time GNSS PPP Time Transfer with IGS Products

The GNSS time transfer technology is the high precision time transfer method based on the navigation satellite system and has been widely applied in time and frequency. Benefiting from the development of GNSS time transfer technology and the expansion of user needs for real-time time service applications, real-time time transfer technology has become an important research direction. GNSS Precise Point Positioning (PPP) is one of the most commonly used methods of GNSS time transfer technology. With the development of the many facilities, the application of the real-time GNSS PPP has become wider and wider. In this paper, we demonstrate and evaluate the performance of the international GNSS service (IGS) products in the near real-time PPP time transfer technology. A set of the PPP solutions were computed from the observed data from the timekeeping laboratories, and three types of products provided by IGS, including Ultra-Rapid (IGU), Rapid (IGR), and Final (IGS final) orbit and clock offset products. IGS final and IGR products have extremely high accuracy and stability and are used as a reference for the time transfer with IGU product. The near real time clock offset and the comparison link performed with the IGU product can provide a time comparison service with an accuracy of 0. 5ns for near real time applications.

Physical Augmentation Factor of Precision in Gnss

Abstract The dilution of precision (DOP) in satellite navigation system provides a simple characterization of the user–satellite geometry and a quantitative assessment of the positioning constellation configuration. The essential idea of physical augmentation factor of precision (PAFP) proposed in this work, is that navigation signals are transmitted at multiple frequencies from each visible satellite in the positioning constellation, while users measure the corresponding multiple pseudoranges of satellites to achieve high precision code positioning. As the multiple pseudoranges of one satellite are measured independently by the corresponding navigation signals at different frequencies, it is reasonable to treat the measurement errors due to the satellite clock and ephemeris, the atmospheric propagation as uncorrelated, random, and identically distributed. The multipath effects and receiver noise are also processed with some empirical models. By measuring user–satellite code pseudoranges at different frequencies, the PAFP offers a scheme that produces the same effect as that of the redundant-overlapping constellation, thus equivalently improving the geometric DOP. It can effectively improve code positioning precision of satellite navigation system.

한국형 위성항법시스템(KPS)을 활용한 군사용 드론의 위치추적 및 회수 방안

Drones are emerging as a primary means rather than a secondary ones to wage war around the world. For this reason, military drones are concentrated in a country’s science and technology, and if they are crash-landed or are seized and fall into the hands of hostile forces, it can be fatal to national security. The Republic of Korea (ROK) armed forces are no exception as it is spurring the deployment of drones while advocating for advanced science and technology forces. Just in time, the Ministry of Science and ICT is promoting the Korean Satellite Navigation System (KPS) project that provides search and rescue services. Therefore, if the ROK armed forces establish a location tracking and recovery system for military drones using KPS in consultation with the Ministry of Science and ICT, it will be possible to stably operate military drones. Through this, the ROK armed forces is able to protect military science and technology in time of emergency.

Використання сучасного програмного забезпечення для визначення дирекційних кутів орієнтирних напрямів

The purpose of the article is to evaluate the accuracy of the method of determining the grid azimuth using the equipment of consumers of satellite navigation systems. Todays, there are several ways to determine the grid azimuth for topogeodetic references. However, due to the development of navigation equipment in the military and in the joint force operation, artillerists use the coordinate method of determining the grid azimuth more and more often. The accuracy and expedience of the method has not been studied yet and requires field research. So, we have already obtained dates as a result of the experiment. Method. The researches have been based on the analysis of available literature sources in this topic and the practical using of the coordinate method for calculates the grid azimuth. The experiment has been carried out to execute topogeodetic survey using GNSS without obstacles to receive GPS-signals and with obstacles one. The conclusions have been based on the results of the experiment and they have been compared with the standart datas and with the other methods. Also the accuracy has been calculated. Results. It has been researched teoretical, methodological and practical problems of using software “Kpopyva”, “Ukrop” and hardware “Bazalt-M” in the army for determining of the grid azimuth by the coordinate method. The experiment has been performed for estimate of accuracy determining of grid azimuth by the coordinate method. The measurements have been performed on the points of the geodetic network. The grid azimuths have been calculated by the datas of the measurements. The calculated grid azimuths have been compared with references datas which have been obtained from catalog of coordinates of geodetic points. The mean squared errors and mean errors by coordinate method have calculated as coordinate differences. The results of experiment and analysis of information open sources have confirmed, that the accuracy of determining the grid azimuths by coordinate method depends from the accuracy of determining coordinates and the distances between points, the coordinates of which have been determined by GNSS. The GNSS, which use in Field Artillery, are providing to use the coordinate method for determining of the grid azimuth onto landmarks for topogeodetic support. If the distance between the points will not less than 400–500 meters and the mean squared of the determining coordinates won’t exceed 3–5 meters, the coordinate method uses. The scientific novelty consist in the researching of the fundamentally new conditions of the use of GNSS and the software in the Joint Force Operation, which provide the necessary accuracy of determining grid azimuth, reduce time for executing, and also it can be the alter method. Practical meaning. The recommendations for using GNSS by tactical level commanders have been developed. The recommendations were based on the analysis of the mean errors of the using of GNSS and comparison of the results with datas of the catalog of coordinates of geodetic points.

