GNSS Research Articles

A Comprehensive Review of GNSS/INS Integration Techniques for Land and Air Vehicle Applications

Navigation systems are of interest for applications in both civilian and military vehicles. Satellite navigation systems and inertial navigation systems are the most applied in this area. They have complementary properties, which has led to a trend of integrating these systems. At present, there are several approaches to GNSS/INS integration: loosely coupled, tightly coupled and deeply coupled and many approaches to their modifications in dependence of application and arising problems with measurements, such as lack of GNSS measurements or poor quality of GNSS and INS measurements. This article presents an extensive review of the available modern approaches and their modifications for integrating INS and GNSS measurements, arranging them and highlights the main problems arising for the considered type of integration approach. The article includes a review of various integration tools based on the Kalman filter and intelligent systems, INS mechanization and features of development of an INS measurement error model that is necessary for integration, the main problems of GNSS/INS integration and a comparative description of the solutions proposed by the authors for solving these problems. The findings of this work are useful for further research in the field of inertial and satellite navigation, as well as for engineers involved in the practical implementation of integrated GNSS/INS systems.

Performance analysis of cross-frequency Doppler-assisted carrier phase tracking

Using the Doppler frequency obtained from tracking a GNSS pilot signal to aid in tracking another signal modulated with higher rate navigation messages in a different frequency band can improve tacking robustness and lower the message demodulation threshold. Based on an analysis of received signal frequency coherence, a linearized mathematical model of the cross-frequency Doppler-assisted carrier phase tracking loop is built, a thermal noise jitter calculation equation for the assisted tracking loop is derived, and its dynamic stress response characteristics are examined. The loop design requirements for eliminating the influence of inter-frequency frequency bias are clarified, as are the cross-frequency assist signal selection criteria. Monte Carlo simulations and preliminary field tests validate the theoretical results using the B1C pilot signal-aided tracking B2b signal of the MEO satellite in the BeiDou satellite navigation system (BDS). Experimental results show that the carrier phase tracking threshold of the B2b signal can be reduced by about 4 dB.

Full-domain collaborative deployment method of multiple interference sources and evaluation of its deployment effect

This paper realizes the full-domain collaborative deployment of multiple interference sources of the global satellite navigation system (GNSS) and evaluates the deployment effect to enhance the ability to disturb the attacker and the capability to defend the GNSS during navigation countermeasures. Key evaluation indicators for the jamming effect of GNSS suppressive and deceptive jamming sources are first created, their evaluation models are built, and their detection procedures are sorted out, as the basis for determining the deployment principles. The principles for collaboratively deploying multi-jamming sources are developed to obtain the deployment structures (including the required number, structures in demand, and corresponding positions) of three single interference sources required by collaboratively deploying. Accordingly, simulation and hardware-in-loop testing results are presented to determine a rational configuration of the collaborative deployment of multi-jamming sources in the set situation and further realize the full-domain deployment of an interference network from ground, air to space. Varied evaluation indices for the deployment effect are finally developed to evaluate the deployment effect of the proposed configuration and further verify its reliability and rationality.

Agricultural Autonomous Robotic Platform Motion Control

A model of the movement of a robotic platform adapted to the conditions of an industrial orchard is proposed. (Research purpose) Development of a motion control system for an autonomous robotic wheeled platform based on inertial and satellite navigation and traversed path calculation, which will allow it to move in an apple orchard and automatically perform various technological operations, such as fertilization, growth diseases control of, fruit harvesting. (Materials and methods) A mathematical model was developed to control the movement of a robotic platform, taking into account the turning radii of three types, the length of the arc of the performed circle, the speed of movement in the garden plantation rows using a garden electronic map. The method used allows implementing a program for the robotic platform automatic movement around a typical orchard using a minimum set of sensors, significantly reducing the load on the onboard computer processor and memory. Software, developed in the Python programming language, enables plotting the robotic platform route, displaying the movement trajectory, and indicating the positioning accuracy at each point in relation to the trees in the garden plantation rows, the movement speed and the wheel rotation angle. (Results and discussion) The robotic platform managed to autonomously pass the preset routes, while the interaction of the software and the robotic platform hardware was provided. A field testing of the developed software was performed. (Conclusions) The specified accuracy of the robotic platform positioning was confirmed for the 3.5-meter aisles of intensive orchards. The maximum deviation from the task map using satellite and inertial navigation system was 164 millimeters, which complies with the agrotechnical requirements for mechanized fruit harvesting.

