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About this book

China Satellite Navigation Conference (CSNC 2020) Proceedings presents selected research papers from CSNC 2020 held during 22nd-25th November in Chengdu, China. These papers discuss the technologies and applications of the Global Navigation Satellite System (GNSS), and the latest progress made in the China BeiDou System (BDS) especially. They are divided into 13 topics to match the corresponding sessions in CSNC2020, which broadly covered key topics in GNSS. Readers can learn about the BDS and keep abreast of the latest advances in GNSS techniques and applications.

Table of Contents

Frontmatter

Satellite Orbit and System Error Processing

Frontmatter

Modeling of BDS Positioning Errors Due to Ionospheric Scintillation and Its Application

In this work, efforts are made to develop models of BDS positioning errors due to ionospheric scintillation. Two aspects are specially considered in the modeling work, namely the lose-of-lock on signals and the range errors under scintillation. Analysis with scintillation data from China shows that the possibility of signal loss of lock follows a Weibull Distribution. With this in mind, a method is developed to determine the signal-locking statue based on the scintillation index. The theoretical model on range errors is improved to expand the range of input parameters. Errors arising from scintillation related ionospheric irregularity are also accounted for. Then, BDS positioning performance is analyzed with the constructed models for typical scintillation scenarios with the output of GISM (Global Ionospheric Scintillation Model). The Results show the rationality of the models.

Dun Liu, Xiao Yu, Jian Feng, Weimin Zhen

A BDSPHERE Solar Radiation Pressure Model for BDS GEO Satellites

The precision of BDS navigation message based on global satellite laser ranging (SLR) analysis is about 60 cm for geostationary earth orbit (GEO) satellites. There is an obvious gap between the POD accuracy of GEO satellites and IGSO & MEO satellites. The reason being that the GEO satellites lie in high and geostationary orbits. Also, the mature GPS solar radiation pressure (SRP) model is used as a reference in orbit determination for GEO satellite. We uses traditional spherical SRP model as background model and estimates the SRP parameters of a 2-yr precise GEO satellite ephemeris with dynamic smoothing method, and builds a continuous SRP parameter sequence. Thoughts on “Fourier series overlaid linear term” modeling are proposed and an empirical SRP model for BDS GEO satellite (BDSPHERE for short) comes into being. We verify the model based on observation data and the results show that: (1) the signal-in-space range error (SISRE(ORB)) of GEOs based on BDSPHERE model amounts to 0.63 m, while the orbital SISRE(ORB) for 8 h, 12 h and 24 h prediction is 0.79 m, 1.24 m and 1.65 m respectively; (2) compared to traditional spherical SRP model, there is an increase of 56.55%, 65.81%, 63.31% and 58.33% with the BDSPHERE model. The precision of radial orbit by global SLR analysis is 0.597 m, an increase of 70.06%.

Rui Guo, Xiaojie Li, Jie Xin, Shan Wu, Shuai Liu

Test and Evaluation of the Distributed Autonomous Orbit Determination with the BDS Inter-satellite Ranging Data

The new generation satellites of the BeiDou navigation satellite system (BDS) all carry the inter-satellite payload in Ka band, which can support the realization of the inter-satellite ranging and information interaction. Firstly, we propose the process of the distributed orbit determination algorithm, develops a ground testing software and propose a strategy for the autonomous orbit determination. Secondly, we analyze the constellation geometry and the inter-satellite ranging error of the 18 Medium Earth Orbit (MEO) satellites in BDS-3 constellation. Finally, the 60 days results of the autonomous orbit determination are given based on the actual inter-satellite ranging data and compared with the precision orbit. The results demonstrate that the inter-satellite status of BDS is rather stable and the constellation geometry can support the autonomous orbit determination for the distributed navigation constellation with 18 MEO satellites; the simulation accuracy of the autonomous orbit determination is 0.80 m, which confirms the validity of the proposed method and establish a firm foundation for the engineering implementation of the autonomous navigation for the BDS.

Jie Xin, Ziqiang Li, Xiaojie Li, Rui Guo, Dongxia Wang, Shuai Liu

DTM2013 Model Parameter Inversion and Correlation Analysis Between Its Accuracy

The framework and the amendment terms of DTM2013 atmospheric model are derived based on the historical DTM series model algorithms. The Legendre polynomial coefficients are derived based on the high-order associated Legendre polynomials algorithm. The long term optimal mean of F30 proxy is derived based on fitting polynomial of the F30 proxy historical measured data. The construction of the DTM2013 model algorithm was completed by integrating the inversion parameters. The correctness of the model is verified by comparing the calculation results of the parameter inversion DTM2013 model with that of the ATMOP DTM2013 model. The DTM2013 model and the MSIS00 model calculation accuracy are calculated based on GOCE atmospheric measured data, and the high correlation between the solar radiation proxy deviations and the model accuracies are derived. The solar radiation proxy factors of the model accuracy of the atmospheric models are explained, which proves that F30 proxy has better application value in atmospheric models.

Wenhui Cui, Wei Qu, Haiyue Li, Ning Chen, Nan Ye, Zhenyu Sun

A Method of Combined Orbit Determination of Multi-source Data with Modified Helmert Variance Component Estimation

The application of inter-satellite link technology, the rise of low-orbit satellite enhancement constellation and the maturity of on-borne GNSS orbit determination technology provide a new method for precise orbit determination different from the traditional ground monitoring station. The method can use a variety of observation data to achieve precise orbit determination under the condition of regional monitoring station. Due to the differences among inter-satellite link, low-orbit satellite-borne GNSS and ground monitoring station data, the reasonable weighting of all kinds of data in joint orbit determination is conducive to improving the accuracy of orbit determination. So this paper proposed a multi-source weighted method of orbit determination data based on Helmert variance component estimation. Meanwhile, it proposed a data processing method of joint orbit determination parameter classification, to solve the limitation of parameter quantity constraint in the process of orbit determination by the rigorous variance component estimation method. The simulation experiment shows that, compared with the weighting strategy based on different observation data accuracy, the Helmert variance component estimation method increases the average RMS of orbital accuracy from 0.073 m to 0.058 m, about 21% up, 31.8%, 13.6%, and 20.4% in R, T, and N directions respectively, by reasonably adjusting the weight allocation of three types of orbital data.