Аналіз навігаційних систем автомобілів як систем автоматизації

У статті зазначено, що в наш час автомобільні навігатори набули широкої популярності, а також викладено особливості застосування глобальних навігаційних супутникових систем як одних із найкращих для функціонування таких навігаторів. Описано історію першої супутникової навігаційної системи — Transit. Крім того, проаналізовано принципи роботи, основні особливості, недоліки, місця розташування і сумісність таких існуючих глобальних навігаційних супутникових систем, як NAVSTAR-GPS, ГЛОНАСС, Galileо, Beidou, QZSS (Michibiki) та NavIC. Зазначено, що найкращі показники роботи пристроїв було отримано при застосуванні глобальних навігаційних систем ГЛОНАСС і GPS. Наведено порівняльні характеристики існуючих типів навігаційних систем автомобілів, зокрема штатних і автономних, і навігаційного програмного забезпечення портативних комп’ютерів і систем. Описано особливості роботи і живлення найчастіше застосовуваної штатної навігаційної системи автомобіля. Висвітлено принцип роботи і будову стандартного автомобільного GPS-навігатора як одного з найкращих. Зазначено також, що серед користувачів найпопулярнішими навігаційними системами вважаються портативний комп’ютер і звичайний смартфон із встановленими навігаційними програмами, докладними актуальними мапами і покроковими інструкціями, на відміну від вбудованих систем. Викладено принцип дії всіх марок автомобільних навігаторів. Значну увагу приділено оцінці переваг і недоліків популярних марок штатних навігаційних систем автомобілів, таких як Garmin, TomTom і Magellan. За результатами проведеного дослідження представлено особливості платних і безкоштовних програм автомобільних навігаторів, які набули популярності серед водіїв автомобілів: Яндекс Навігатор, iGo Primo, TomTom, Waze, Google карти, Автоспутник, OsmAnd, 2ГИС і Sygic Car.

Improved F-RRT ∗ Algorithm for Flight-Path Optimization in Hazardous Weather

Hazardous weather has become a major cause of flight delays in recent years. With the development of satellite navigation systems, the study of flight-path optimization under hazardous weather conditions has become especially important. In this study, radar data were used as the basis for the initial flight-restricted area under hazardous weather conditions, and the Graham algorithm was used to delineate the dynamic flight-restricted area by comprehensively considering the hazardous weather boundary changes along with the speed and direction. Then, under the grid environment model, the range of influence, size, and distribution characteristics of the flight-restricted area was examined, and the path optimization model was created according to constraints related to the path distance, corner size, and number of turning points. An improved F-RRT ∗ algorithm was developed to solve the model. The algorithm can overcome the problems of traditional path planning algorithms, such as strong randomness, poor guidance, slow convergence speed, unsmooth paths, and poor tracing smoothness. Finally, a simulation analysis was conducted on the Guiyang–Guangzhou route in China as an example. This study can address the drawbacks of existing research on route change and provide sufficient theoretical support and reference for the implementation of specific route change plans in the future.