Improving Consistency of GNSS-IR Reflector Height Estimates between Different Frequencies Using Multichannel Singular Spectrum Analysis

Previous studies of GNSS-IR mainly focused on the legacy L1C signal; the potential of modernized signals (L2C and L5Q) has not yet been fully exploited. In this paper, we applied the Multichannel Singular Spectrum Analysis (M-SSA) method to extract common interference patterns from different frequencies simultaneously. The three-frequency (L1C, L2C, and L5Q) signal-to-noise ratio (SNR) measurements from a total of 840 satellite rising and setting arcs, occurring between day of year 250 to 279 in year 2020 and 2021, were used. By comparing GNSS-IR reflector heights obtained from the original and M-SSA-reconstructed SNR time series, we found that M-SSA significantly improves the between-frequency consistency, as shown by an increase in the values of R-squared of linear regression from (0.69, 0.67, 0.89) to (0.95, 0.96, 0.98), and a decrease in RMSE from (0.10 m, 0.10 m, 0.06 m) to (0.04 m, 0.04 m, 0.02 m) for S1C-S2C, S1C-S5Q, and S2C-S5Q pair, respectively. Our results validate (1) the effectiveness of the M-SSA method in extracting common interference patterns from multi-frequency SNR time series, and (2) the superiority of modernized civil signals L2C and L5Q over the legacy L1C signal in GNSS-IR studies. We also emphasize the important role that the L5 signal will play in future GNSS-IR research because of its compatibility and interoperability among different satellite navigation systems.

Analysis of ranging biases of BOC signal threat based on non-ideal channel group delay characteristics

Satellite signal threat is an important kind of satellite signal anomaly, which will lead to ranging biases of user receiver. BOC modulation is used more and more widely in the field of satellite navigation system. In the existing literature, there is a shortage that the non-ideal characteristics of the channel are not taken into account in the ranging biases analysis of BOC signal threat. The non-ideal characteristic of the receiving channel is one of the main bias sources of navigation signal reception. In the process of receiving navigation signal, due to the jitter caused by channel noise and the non-ideal phase of the channel, ranging biases will be introduced. To solve this problem, this paper proposes the analysis model of ranging biases of BOC signal threat based on non-ideal channel characteristics, and analyzes the non-ideal group delay characteristics of BOC (1,1) signal incoherent ranging mode. From the analysis results of ranging biases under multiple threated signals, it can be seen that the non-ideal group delay characteristics will worsen the ranging biases of BOC signal threat in most cases. In the sense of minimum ranging biases caused by BOC signal threat, 0.3chip∼0.35chip is the recommended parameter for non-coherent reception of BOC (1,1) early late code.

FAIR data and metadata: GNSS precise positioning user perspective

ABSTRACTThe FAIR principles of Wilkinson et al. [1] are finding their way from research into application domains, one of which is the precise positioning with global satellite navigation systems (GNSS). Current GNSS users demand that data and services are findable online, accessible via open protocols (by both, machines and humans), interoperable with their legacy systems and reusable in various settings. Comprehensive metadata are essential in seamless communication between GNSS data and service providers and their users, and, for decades, geodetic and geospatial standards are efficiently implemented to support this. However, GNSS user community is transforming from precise positioning by highly specialised use by geodetic professionals to every-day precise positioning by autonomous vehicles or wellness obsessed citizens. Moreover, rapid technological developments allow alternative ways of offering data and services to their users. These transforming circumstances warrant a review whether metadata defined in generic geospatial and geodetic standards in use still support FAIR use of modern GNSS data and services across its novel user spectrum. This paper reports the results of current GNSS users’ requirements in various application sectors on the way data, metadata and services are provided. We engaged with GNSS stakeholders to validate our findings and to gain understanding on their perception of the FAIR principles. Our results confirm that offering FAIR GNSS data and services is fundamental, but for a confident use of these, there is a need to review the way metadata are offered to the community. Defining standard compliant GNSS community metadata profile and providing relevant metadata with data on-demand, the approach outlined in this paper, is a way to manage current GNSS users’ expectations and the way to improve FAIR GNSS data and service delivery for both humans and the machines.