Laiping Feng, Rengui Ruan, Anmin Zeng

The Influence of Station Distribution on the BeiDou-3 Inter-satellite Link Enhanced Orbit Determination

The basic system of the third generation BeiDou Global Satellite Navigation System (BeiDou-3 or BDS-3) has been completed by the end of 2018, and the complete system is planned to be completed by 2020. The inter-satellite link technology is deployed by BDS-3, which not only can realize the autonomous navigation of the constellation, but also can be used to enhance the orbital determination under normal operating conditions. In this paper, the influence of ground monitoring station distribution on the BDS-3 inter-satellite link enhanced orbit determination is analyzed. The results show that, with the ISL, the orbital accuracy based on three monitoring stations separated by several hundred kilometers is almost equal with that based on eight domestic monitoring stations. The ISL greatly reduces the ground monitoring station number and distribution requirements of the orbit determination. Only a few ground stations are needed to constrain the positional relationship between the constellation and the earth, thereby weakening the rotation and translation of the entire constellation with regard to the earth.

Yufei Yang, Yuanxi Yang, Rui Guo, Chengpan Tang, Zhixue Zhang

Initial Results of BDS3 GEO Orbit Determination with Inter-satellite Link Measurements

Owning to some successful applications of RDSS and RNSS, keeping GEO satellites in BeiDou Navigation Constellation becomes one of the key differences between BDS and other Global Navigation Satellite Systems (GNSS). And for the first time, BDS GEO works as a node of Inter-Satellite Links. It makes precise orbit determination (POD) based on Inter Satellite Ranging (ISR) for GEO possible. Orbit, hardware delay and solar radiation pressure parameters are estimated in POD process. Mean value of estimated hardware delay is 1189.18 ns and STD is 0.15. RMS of post-fit residuals of ISR, between 10 of 18 MEO satellites and GEO satellite is less than 45 cm, and that between the other 8 MEO satellites and GEO satellite is less than 56 cm. RMS of GEO 48-h OOD is no greater than 2.4 m in position and no greater than 0.2 m in radial direction.

Zongbo Huyan, Jun Zhu, Yanrong Wang, Xia Ren

Evaluation and Analysis of Orbit Determination Accuracy of BDS Satellite Under Clock Offset Constraint

High-precision satellite orbit determination is the premise for the satellite navigation system to achieve high-performance services. The BDS improves the accuracy of orbit determination through the use of inter-satellite link (ISL) observation data, and realizes the rapid orbit recovery after satellite maneuvering with the support of satellite-earth bidirectional time synchronization data. Based on BDS 18 MEO, 1 IGSO and 1 GEO satellites, the satellite orbit determination under clock constraint, use the ISL, and use only satellite-earth observation data by data from nine tracking stations in China were used. And the orbit errors and orbit prediction accuracy of the three orbit determination method are analyzed. Two high orbit satellites were tested for orbit determination during recovery after maneuvering, and the precision of orbit determination during recovery was evaluated. The results show that: for the BDS satellite orbit determination under the constraint of clock error, the position error RMS of the overlapping orbit is 1.25 m, and the predicted 24-h orbit position deviation is 2.12 m. Compared with the combined orbit determination results of the ISL data, the IGSO/MEO satellite orbit URE is 0.29 m, while the GEO satellite has an orbit deviation exceeding 10 m in tangential direction. The satellite orbit determination method under the constraint of clock offset can realize the rapid orbit recovery after the maneuver of BDS satellite. The apparent direction accuracy of the two BDS high-orbit satellites within 4 h after the maneuver is better than 0.5 m, and the orbit URE is better than 0.75 m.

Shuai Liu, Rui Guo, Xiaojie Li, Qian Chen

A Combined RDSS/RNSS Orbit Determination Method to Improve the Service Performance of RDSS

Radio determination satellite service (RDSS) is the advantage and particular characteristics of Beidou system (BDS). Due to the aging of RDSS equipment, there is a long-term drift in various types of RDSS equipment time delays. At present, the time delay calibration is cumbersome and time-consuming. The service performance and availability of the RDSS system are greatly degraded. In this paper, the combined orbit determination method with the RDSS/radio navigation satellite service (RNSS) data was adopted to perform the RDSS time delay calibration. The experiments were made by Beidou actual RNSS/RDSS data. The results showed that the accuracy of the RDSS time delay was 3.73 ns in continuous 7 days. The positioning experiments were made respectively by the original and adjusted time delay values. The mean horizontal positioning accuracies of the five RDSS users were increased from 15.01 m to 2.46 m.

Xiaojie Li, Rui Guo, Chengpan Tang, Shuanglin Huang, Shuai Liu, Jie Xin, Junyu Pu, Jianbing Chen

Error Analysis and Strategy Optimization of East-West Control for BEIDOU GEO Satellite

Orbit determination error, thruster calibration coefficient, angular momentum unloading, eccentricity, inclination, etc. are important factors affecting the control amount, prediction after control, holding period and annual control times of the East-West keeping control for BEIDOU GEO satellite. Here, we deduce the common parameters of East-West keeping control; analyse the influence of various factors of the East-West keeping control strategy; establish the prediction model of angular momentum and its influence on the semi-major axis; give the selection strategy of thruster calibration coefficient; give the optimization steps of East-West keeping control strategy. These can improve the accuracy of the East-West keeping control, reduce the times of the East-West keeping control as much as possible, reduce the impact of the control task on the satellite business.

Xiaoying Wei, Lei Shi, Quanjun Li, Lusha Wang, Donglin Li

Estimation of BeiDou Satellites Antenna Phase Center Offsets

Using the global distributed iGMAS and MGEX multi-GNSS observation data, the theory of satellite antenna phase center correction is studied. The Phase Center Offsets (PCOs) of BDS-II IGSO and MEO satellites are estimated with real observation data, and the impacts of PCO on the precise orbit determination and station coordinates Precise Point Positioning (PPP) are also analyzed. The results show that the estimated PCO parameters could be used to improve the accuracy of orbit overlaps. The 3-D orbit accuracy of IGSO and MEO satellites is improved by 17.7% and 24.8% respectively. Among them, the accuracy of R direction is more significantly improved by 28.8% and 46.4% respectively. In addition, with the estimated PCO parameters, the RMSE of station coordinates static PPP is reduced by 11.9% and 9.5% in the horizontal and elevation directions respectively.