BDS/IMU Integrated Auto-Navigation System of Orchard Spraying Robot

To improve the accuracy and reliability of orchard spraying robots, an integrated navigation system was developed, consisting of a real-time kinematic positioning-Beidou satellite navigation system (RTK-BDS) receiver, an inertial measurement unit (IMU), a navigation controller, and servo motors. Using the loose coupling combination method, an error Kalman filter algorithm based on the measurement of position and heading angle is implemented to correct the error of the inertial measurement unit in real time. Combining the kinematics model and the pure pursuit model of the spraying robot, a path-tracking control algorithm is proposed. Path planning was conducted according to the terrain characteristics of orchards. Field experiments were carried out on a spraying robot to evaluate the proposed auto-navigation system. The results showed that when the spraying robot was static, the positioning performances of BDS alone and that of the BDS/IMU combined system were similar, the positioning error was less than 1.5 cm, and the heading angle errors were within 0.3°; when the spraying robot moving alone to a straight line at the speed of 0.4 m/s, the position error of the navigation system only using BDS was less than 5.29 cm, the heading angle error was within 3°, while the position error of BDS/IMU integrated navigation system was less than 2.49 cm, and the heading angle error was within 2°. The accuracy of BDS/IMU integrated navigation system is significantly improved. When the orchard spraying robot was moving at the speed of 0.4 m/s, the maximum offset error was lower than 10.77 cm, the average offset error was not higher than 3.55 cm, and the root mean square error (RMSE) of the lateral deviation was 1.19 cm. The results showed that the proposed auto-navigation system could make the spraying robot track the pre-set path smoothly and stably.

A Review on Multi-GNSS for Earth Observation and Emerging Applications

Global Navigation Satellite System (GNSS) has drawn the attention of scientists and users all over the world for its wide-ranging Earth observations and applications. Since the end of May 2022, more than 130 satellites are available for fully global operational satellite navigation systems, such as BeiDou Navigation Satellite System (BDS), Galileo, GLONASS and GPS, which have been widely used in positioning, navigation, and timing (PNT), e.g., precise orbit determination and location-based services. Recently, the refracted, reflected, and scattered signals from GNSS can remotely sense the Earth’s surface and atmosphere with potential applications in environmental remote sensing. In this paper, a review of multi-GNSS for Earth Observation and emerging application progress is presented, including GNSS positioning and orbiting, GNSS meteorology, GNSS ionosphere and space weather, GNSS-Reflectometry and GNSS earthquake monitoring, as well as GNSS integrated techniques for land and structural health monitoring. One of the most significant findings from this review is that, nowadays, GNSS is one of the best techniques in the field of Earth observation, not only for traditional positioning applications, but also for integrated remote sensing applications. With continuous improvements and developments in terms of performance, availability, modernization, and hybridizing, multi-GNSS will become a milestone for Earth observations and future applications.

Analysis of Orbital Atmospheric Density from QQ-Satellite Precision Orbits Based on GNSS Observations

Atmospheric drag provides an indirect approach for evaluating atmospheric mass density, which can be derived from the Precise Orbit Determination (POD) of Low Earth Orbit (LEO) satellites. A method was developed to estimate nongravitational acceleration, which includes the drag acceleration of the thermospheric density model and empirical force acceleration in the velocity direction from the centimeter-level reduced-dynamic POD. The main research achievements include the study of atmospheric responses to geomagnetic storms, especially after the launch of the spherical Qiu Qiu (QQ)-Satellite (QQ-Satellite) with the global navigation system satellite (GNSS) receiver onboard tracking the Global Positioning System (GPS) and Beidou System (BDS) data. Using this derivation method, the high-accuracy POD atmospheric density was determined from these data, resulting in better agreement among the QQ-Satellite-derived densities and the NRLMSISE-00 model densities. In addition, the POD-derived density exhibited a more sensitive response to magnetic storms. Improved accuracy of short-term orbit predictions using derived density was one of the aims of this study. Preliminary experiments using densities derived from the QQ-Satellite showed promising and encouraging results in reducing orbit propagation errors within 24 h, especially during periods of geomagnetic activity.