Satellite Navigation Signal Authentication in GNSS: A Survey on Technology Evolution, Status, and Perspective for BDS

As the Global Navigation Satellite System (GNSS) is widely used in all walks of life, the signal structure of satellite navigation is open, and the vulnerability to spoofing attacks is also becoming increasingly prominent, which will seriously affect the credibility of navigation, positioning, and timing (PNT) services. Satellite navigation signal authentication technology is an emerging technical means of improving civil signal anti-spoofing on the satellite navigation system side, and it is also an important development direction and research focus of the GNSS. China plans to carry out the design and development of the next-generation Beidou navigation satellite system (BDS), and one of its core goals is to provide more secure and credible PNT services. This paper first expounds on the principles and technical architecture of satellite navigation signal authentication, then clarifies the development history of satellite navigation signal authentication, and finally proposes the BDS authentication service system architecture. It will provide technical support for the construction and development of the follow-up Beidou authentication service.

Realtime wide-area vehicle trajectory tracking using millimeter-wave radar sensors and the open TJRD TS dataset

• A system based on millimeter wave radar is introduced for tracking vehicles. • Trajectory splicing is applied for tracking vehicles in wide-area level. • Validation results show a reliable and stable performance of the system. • The system performs well in detecting speeding fractions through pilot project. • TJRD TS Platform is introduced in sharing wide-area trajectory dataset (open). This paper presented a real-time millimeter wave radar-based system for tracking vehicle trajectories in a wide area (continuously along a roadway with essentially no length limit in practice). The trajectory tracking results were first validated for single vehicle trajectory tracking using the Real-Time Kinematic positioning technology based on the Beidou satellite navigation systems. The validation showed that the vehicle positions were captured with a mean lateral offset of −0.284 m and a mean longitudinal offset of −0.352 m. The mean estimated speeds were found to have a difference of only −0.048 km/h from the ground truths. The trajectory tracking results were also validated through multi-object tracking using video data from an unmanned aerial vehicle (UAV). Compared with the UAV video footage, the millimeter wave-based system was found to correctly capture around 92% of the total number of vehicles. For the correctly captured vehicles, their positions were found to be within 0.99 m (about a quarter of the width of a regular traffic lane) of the ground truth. In this paper, we also would like to share openly the entire validated datasets which has been recently published online as the TJRD TS platform. Additionally, a demonstration in using the dataset to detect aggressive driving behaviors, such as speeding was presented. It is expected that the open dataset will help enable researchers and practitioners to further explore the behaviors of road users, track the dynamics of safety risks and congestion formation, and evaluate incident impacts in a more microscopic but comprehensive way.

Improved BDS-2/3 Satellite Ultra-Fast Clock Bias Prediction Based with the SSA-ELM Model

Ultra-fast satellite clock bias (SCB) products play an important role in real-time precise point positioning. Considering the low accuracy of ultra-fast SCB, which is unable to meet the requirements of precise point position, in this paper, we propose a sparrow search algorithm to optimize the extreme learning machine (SSA-ELM) algorithm in order to improve the performance of SCB prediction in the Beidou satellite navigation system (BDS). By using the sparrow search algorithm's strong global search and fast convergence ability, we further improve the prediction accuracy of SCB of the extreme learning machine. This study uses ultra-fast SCB data from the international GNSS monitoring assessment system (iGMAS) to perform experiments. First, the second difference method is used to evaluate the accuracy and stability of the used data, demonstrating that the accuracy between observed data (ISUO) and predicted data (ISUP) of the ultra-fast clock (ISU) products is optimal. Moreover, the accuracy and stability of the new rubidium (Rb-II) clock and hydrogen (PHM) clock onboard BDS-3 are superior to those of BDS-2, and the choice of different reference clocks affects the accuracy of SCB. Then, SSA-ELM, quadratic polynomial (QP), and a grey model (GM) are used for SCB prediction, and the results are compared with ISUP data. The results show that when predicting 3 and 6 h based on 12 h of SCB data, the SSA-ELM model improves the prediction model by ~60.42%, 5.46%, and 57.59% and 72.27%, 44.65%, and 62.96% as compared with the ISUP, QP, and GM models, respectively. When predicting 6 h based on 12 h of SCB data, the SSA-ELM model improves the prediction model by ~53.16% and 52.09% and by 40.66% and 46.38% compared to the QP and GM models, respectively. Finally, multiday data are used for 6 h SCB prediction. The results show that the SSA-ELM model improves the prediction model by more than 25% compared to the ISUP, QP, and GM models. In addition, the prediction accuracy of the BDS-3 satellite is better than that of the BDS-2 satellite.