Yanan Fang, Jie Li, Chong Wang, Jiasong Wang

Influence Analysis of Multi-LEO Augmentation MEO Satellite Orbit Determination Under Regional Station Layout

Since the ground monitoring stations layout for BeiDou navigation satellite system (BDS) is regional, the problem of bad orbit precision of BDS satellites needs to be resolved. Many scholars propose to use the low earth orbit (LEO) spaceborne observations to enhance the precise orbit determination (POD) of navigation satellites. In this contribution, the orbit determination enhancement of global positioning system (GPS) is researched by adding three LEOs under the Asia-Pacific regional station distribution based on measured data. Combining the three LEOs, GRACE-A, HY2A, Jason-2 and 6, 10 and 20 regional stations, respectively, four experimental designs are processed: the ground-only POD, the combined POD with ground stations and 1, 2 and 3 LEOs, respectively. Results show that the improvement of GPS satellite orbits is excellent when adding LEO GPS data, with the biggest percentage of 72.6%. The less ground stations and adding the more LEOs, the improvement of orbit precision is bigger. When joining in different types of LEO, the more LEOs, the improved differentiation is more obvious.

Tian Zeng, Lifen Sui, Laiping Feng, Xiaolin Jia

A New Ambiguity Resolution Method Applied to Uncombined Precise Orbit Determination

With the continuous refinement of multi-GNSS and multi-frequency data processing, there is an increasing interest for the observation model based on uncombined (UC) strategy. Ambiguity resolution is an important issue in the field of GNSS. The ambiguity fixing of wide-lane (WL) is based on the MW combination of pseudo-range and carrier phase observations, with the geometry-free and ionospheric-free (IF) characteristic. A significant disadvantage of MW combination is that it is contaminated by pseudorange observations. This study proposes a method that does not need to use MW combination to derive the WL ambiguity. Instead, the original UC float ambiguity is used to obtain the WL ambiguity. The float ambiguity obtained through parameter adjustment is measured using the carrier phase observation, which is more accurate than the MW combination observations. The new method is applied to the dual-frequency UC precision orbit determination experiment. The residual distribution of WL DD ambiguity is first analyzed, and results show that the new method is closer to the integer value than the residual distribution of the MW strategy. Then use the GPS observation data of about one month to verify orbital accuracy of the new method, and compare with results of the UC and IF strategies, respectively. Results show that the orbit and clock products obtained by the new method receive the best accuracy. The new method is also applicable to other UC ambiguity resolution situations, such as UC precise positioning.

Tian Zeng, Xiaodong Qin, Lifen Sui, Rengui Ruan, Xiaolin Jia, Guorui Xiao

Study on Operation Safety of RNSS and Long-Term Evolution of Disposal Orbit

Considering that regional navigation satellite system (RNSS) will deploy more and more satellites in inclined geosynchronous orbit (IGSO) in the future, it is necessary to carry out research on operational safety of RNSS and the long-term evolution of disposal orbit. With reference to the technical study and international guidelines of satellite at the end of life (EOL) disposal, the study on the stability of disposal orbit of IGSO satellites has been carried out in the report. It has been proved that the stability of disposal orbit is dependent on the initial orbit parameters in the report. The application of the disposal strategy proposed in this report can significantly prevent the rapid growth of orbit eccentricity and successfully establish a stable disposal orbit. The recommendation on specific disposal parameters of BDS, QZSS and IRNSS IGSO satellites have been given in the report so that the disposal orbit would be stable after the satellite de-orbited or the satellite would re-enter the atmosphere as soon as possible.

Jing Zhou, Hui Yang

An Angular Momentum Allocation Strategy to Extend the Available Time of GEO Navigation Satellites

In order to maintain the orbit accuracy of the GEO (geostationary orbit) navigation satellite, the thruster is not allowed to use during long-term orbital operation. The disturbance torque is absorbed by the reaction wheel system to maintain the three-axis nominal attitude. Because the reaction wheel absorbs the angular momentum accumulated by the disturbance torque, the rotation speed continues to increase. When the reaction wheel speed exceeds the safety threshold, it is necessary to switch to other working modes and use the thruster to perform angular momentum unloading. At this time satellite services were unavailable due to the effects of thruster on orbit. In order to maintain a certain degree of redundancy, usually 4 or more reaction wheels are installed on the satellite to form a redundant system. An angular momentum allocation strategy based on a pseudo-inverse solution is adopted. This allocation strategy is an energy minimization strategy. This paper proposes a distribution strategy based on the minimization of the infinite norm of the angular momentum vector. Using this distribution strategy, the maximum capacity of the reaction wheel system can be exerted, under the condition that the angular momentum accumulated by the reaction wheel system is the same, the maximum speed of the reaction wheel is the lowest. This extends the time for the reaction wheel to reach the safe threshold speed, and extends service time for GEO navigation satellites. In this paper, the reaction wheel system with a pyramid configuration is taken as an example for analysis. The angular momentum of the reaction wheel system is decomposed into a linear combination of pseudo-inverse solution and zero space vector, and it is solved under the criterion of infinite norm minimization. At the same time, this paper compares two allocation strategies for 4π space. Analysis and simulation show that the use of infinite norm minimization allocation strategy can significantly increase the available time of navigation satellites.