Evaluation and comparison of the performance of BDS-3 space-borne atomic clocks

At present, most of the space-borne atomic clocks used by the major global navigation satellite systems include rubidium atomic clocks, passive hydrogen master (PHM) clocks and cesium atomic clocks. The new independently developed space-borne rubidium atomic clocks and PHM clocks on BeiDou Global Navigation Satellite System (BDS-3) are important hardware improvements. In this paper, performances of new Beidou domestic atomic clocks are evaluated using precise clock offset data from September 2019 to September 2021 and compared with the mainstream space-borne atomic clocks of other satellite navigation systems. The results show that the BDS-3 space-borne PHM clocks have low drift rate and high stability at 86400s interval, which respectively reaches 8.26 × 10−16 and 5.13 × 10−15. These performances are only slightly lower than Galileo PHM clocks. The frequency stability at 86400s interval of BDS-3 rubidium clock is up to 9.03 × 10−15, which is 27.76% higher than GPS rubidium clocks.

BeiDou Satellite Radiation Force Models for Precise Orbit Determination and Geodetic Applications

China's BeiDou satellite navigation system (BDS) has completed its full constellation in orbit since June 2020. Services have been evolved from regional (BDS-2) to global (BDS-3). This contribution evaluates the impact of solar radiation pressure (SRP) modeling on satellite orbits and geodetic parameters. To that end, we process 2 years of BDS observations (2019-2021), collected by a network of 100 ground stations. A physical a priori box-wing model based on the estimated optical properties is introduced. Various physical effects, such as radiator emission and thermal radiation of solar panels are considered. The ECOM (Empirical CODE orbit Model), ECOM+along-track and ECOM2 models are employed on top in the experiment. We show that without the use of the a priori box-wing model, the ECOM+along-track model shows clear better orbit solutions during eclipse seasons for BDS-3 satellites. This is proven to be mainly due to the thermal radiation of the solar panels. However, the along-track acceleration is highly correlated with LOD (length of day) and ECOM parameters. LOD estimates in this case are contaminated. When using the physical a priori box-wing model satellite orbital errors are greatly reduced for all the ECOM models. For instance, orbit misclosures of BDS-3 CAST (China Academy of Space Technology) satellites improve by a factor of two for the ECOM model during eclipse seasons. Furthermore, the use of the a priori box-wing model mitigates a great majority of the spurious signals in the geodetic parameters.

Spacecraft tracking control and synchronization: An assessment of conventional, unconventional, and combined methods

Artificial intelligence (AI) promises breakthroughs in space operations, from mission design planning to satellite data processing and navigation systems. Advances in AI and space transportation have enabled AI technologies in spacecraft tracking control and synchronization. This study assesses and evaluates three alternative spacecraft tracking control and synchronization (TCS) approaches, including non-AI TCS methods, AI TCS methods, and combined TCS methods. The study proposes a hybrid model, including a new model for defining weight coefficients and interval type-2 fuzzy sets based combined compromised solution (IT2FSs-CoCoSo) to solve the spacecraft TCS problem. A new methodology is used to calculate the weight coefficients of criteria, while IT2FSs-CoCoSo is applied to rank the prioritization of TCS methods. A comparative analysis is conducted to demonstrate the performance of the proposed hybrid model. We present a case study to illustrate the applicability and exhibit the efficacy of the proposed method for prioritizing the alternative TCS approaches based on ten different sub-criteria, grouped under three main aspects, including complexity aspects, operational aspects, and efficiency aspects. AI and non-AI methods combined are the most advantageous alternative, whereas non-AI methods are the least advantageous, according to the findings of this study.

Assessment of the Water Vapor Tomography Based on Four Navigation Satellite Systems and Their Various Combinations

With the gradual improvement of Galileo and the opening of BDS-3 services, water vapor tomography based on multi-GNSS can be effectively carried out to reconstruct three-dimensional water vapor distribution. In this paper, experiments in Hong Kong were conducted to analyze and assess the performances of GPS, BDS, GLONASS, and Galileo and their combinations in water vapor tomography. Numerical results show that the number of available signal rays varies widely in the four satellite systems, and the value can be increased by the combination of satellite systems; the combinations also increase the number of voxels crossed by signal rays, but this value is not directly related to the number of available signal rays; the number and distribution of the voxels with sufficient signal rays, which most closely related to the structure of the tomographic model, show no obvious differences in the four satellite systems and their combinations. Comparative results of slant water vapor (SWV) estimated by GNSS data and water vapor density derived from radiosonde data reveal that the differences in the water vapor tomography of the four satellite systems are small, and their combinations have limited improvement in the tomographic results.