Fully Autonomous Orbit Determination and Synchronization for Satellite Navigation and Communication Systems in Halo Orbits

This paper presents a solution for autonomous orbit determination and time synchronization of spacecraft in Halo orbits around Lagrange points using inter-satellite links. Lagrange points are stable positions in the gravitational field of two large bodies that allow for a sustained presence of a spacecraft in a specific region. However, a challenge in operating at these points is the lack of fixed landmarks for orbit determination. The proposed solution involves using inter-satellite links to perform range and range-rate measurements, allowing for accurate computation of the spacecraft’s orbit parameters without the need for any facilities on Earth. Simulations using a fleet of three satellites in Near Rectilinear Halo Orbits around the Earth–Moon Lagrange point, proposed for the Lunar Gateway stations, were conducted to demonstrate the feasibility of the approach. The results show that inter-satellite links can provide reliable and accurate solutions for orbit determination with a DRMS error lower than one meter (90th percentile) and synchronization errors of around one nanosecond. This solution paves the way for a fully autonomous fleet of spacecraft that can be used for observation, telecommunication, and navigation missions.

A Hypothesis Test-Constrained Robust Kalman Filter for INS/GNSS Integration With Abnormal Measurement

This paper presents a hypothesis test-constrained robust Kalman filter for INS/GNSS (inertial navigation system/global navigation satellite system) integrated navigation in the presence of measurement outliers. This method estimates measurement noise covariance by combining hypothesis test with the maximum likelihood theory to handle measurement outliers. A chi square test and an improved sequential probability ratio test are established to characterize abrupt and slow-growing measurement outliers, respectively. Subsequently, these two hypothesis tests are used to constrain the maximum likelihood estimation of measurement noise covariance to accommodate measurement outliers. Based on the hypothesis test-constrained maximum likelihood estimation of measurement noise covariance, a robust Kalman filter is developed for INS/GNSS integrated navigation in the presence of measurement outliers. Simulation and experimental results demonstrate that the proposed method can effectively deal with measurement outliers. The resultant navigation accuracy is about 46% and 30% higher than that of the Kalman filter and maximum likelihood-based robust Kalman filter for INS/GNSS integrated navigation.

High-precision Positioning Method for BD3 System Based on Adaptive Optimization

It is of great significance to locate faults quickly and accurately in power distribution system to improve system reliability and recover quickly. With high positioning accuracy, strong anti-interference ability in mountainous areas and cities, and the ability to provide all-weather and all-round services, the BeiDou-3 (BD3) navigation satellite system has broad application prospects in power systems. Using the filtering principle of normalized least mean square (NLMS) filter, a high-precision positioning method for BD3 system based on adaptive optimization is propose to eliminate the pseudo-range error caused by electromagnetic interference. Simulation results show that NLMS-based adaptive pseudo-range filtering method can availably decrease the pseudo-range error caused by high proportional electromagnetic interference in the power system, achieve adaptive optimization of power system device positioning, and improve positioning accuracy.

Signal-in-Space Range Error of the Global BeiDou Navigation Satellite System and Comparison with GPS, GLONASS, Galileo, and QZSS