Zhen Cui, Bin Chen, Jiajia Feng, Ye Ji, Weijie Liu

Quality Analysis of Multi-GNSS Observation Data Based on IGMAS

The quality of GNSS (Global Navigation Satellite System) observation data is the primary factor affecting the accuracy of navigation satellite orbit determination, and it is an important reference for the application of observation data. Based on the GNSS observation data of iGMAS (International GNSS Monitoring & Assessment System) tracking stations, GPS, BeiDou, Galileo and GLONASS observation data quality are compared and analysed, including carrier-to-noise ratio (C/N0), multipath effect (MP) and carrier phase noise. The characteristics of BeiDou global experimental satellites (BDS-3) signal quality are studied. The differences of inter system biases (ISB) of BDS-3 and the regional BeiDou satellite navigation system (BDS-2) relative to GPS are analysed. The results show that the C/N0 of BDS-3 B1I and B3I signals are improved comparing with that of the same signals of BDS-2. The C/N0 of BDS-3 B1C and B2a signals are comparable to that of GPS and Galileo signals at the same frequency. The MP effects of BDS-3 signals do not exist the elevation-dependent systematic biases which exist in that of BDS-2 signals. The MP effects of BDS-3 B1I and B3I signals are smaller than those of the same signals of BDS-2. The MP effects of BDS-3 B1C and B2a signals are equivalent to those of GPS and Galileo signals at the same frequency. The carrier phase noise of BDS-3 B1I-B3I combination is the smallest. The carrier phase noise of BDS-3 B1C-B2a combination is smaller than that of GPS L1-L5 and Galileo E1-E5a. The daily ISB variation of BDS-3 relative to GPS is more stable than that of BDS-2 relative to GPS.

Houzhe Zhang, Kai Shao, Defeng Gu, Xiaojun Duan

Orbit Residual Analysis of BDS Satellite Based on Ranging Information and Telemetry Parameters

Navigation satellites provide navigation, positioning, and timing services to users by broadcasting navigation ephemeris. The ground operation control system establishes a space reference to maintain the system, performs precise satellite orbit determinations, and completes satellite broadcast ephemeris forecasting. As of now, BDS-2 regional system has provided service for more than seven years. During the long-term on-orbit operation, the system provided stable navigation services in the Asia-Pacific region. It is inevitable that a single satellite is in orbit failure. With the continuous improvement of ranging accuracy, orbit determination, and broadcast ephemeris and breakthroughs in key technologies, it provides a certain empirical basis for the treatment of abnormal in-orbit problems. Taking the C06 satellite of the BDS-2 system as an example, this article detailed the process of the C06 satellite’s two orbital URE divergences in April and September 2018. Based on the results, the possible causes were analyzed from the two aspects of ranging data and in-orbit telemetry parameters. This provides a certain reference method for similar orbit residual mutations and cause analysis.

Xu Zhang, Hui Yang, Qiuli Chen, Chen Wang

Spatial Frames and Precise Positioning

Frontmatter

Modeling and Assessment of BDS/GPS Triple-Frequency Precise Point Positioning

Beidou Navigation Satellite System (BDS), the first satellite navigation system with the capability of providing B1, B2 and B3 triple-frequency civil signals, can provide the services of positioning, navigation, and timing in the whole Asian-Pacific region and most of the world under current satellite constellation. With the modernization and upgrading of GPS, the number of GPS satellites with triple-frequency signals L1, L2, and L5 is also increasing. Currently, the precise point positioning (PPP) based on BDS and/or GPS is mainly adopting the B1/B2 and/or L1/L2 dual-frequency observations. To make full use of triple-frequency observations, this paper introduces a triple-frequency PPP model by using the raw observations of BDS/GPS. In this paper, three IGS (International GNSS Service center) stations’ data are adopted, and the data are processed with six modes: GPS dual-frequency PPP, GPS triple-frequency PPP, BDS dual-frequency PPP, BDS triple-frequency PPP, GPS + BDS dual-frequency PPP, and GPS + BDS triple-frequency PPP. Results illustrate that GPS + BDS dual-frequency PPP provides the shortest convergence time and the highest positioning accuracy compared to the other PPP modes. GPS + BDS triple-frequency PPP has a relatively longer convergence, and the positioning accuracy is slightly lower than GPS + BDS dual-frequency PPP. The main reason is that the satellite number of providing triple-frequency observations is much less than that of dual-frequency observations. The performance of BDS dual-frequency PPP is worse than that of GPS due to the lower accuracy of orbit and clock of BDS satellites. However, due to the less available number of GPS even cannot provide solutions when using triple-frequency observations, while BDS can offer centimeter-level positioning solutions.

Jie Lv, Zhouzheng Gao, Junhuan Peng

Baseline-Constrained GNSS Single-Frequency Single-Epoch Attitude Determination Based on Attitude Domain Search

The strength of angle constraint greatly affects the performance of attitude domain search in GNSS single-frequency single-epoch attitude determination. In this paper, given a constant baseline length constraint, we make use of the integer least squares to improve the conventional search method in attitude domain. First, we use the objective function based on ILS to derive the angle-related term, which is used to compress the attitude search space. Second, the ambiguity candidates are determined through 2D search in the attitude search space. At last, a strategy that utilizes unconstrained the least-squares solution to eliminate the pseudo candidates is proposed to accelerate search speed, and the ambiguities are fixed while the objective function is minimum. As the experiments revealed, our new method overcomes two problems of conventional search method in coordinate domain: multi-peak phenomenon and long computation time, and has high success rate and high real-time performance.

Hongtao Wu, Yu Jiao, Longnan Bao

Estimation of GLONASS Carrier Phase Inter-frequency Biases

Because GLONASS employs frequency division multiple access technique, the inter-frequency biases (IFBs) generate in the double difference observations from different types of receivers. Therefore, it is significant to eliminate the IFBs for GLONASS high-precision positioning. The size of the phase IFBs rate is generally millimeter or centimeter, the IFBs of L1 and L2 are almost equivalent, and possess a certain linear relationship with the frequency number, which is conducive to the separation of the IFBs and the ambiguities. In this paper, two methods of phase IFBs correction are adopted to compare, including pre-calibration and real-time estimation. In the pre-calibration, the function model of the widelane observation residuals and the IFBs rate is established, and the IFBs rate is estimated by sequential estimation; in the real-time estimation, the GLONASS mathematical model considering IFBs is constructed, and the IFBs rate is estimated by Kalman filter. In the data preprocessing, the triple difference observations are used to construct slip test statistics for cycle slip detection. The LAMBDA method is used to fix the ambiguity. The experimental results show that the two methods can effectively estimate GLONASS IFBs rate and both the fixed rate and positioning accuracy are improved evidently after the IFBs elimination. The filtering method is more stable and suitable for real-time solution.