Research on the Rotational Correction of Distributed Autonomous Orbit Determination in the Satellite Navigation Constellation

The autonomous orbit determination of the navigation constellation uses only bidirectional ranging data of the inter-satellite link for data processing. The lack of space-time benchmark information related to the Earth inevitably causes overall rotational uncertainty in the constellation, leading to a decrease in orbit accuracy and affecting user positioning accuracy. This study (1) introduces a method for rotation correction in distributed autonomous orbit determination based on inter-satellite bidirectional ranging; (2) conducts constellation autonomous orbit determination and time synchronization processing experiments based on inter-satellite ranging data for the 24 medium Earth orbit (MEO) satellites in the Beidou-3 global satellite navigation system (BDS-3); and (3) makes comparative analyses on the accuracy of autonomous orbit determination based on three rotation correction cases, including a no-rotation-correction case, independent satellite constraints case, and global satellite constraints case. The experimental results are described as follows. For the no-rotation-correction case, the prediction error of the orbital inclination angle (iot, i) for the entire constellation on the 30th day was 2.11 × 10−7/rad, the prediction error of the right ascension of the ascending point (Omega, Ω) was 2.25 × 10−7/rad, and the average root mean square (RMS) of the user range error (URE) for the entire constellation orbit was 1.41 m. In the autonomous orbit determination experiment with independent constraints on satellites, the prediction error of i for the entire constellation on the 30th day was 5.43 × 10−7/rad, the prediction error of Ω was 2.03 × 10−7/rad, and the average RMS of the orbital URE for the entire constellation was 1.09 m. In the autonomous orbit determination experiment with global satellite constraints, the prediction error of i for the entire constellation on the 30th day was 5.31 × 10−7/rad, the prediction error of Ω was 1.95 × 10−7/rad, and the RMS of the orbital URE for the entire constellation was 0.94 m. According to the analysis of the above experimental results, compared with the autonomous orbit determination under the no-rotation-correction case, the adoption of an algorithm for independent satellite constraints to correct the overall constellation rotation weakens the constellation rotation influence; however, it may destroy the overall constellation configuration, which affects the stability of autonomous orbit determination. Finally, the algorithm based on global satellite constraints both impairs the influence of constellation rotation and maintains the overall constellation configuration.

Precise point positioning with BDS-2 and BDS-3 constellations: ambiguity resolution and positioning comparison

The full operational capability of the Chinese BeiDou Satellite Navigation System (BDS) has injected additional energy into the GNSS field. Along with the visibility of more BDS satellites, as well as the precise products generated by analysis centers, ambguity float and fixed Precise Point Positioning (PPP) performance with the complete BDS constellation are evaluated in this study. Inter-system biases (ISBs) between BDS-2 and BDS-3 are first evaluated, and Fractional Cycle Bias (FCB) with and without consideration of ISBs are assessed. Results show that when considering ISBs, the standard deviations of ambiguity residuals are smaller, thus the ISB parameter should be taken into consideration in BDS PPP. BDS-3 FCBs are more stable than those of BDS-2, at the same time, the ambiguity residuals are smaller for BDS-3 satellites. In terms of PPP performance, BDS-3 outperforms BDS-2 in positioning accuracy, convergence time and time to first fix. For the test data, the convergence time of BDS-2 static solution is 48.8 min, while for BDS-2 + 3 it is 19.7 min, representing an improvement of 59.6% when BDS-3 satellites are included. The positioning accuracy of static BDS-2, BDS-3 and BDS-2 + 3 PPP can reach the same millimeter-level after a long time of convergence, while kinematic solution with BDS-2 + 3 has the highest accuracy compared to BDS-2 and BDS-3, which could reach 1.7, 1.3 and 4.3 cm in East, North and Up components, respectively, in fixed solution. The performance of BDS PPP with the whole constellation is comparable with that of GPS and Galileo, and the PPP performance is promising with receiver updates for MGEX stations in the near future.