Based on the standard of precise multisystem orbit and clock offset, the evaluation methods of satellite orbit, satellite clock offset and the signal-in-space range error (SISRE) from broadcast ephemeris were given in this study. The SISRE was used as a key performance index to compare the global BeiDou navigation satellite system (BDS-3) with the regional navigation satellite system (BDS-2), Global Positioning System (GPS), Galileo, Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS), and Quasi-Zenith Satellite System (QZSS). Through the combination of domestic tracking stations and inter satellite links, the orbit determination accuracy of BDS-3 has been significantly improved. The radial (R), tangential (T) and normal (N) direction orbit accuracies of BDS-3 medium Earth orbit (MEO) satellites were 0.08, 0.37, and 0.34 m, respectively, which were considerably better than those of other satellite navigation systems. The R-, T-, and N-direction orbit accuracies of BDS-3 inclined geosynchronous orbit (IGSO) satellites were 0.17, 0.59, and 0.56 m, respectively, which were better than those of QZSS IGSO satellites. The R-, T-, and N-direction orbit accuracies of BDS-3 geostationary earth orbit (GEO) satellites were 0.27, 3.42, and 1.29 m, respectively, revealing considerable accuracy advantages in the R and N directions compared with QZSS GEO, although performance in the T direction was inferior. For the clock offset, the BDS-3 MEO satellites had an accuracy of 1.83 ns, which was noticeably superior, similar, slightly inferior, and superior to those of BDS-2, GPS, Galileo, and GLONASS. The clock offset accuracies of BDS-3 IGSO and GEO satellites were 3.13 and 3.17 ns, respectively, which were slightly better than those of QZSS IGSO and GEO satellites but did not have an obvious advantage over BDS-2. The primary reason could be that the launch time of the two types of BDS-3 satellites was close to the analysis period, and therefore, the clocks may be still in the aging process. Considering only orbit error, the average SISRE (orb) of BDS-3 MEO, Galileo, GPS, and GLONASS was 0.10, 0.28, 0.57, and 1.03 m, respectively. The SISRE (orb) of BDS-3 IGSO was 0.19 m, which was marginally greater than that of BDS-3 MEO but smaller than those of the other systems and considerably smaller than that (0.90 m) of QZSS IGSO. The SISRE (orb) of BDS-3 GEO was 0.60 m, which was comparable to that of GPS (0.59 m) and considerably smaller than that of QZSS GEO (0.91 m) satellites. Considering both orbit and clock offset error, the SISRE of BDS-3 MEO satellites was 0.52 m, which was slightly greater than that of Galileo (0.40 m), marginally smaller than that of GPS (0.59 m), and considerably smaller than that of GLONASS (2.33 m). The BDS-3 IGSO satellites had a SISRE of 0.90 m, which was greater than those of GPS and Galileo but comparable to that of QZSS IGSO (0.92 m). The average SISRE of BDS-3 GEO satellites was 1.15 m, which was greater than those of GPS and Galileo and slightly greater than that of QZSS0.95 m GEO satellites, but smaller than that of GLONASS.

A Novel Decoupling Feeding Network for Circularly Polarized Patch Arrays Using Orthogonal Mode Decomposition

A new decoupling feeding network (DFN) is proposed for circularly polarized (CP) patch arrays with an arbitrary number of elements. Different from linearly polarized (LP) patch arrays, a dual-feed structure is adopted for each element to enhance the CP performance. The dual-feed structures should be integrated into the DFN, and hence the coupling paths become very complicated. An orthogonal mode decomposition (OMD) method is established to analyze the coupling mechanism between the CP patch elements. Based on the OMD, a network model of the mutual coupling between the CP patch elements is established, which can be used to assist design of the DFN. To verify the decoupling effect, a prototype of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times $ </tex-math></inline-formula> 2 CP patch array for a satellite navigation system is fabricated and measured. After applying the DFN, mutual coupling between all ports is reduced to below −33 dB at the center frequency of 1.26 GHz, and the decoupling effects reach 15–23 dB. The CP patch array maintains stable radiation patterns with a realized gain of ~9.4 dBi. The proposed OMD approach is applicable to other CP arrays with an arbitrary number of elements.

Learning From FM Communications: Toward Accurate, Efficient, All-Terrain Vehicle Localization

Vehicle localization service is a fundamental component of intelligent transportation systems. The widely used satellite navigation systems perform poorly in urban areas because the lines of sight to satellites are blocked by complex terrain characteristics, e.g., buildings, elevated streets and interchanges. In this paper, we design RadioLoc, a novel system achieving accurate, efficient, all-terrain vehicle localization with two key design points. First, RadioLoc harvests the frequency modulation (FM) signal, which has higher availability than satellite signal in complex terrains, as the signal source for localization. Second, RadioLoc integrates modern machine learning techniques into the processing of FM signals to efficiently learn the accurate vehicle localization in all-terrain environments. We validate the feasibility of FM-based vehicle localization and corresponding challenges and practical issues via field tests (e.g., signal distortion, signal inconsistency and limited in-vehicle radio bandwidth), and develop a series of advanced techniques in RadioLoc to address them, including adaptive batching, frequency sweeping, a novel multipath delay spread filter, a reconstructive PCA denoiser and a tailored FM feature extractor. We then develop a generic, modular localization module in RadioLoc, and design different learning-based 3D position identification algorithms for this module. We implement a prototype of RadioLoc and perform extensive field experiments to evaluate its efficiency and efficacy. Results show that (1) RadioLoc achieves a real-time localization latency of less than 100 milliseconds; (2) RadioLoc achieves a worst-case localization accuracy of <inline-formula> <tex-math notation="LaTeX">$99.6\%$</tex-math> </inline-formula> even in an underground parking lot, and (3) the horizontal error of RadioLoc is only one sixth of a dedicated GPS device even when the vehicle is moving at a high-speed (i.e., <inline-formula> <tex-math notation="LaTeX">$80$</tex-math> </inline-formula> km/h) in a complex highway scenario.