Wei Yang, Qinggen Yi, Zhuoshan Wu, Guoli Lin

An Improved Clock Jump Detection Method in Real - Time PPP

In view of the fact that most current cycle clip detection methods do not take into account the clock jump of receivers, which results in the reduction of PPP data processing accuracy and efficiency, this paper introduce the GNSS receiver clock jump theory systematically, to analyze its impact on the observed data and the cycle clip detection principle of interference, and improvement based on domain using doppler observations of clock jump detection method. The clock jump in the simulation data and the original BDS data was successfully detected without the first time excluding the cycle jump.

Kaidi Jin, Hongzhou Chai, Changjian Liu, Chuhan Su

Functional Model Compensation of Residual Systematic Errors in GNSS Precise Positioning

Global Navigation Satellite System (GNSS) residual systematic errors have adverse impacts on precise positioning. However, most of existing studies mainly focus on handling the part of systematic errors that can be properly modeled. This research comprehensively studies and proposes the method of functional model compensation for processing the residual systematic errors. At first, the classical additional parameter correction and least squares collocation models that cannot directly achieve the residual systematic error compensation are studied. Accordingly, the multi-epoch partial parametric correction and collocation methods are derived. Finally, a functional model compensation system for the residual systematic errors is designed and implemented, where the key issues such as the feasibility of the overall test, selection of the partial parameterization and setting of the moving window size are solved. Taking the real-time kinematic positioning with real BeiDou data as an example, the effectiveness of the proposed functional model compensation is verified, which can improve the precision by approximately 15% on average.

Zhetao Zhang, Bofeng Li, Yunzhong Shen, Xiufeng He

The Detection and Repair of BDS Triple-Frequency Cycle-Slip of Weakening the Influence of Ionosphere

In order to overcome the high misdetection rate of cycle-slip in strong ionospheric activity, three-frequency GFIF carrier phase linear combination, HMW combination and ionospheric-correction geometric-free linear phase combination are used for cycle-slip detection. A narrow lane code-phase combination compensated by ionospheric delay, GFIF carrier phase linear combination and HMW combination are used for cycle-slip repair to solve the ill-posed problem of repair equation system. Finally, the tri-frequency data of JFNG and XMIS stations are used for experimental verification. The results show that even under the condition of strong magnetic storm, the algorithm can effectively detect and repair the simulated random cycle slip, and there is no insensitive cycle slip.

Jiale Lin, Shubo Qiao, Ke Yan, Xi Zhang

First Implementation and Evaluation of Five Systems Network RTK

Currently, five navigation satellite systems (BDS-2/BDS-3, GPS, GLONASS, Galileo and QZSS) are broadcasting navigation signals. With more navigation system observations, positioning performance and reliability are expected to be improved. In this study, we developed a software that can provide five systems network RTK augmentation service to users at the first time. A network RTK algorithm that can process five systems observations is proposed. All available observations from different GNSSs are fully used for our software. The characteristics of ambiguity solutions and atmosphere interpolated values for each navigation system are analyzed in detail and the improvement of combined five systems for network RTK performance are carefully evaluated. Firstly, the number of visible satellites of five-system observations are shown. Then, the characteristics of the fractional parts of float wide-lane and narrow-lane ambiguities are analyzed. Except for GLONASS, characteristics of the fractional parts of float extra-wide-lane ambiguities are also analyzed. The modelling accuracy of interpolated ionospheric and tropospheric delays for each navigation system is investigated. Lastly, rover fixing rate and positioning accuracy of combined five systems are computed and evaluated. It is shown that better accuracy and reliability can be obtained for combined five systems, especially when low elevation signals are obscured.

Xiyang He, Jinpei Chen

Analysis and Modeling of the Inter-system Bias Between BDS-2 and BDS-3

The BDS-3 system has provided positioning navigation and timing (PNT) service since December 2018, while applications show that there is inter-system bias (ISB) between the BDS-2 and BDS-3 systems. Origin of the ISB and its influences on Beidou positioning are analyzed, and then the positioning algorithm including ISB is presented in order to improve Beidou navigation and positioning precision from the perspective of users. Judging by improvement effect on the BDS-2 and BDS-3 joint positioning, three ISB estimation models, such as white noise model, piecewise constant model, and random walk model, are analyzed, using Asia-Pacific observations and precision orbit and clock products of IGS. Results show that ISB estimation methods can effectively improve the precision of BDS-2 and BDS-3 joint standard point positioning (SPP), and the improvement of three methods can reach 22%, 23% and 36% respectively, while for BDS-2 and BDS-3 joint precise point positioning (PPP), the improvement is 17%, 16% and 18% respectively.

Ziyuan Song, Junping Chen, Bin Wang, Chao Yu

Single-Frequency GNSS-Based Measurement-Domain Attitude Determination Algorithm with Inter-system Bias Calibration

Under satellite-deprived environments, the accuracy and continuity of the traditional GNSS-based attitude determination methods would be degraded. In this contribution, we derive the tightly coupled measurement-domain approach for single-frequency attitude determination, which could improve the performance of ambiguity resolution and attitude determination accuracy. However, the appearance of inter-system bias (ISB) and inter-frequency bias (IFB) are due to hardware delays and frequency inconsistencies between systems. Therefore, the time-domain stability of ISB is applied to construct ISB estimation observations, to eliminate the influence of ISB on integer ambiguity resolution. The narrowly spaced frequency of GPS L1 and BDS B1 effectively suppresses the influence of IFB by roughly estimating the single difference ambiguity of the pivot satellite at the same time. The kinematic and static experiments are conducted in simulated urban areas, which are based on single-frequency observations from GPS L1 and BDS B1. The result shows that the proposed method can enhance the accuracy and continuity of attitude determination when compared with the traditional MAD methods.

Jingze Li, Liang Li, Jiachang Jiang, Chun Jia, Lin Zhao

Phase Multipath Detection and Its Effect on Positioning Based on Multi-GNSS

The multipath effect is one of the main error sources of Global Navigation Satellite System (GNSS) positioning. However, due to the complexity of the multipath effect in the time domain and space domain, even with the improvement of multiple systems, the error cannot be eliminated by conventional methods. Nevertheless, the multipath effect will have different effects on carrier phase observations at different frequencies, and the carrier-to-noise-power-density ratio (C/N0) can reflect this effect. Based on this basic idea, scholars have proposed two kinds of multipath detection methods: reference function method and double statistics method. There are significant differences between the constellations and the signal of different systems, it is necessary to demonstrate the different results of the reliability of each system, and then explores the feasibility of using the phase multipath detection method to improve the positioning accuracy. The experimental results show that after two methods have been corrected, the positioning accuracy is significantly improved, and the improvement in the N and E directions is relatively weak, but the improvement in the U direction is particularly obvious: the accuracy of the reference function method correction is increased by 56.00%, and the improvement of the double statistic method correction is 63.19%. At the same time, these two methods can be applied not only to the static, but also to the dynamic real-time domain, providing a new idea for the study of phase multipath.

Zhiwen Ren, Cuilin Kuang, Zhetao Zhang

Postseismic Deformation of the MS 8.1 Nepal Earthquake in 2015 from GPS Observations

On April 25, 2015, the Nepal MS 8.1 earthquake took place in the Himalayan seismic belt on the southern margin of Tibetan Plateau. After the earthquake, the China Earthquake Administration established Immediately 13 postseismic GPS continuous stations in the southern Tibetan region. In this study, such data, the data of China’s crustal movement observation network in the southern Tibet region and the data of GPS continuous stations in Nepal are used to estimate the postseismic deformation of the GPS station. Three postseismic deformation models, i.e., a logarithmic model, an exponential model and an integrated combination, are used for fitting GPS postseismic deformation. The Markov Chain Monte Carlo algorithm, based on a Bayesian framework, is applied to invert model parameters. The results show that the integrated model for the logarithmic model and exponential model can accurately fit the postseismic deformation observed by GPS, indicating that the postseismic deformation observed by GPS may involve two different deformation mechanisms with multi-scale characteristics. Based on the analysis of the spatial-temporal distribution of the postseismic deformation field and its comparison with the coseismic deformation field, it is considered that the afterslip mainly occurs in the deep area where the coseismic rupture extends northward, while the seismic risk in the shallow area where the coseismic rupture is not broken still deserves further attention.

Xiaoning Su, Lianbi Yao, Guojie Meng

Performance Assessment of Real-Time Precise Point Positioning Using SSR Corrections

Centre National d’Etudes Spatiales (CNES) now provides real-time correction information such as orbits/clock correction, code/phase bias, and ionospheric spherical harmonic coefficients, which are so-called SSR corrections, and it can better support real-time precise point positioning (RTPPP) compared to ultra-rapid products. In order to assess the performance of RTPPP using SSR corrections, this paper performed static experiments and Unmanned Arial Vehicle (UAV) flight experiments. The experimental results show that PPP using SSR corrections can achieve the performance similar to PPP using the final product, and the ionospheric correction of SSR corrections is better than that of the final ionospheric grid product, but the correction of orbit and clock is slightly worse. There is still a gap between the actual positioning performance of dual-frequency PPP and real-time accurate positioning requirement, and single-frequency PPP still has a long way to go before it can be practically used.

Ruijin Qiu, Zheyu Feng, Chenzhong Gu, Zhimin Yuan, Jianwen Li

Comparative Analysis of Velocity Estimation Methods for GNSS Coordinate Time Series in Southwest China

In order to estimate the velocity results of crustal movement in Southwest China, the coordinate time series of 54 GNSS fiducial stations of CMONOC in the area from 2011 to 2018, are selected in this paper. The velocities and uncertainties about the GNSS coordinate time series are obtained and compared by two methods, i.e. Maximum Likelihood Estimation (MLE) and Median Interannual Difference Adjusted for Skewness (MIDAS). And the experimental results suggest that the area of Southwest China has a trend of southeast-ward movement in the horizontal direction under the framework of ITRF2014. The average velocity in the E direction is 34.44 ± 0.25 mm/a, and the mean value in the N direction is −12.26 ± 0.19 mm/a, the results are obtained by the MLE method under the optimal noise model of each station. While the corresponding results of the MIDAS method in the E and N directions are 34.41 ± 0.24 mm/a, −12.33 ± 0.20 mm/a, respectively. In the U direction, the velocity uncertainty of each station is large, the stations differ widely in movement direction and velocity magnitude. Furthermore, the results between the MLE method and the MIDAS method are slightly different in the U direction. In general, the results obtained by the two methods are not much different, the MIDAS method is resistant to offsets and seasonality, with fast computation speed, and this approach is more robust than the MLE approach.

Chunqiao Xie, Cuilin Kuang, Jiugang Xie

Research on Position-Domain GNSS Multipath Error Modelling Method Based on Sidereal Filtering

Multipath error modelling based on sidereal filtering is an effective method to mitigate the effect of multipath in positioning. The effectiveness of the model mainly depends on the purity of multipath error in the extraction process and the reproducibility of relevant factors in the second positioning period. For the extraction of multipath error, this paper summarized an effective method by analyzing the propagation process of multipath error from observation to position. For the recurrence of positioning scene, this paper proposed a method to match the epochs in two periods via satellite positions, rather than constant lag which is used in traditional methods. Experimental results indicated that the accuracy of the final positioning results corrected by the model produced by the new method is hard to get obvious improvement compared with traditional methods. The number of outliers decreasing significantly showed that the model is able to reduce the number of invalid epochs and is more reliable than traditional methods.

Shangwei Han, Beiping Wu, Guangxing Wang, Zhihao Yin

Score Test Method of Real-Time Cycle Slip Detection Considering the Influence of Gross Error

The appearance of gross error in un-differenced observations will cause the false detection of cycle slip, but the existing real-time cycle slip detection algorithm has little research on it, this paper introduces the score test model in hypothesis test, and on this basis, constructs a score test method that both gross error and cycle slip are processed at the same time. Considering the characteristics of less information available and irreversible processing in real-time cycle slip detection, the score test model is optimized by using the prediction residual instead of the fitting residual of the original model. In the detection process, select the appropriate window width, test GF (geometry free) data series by using the idea of sliding and score test, mark the detected abnormal points, and use the abnormal situation of the next point as the judgment index of gross error and cycle slip. The experimental results show that this method can not only effectively separate the gross error and cycle slips in the un-differenced observations, but also identify the small, continuous and special cycle slips in the data.