Limitations of Multi-GNSS Positioning of USV in Area with High Harbour Infrastructure

Satellite surveying techniques are currently among the main measuring technologies in geodesy and the main technologies in navigation. Modern navigation requires high accuracy of position coordinate determination, particularly in bathymetric surveys and aerial photogrammetry. In most cases, the terrain conditions enable positioning with high accuracy and reliability. These particularly involve the terrain conditions, i.e., high harbour infrastructure for bathymetric surveys and trees for railway surveys that hinder the measurement performance with a pre-determined accuracy. This article presents the limitations in unmanned survey vehicle (USV) positioning in an area restricted by a high quay, and difficult observational conditions in the surrounding high harbour infrastructure. The positioning used a four-system receiver that determined position coordinates based on the signals from one, two, three and four satellite navigation systems. The number of available satellites was determined under conditions of the open upper hemisphere and the partially obscured hemisphere based on the surrounding geometry. The determined position coordinates were related to the position determined using robotic total station (RTS). An area was identified in which it becomes difficult or impossible to maintain the required positioning accuracy.

A Novel Ionospheric Disturbance Index to Evaluate the Global Effect on BeiDou Navigation Satellite System Signal Caused by the Moderate Geomagnetic Storm on May 12, 2021.

In this paper, we propose a new method to quantitatively evaluate the quality of the carrier phase observation signals of the BeiDou Navigation Satellite System (BDS) during weak and moderate geomagnetic storms. We take a moderate geomagnetic storm that occurred on 12 May 2021 during the 25th solar cycle as an example. The results show that the newly defined PAS (Percentage of Affected Satellites) index shows significant anomaly changes during the moderate geomagnetic storm. Its variation trend has good correlations with the geomagnetic storm Kp index and Dst index. The anomaly stations are mainly distributed in the equatorial region and auroral region in the northern and southern hemispheres. The proposed PAS index has a good indication for both BDS2 and BDS3 satellites. We further validated this index by calculating the Precise Point Position (PPP) positioning error. We found that the anomaly period of PAS has strong consistency with the abnormal period of PPP positioning accuracy. This study could provide methodological support for the evaluation of the signal quality and analysis of positioning accuracy for the BeiDou satellite navigation system under different space weather conditions.

A Comprehensive Overview of Atomic Clocks and their Applications

Time is ubiquitous, and integral to our everyday lives. Precise measurement of time intervals is basic to various activities humans are dependent up on, such as accurate positioning using satellite navigation, telecommunication, aviation, definition of International Time, secondary applications using positioning, military applications etc. Atomic clocks formulate the heart of precise time measurement and hence enable the positioning and navigation and niche time and frequency dependent technologies that we rely upon directly or otherwise. This paper gives a comprehensive overview of history of time measurement and evolution of clocks towards atomic clocks. It broadly covers various types of atomic clocks ranging from laboratory clocks to miniature commercial clocks along with the key applications with a focus on microwave atomic clocks (or frequency standards). Further, the satellite navigation systems operational around the globe by various countries and the types of clocks used for such navigation systems are briefly covered with a focus on the rubidium atomic frequency standard and other space clocks.

Improved service method and its positioning performance of the Galileo satellite clock correction

The service of the Global Satellite Navigation System (GNSS) satellite clock correction should be provided to achieve a high-precision user positioning. To explore new method for improving the real-time service capability of the Galileo satellite clock correction, its positioning performances of modeling and extrapolation with the polynomial and harmonics-based function are tested. The single point positioning result of the strategy, which employs the 1-h satellite clock correction series to fit the 4-h extrapolation coefficients of 1st order polynomial, is comparable to the current broadcast ephemeris of 10-min age. This shows that the age of the Galileo broadcast ephemeris can be extended. The precise point positioning (PPP) performances of the different extrapolation strategies are analyzed to establish an optimal Galileo real-time service (RTS) strategy, which supports a longer update interval of the transmitted coefficients. The PPP results show that the 6th order polynomial is suitable to establish the RTS of 1- and 2- min update intervals, while that of 2nd order polynomial has the best performance in 5- min interval RTS and the 1st order polynomial is the best one in the 10-min interval RTS. In these RTS strategies, the 1-h satellite clock correction series is optimal to fit the transmitted coefficients.