Lei Xia, Yufeng Yang, Chenxin Qing, Changsong Mei, Xiong Pan

Precision Analysis of Terrestrial Reference Frame Parameters Based on EOP A-Priori Constraint Model

Earth Orientation Parameters (EOPs) are quantitative parameters that reflect the Earth spatial motion and its rates along the rotation axes. Precession and nutation parameters can be precisely described by the theoretical model, while the complex variation of the pole motion and LOD (length of day) is difficult to be modelled and hard to be predicted with high precision. With the development of Global Navigation Satellite System (GNSS), the spatial and temporal resolution of EOP products have been greatly improved. In GNSS data analysis, a-priori EOPs are normally used as the prediction from the IERS, and the constraint applied on a-priori EOP parameters has much impact on the estimates of GNSS solutions. This paper studies this impacts and develops an a-priori EOP constraint model. GPS data of 142 evenly distributed IGS stations from the beginning of 2010 to the end of 2015 are used for data analysis. Firstly, the precision of the pole motion, LOD and station coordinates under two mostly-used constraint conditions are compared and analyzed, which proves the impact of a-priori EOP constraint on GNSS solutions. Secondly, an a-priori EOP constraint model (pole motion composed of four periodical terms, while LOD composed of two periodical terms) is then developed, where the periodical terms are determined using the Least Square Spectrum Analysis (LSSA) approach. Lastly, the new model is used as the constraint conditions in GNSS solutions. Compared with above two mostly-used constraints, the pole motion and LOD parameters under the new constraint model is closer to the IGS products with largest improvement of 75%, which demonstrates that the new EOP a-prior constraint model can effectively improves the precision of GNSS parameters.

Jiao Liu, Junping Chen, Bin Wang

Time Primary Standard and Precision Time Service

Frontmatter

Research on Main Kinds of Frequency Biases of Optically-Pumped Cesium Beam Frequency Standard

There are two main indices used to evaluate the performance of cesium clock, one is accuracy, the other is stability. On the one hand, frequency bias in cesium clocks is the decisive factor of accuracy, and their fluctuations have significant influence on long-term stability. Hence, the systematic study on frequency biases is of great importance for the evaluation of accuracy and the improvement of long-term stability. In this article, we give some kinds of frequency biases and study their order of magnitude and sensitivity to the power of microwave field are studied. Finally, we deduce their fractional frequency offset, point out the method to reduce the frequency offset, and find the way to improve the long-term stability. At present, the frequency stability achieved by the Peking University optically-pumped cesium beam frequency standard has reached two to three times of the HP5071A high performance tube’s frequency stability, and the overall indicator has reached the international leading level.

Weibin Xie, Xuan He, Shengwei Fang, Nan Chen, Jiachen Yu, Qing Wang, Xianghui Qi, Xuzong Chen

Key Parameters Control of Optically Pumped Cesium Beam Atomic Clock

Cesium beam clock is long-term punctual atomic clock. It plays an important role in the field of satellite positioning and navigation. Its stability directly determines the positioning accuracy of the global positioning system. It is one of the key technologies that China needs to develop in the field of time and frequency. The current commercialized cesium beam clocks are all magnetically-selected cesium atomic clocks, and optically pumped cesium beam atomic clocks have been proposed to achieve better stability because of their high utilization of atoms. Many institutions have carried out research for this purpose for many years. Nowadays, the development of commercialized optically pumped Cesium beam clock is advanced gradually. The Atomic Clock Technology group of Peking University has been working on the research of optically pumped atomic clocks for many years. The experimental prototype has made a breakthrough. This paper aims to introduce the key parameters control of the clock, which affect the performance of the atomic clock. By studying the control circuits, we improve and make full use of the high signal-to-noise ratio of the optically pumped atomic clock. So, we realized the effective improvement of the short-and-medium-term stability of the optically pumped atomic clock, two to three times better than 5071A High Performance. Meanwhile, our products could have three times longer lifetime. The overall indicator has reached the leading level in the world.

Xuan He, Weibin Xie, Shengwei Fang, Nan Chen, Qing Wang, Xianghui Qi, Xuzong Chen

Considering Receiver Clock Modeling in PPP Time Transfer with BDS-3 Triple-Frequency Un-combined Observations

In this work, two models of precise time transfer are presented, firstly, based on the four-frequency un-combined observations of BDS-3, namely TF-UC1 (B1I/B3I/B2a) and TF-UC2 (B1I/B3I/B1C). Then, TF-UC1 and TF-UC2 time transfer with a receiver clock model are introduced and developed. In TF-UC1 and TF-UC2 models, except for the traditional coordinates, troposphere delay and receiver clock parameters, ionosphere delays are estimated as unknown parameters. In addition, receiver differential inter-frequency bias (IFB) are also estimated as parameters. The standard dual-frequency ionosphere-free model is also presented, named as DF-IF. To assess the performance of the two prosed models, datasets from iGMAS were employed. The experimental results show that the TF-UC1 and TF-UC2 models can be utilized for precise time transfer, with accuracy and stability identical to those of the DF-IF model. Furthermore, the performance of TF-UC1 and TF-UC2 models can be improved significantly by using a receiver clock model. The accuracy of TF-UC1 and TF-UC2 is improved approximately 16.6 and 17.7%, respectively, with the receiver clock model. Furthermore, the maximum of frequency stability is up to 79.4 and 80.3% for of TF-UC1 and TF-UC2.

Shuo Ding, Yulong Ge, Peipei Dai, WeiJin Qin, Xuhai Yang, Ye Yu

Performance Evaluation and Analysis of Galileo Satellite Clock in Orbit

The Galileo system is currently the only satellite navigation system for large-scale, normalized assembly of high-precision, high-performance space-borne hydrogen atomic clocks. The analysis of the long-term performance of its satellite clocks contributes to the overall assessment of the system. Based on the precision clock offset products of the German Geoscience Research Center, the frequency accuracy and frequency drift rate of the satellite clock are calculated by the least squares fitting clock offset data. The frequency stability of the satellite clock is discussed by using the overlapping Hadamard variance. At the same time, the long-term variation characteristics of the residual sequence of the Galileo satellite clock offset model are analyzed and the accuracy statistics are obtained. Then the periodic term of the satellite clock is extracted according to the spectrum analysis method. Finally, the noise type of the satellite clock is identified by the Lag1 autocorrelation method. The indicators obtained by the above method comprehensively evaluate the performance of the Galileo satellite clock in orbit. The results show that the mean of frequency accuracy, frequency daily drift rate, frequency stability in ten thousand seconds and model fitting residual accuracy of the Galileo satellite clock are respectively $$ 1.79\; \times \;10^{ - 11} $$, $$ 1.46\, \times \,10^{ - 14} $$, $$ 1.32\, \times \,10^{ - 14} $$ and $$ 0.102\;{\text{ns}} $$; The Galileo satellite clock offset sequence has significant periodic characteristics, and the first three main periods are approximately 0.5, 1 and 0.33 times of its satellite orbital period; The Galileo satellite clock is mainly affected by WFM, FFM and RWFM at different smoothing times.

Yufeng Yang, Changsong Mei, Chenxin Qing, Lei Xia, Xiong Pan

A Method for Evaluating BDS Real-Time Satellite Clock Offset Based on Satellite-Specific Weighting

The precision evaluation of the BeiDou (BDS) real-time satellite clock offset is susceptible to the difference in orbital accuracy between GEO, IGSO and MEO satellites. Therefore, a method for evaluating BDS real-time clock offset is proposed based on a satellite-specific weighting scheme. By reducing the weight of GEO and IGSO satellites, less errors of GEO and IGSO clock offset will be assimilated by the timescale bias estimator. As a result, the precision of BDS satellite clock offset can be assessed more objectively. The experimental results show that compared with the traditional Multi-satellite Method (MSM), the evaluated STDs of the proposed method are more consistent with reference values. The mean evaluation result deviation of GEO, IGSO, and MEO is −0.19, −0.03, and 0.15 ns for MSM, respectively. In contrast, the mean deviation of GEO, IGSO, and MEO is −0.05, −0.04, and −0.04 ns for the proposed method, respectively. In addition, the proposed method can achieve ideal performance when the MEO satellite-specific weight factors are 1, and the factors of GEO and IGSO are set from 0.05 to 0.2.

Zhimin Yuan, Changsheng Cai, Yanjie Li, Guang Liu

Controlling the Microwave Power in Optically Pumped Cesium Beam Frequency Standard

Microwave power is an important factor on the long-term stability of the cesium beam (OPCB) frequency standard. In this paper, we present a new linewidth locking method to control the microwave power in OPCB frequency standards in theory. The responses of OPCB tubes and classical magnetic state selection cesium beam (MSCB) tubes are analyzed and compared against the power of the microwave field. Because of the wide probability distribution of atomic velocity resulting from the optical state preparation and detection, the linewidth of the Ramsey pattern is sensitive to the microwave power. This result can be used to control the microwave power instead of the traditional extremum method. When the microwave power is well controlled at a low level using the linewidth locking method, the ultimate stability of cesium beam clocks can be improved to a certain degree for the reduction of the Ramsey pattern linewidth.

Nan Chen, Qing Wang, Xuan He, Weibin Xie, Shengwei Fang, Zezheng Xiong, Xianghui Qi, Xuzong Chen

Performance Analysis of the On-board Atomic Clocks for BeiDou-3 Satellites

15 BeiDou-3 MEO satellite clocks have been chosen to be studied by using the MGEX (Multi-GNSS Experiment) final clock offsets product provided by the IGS (International GNSS Service) MGEX Analysis Centre - WUHAN University. These clock offsets cover from January 1st to July 1st, 2019, or day-of-year (DOY) 001 to 182. After pre-processed these clock offsets are used to calculate the overlapping Hadamard deviation at the 1000 s and 10000 s time interval, and the method of quadratic polynomial fitting is performed to obtain the daily frequency drift. The characterization of every On-board atomic clock for the 15 BeiDou-3 satellites is analyzed. It shows that the frequency stability of satellite clocks is on the order of E-14. The day frequency drifts of C19–C24, C32 and C33 are generally within the order of E-13. Those of C25–C30 and C34 are generally within the order of E-14. Comparing the on-orbit performance of C19–C24 satellite clocks with their ground test records, the results show that these twos are equivalent for thousand-second frequency stability, and as for ten-thousand-second frequency stability on-orbit performance of these satellite clocks is slightly worse than their ground test records for which an analysis is given. Except for the satellite C24, the daily frequency drifts of the other 14 satellite clocks are better than the ground test records or at least equivalent.

Yunfeng Sun, Yansong Meng, Erwang Du, Guanwen Huang, Wei Xie

New Research Progress in Active Hydrogen Maser in BIRMM

The active hydrogen maser is a core piece of equipment for the time-frequency system. Its stability and reliability directly influence system performance. The optimization of temperature coefficients for physical and circuit systems provides a direct means to further improve performance of active hydrogen masers. Based on the existing sapphire active hydrogen maser, the microwave cavity, magnetic shield, and other components of its physical package have been optimally designed, resulting in new dielectric-loaded cavity and full-size cavity, with a temperature coefficient of −10 kHz/℃ and −1 kHz/℃, respectively. Taking into account the two newly designed cavities, we have achieved active hydrogen masers with volume in completely two different directions. The hydrogen maser with a dielectric-loaded cavity achieved a stability of 2.1E-13/1s and 2.3E-15/d, and that with a full-size cavity achieved a stability of 1.5E-13/1s and 1.6E-15/d when cavity servo system was not installed. The physical package of the active hydrogen maser with a dielectric-loaded cavity can achieve a size of Φ220 mm × 500 mm, and this technical solution is the best choice for space applications.

Tiezhong Zhou, Mengzhi Wang, Shiqing Ren, Qiong Wu, Xiumei Wang, Chenyuan Zhang, Chunyan Cao, Yaxuan Liu, Liang Wang, Lianshan Gao

A Method of Remote Nanosecond Time Reproduction

With the development of science and technology, nanosecond Time-Frequency Signal are needed in astronomical observation, national defense security, communication and other fields. The time comparison system developed abroad can reproduce the standard time signal with an uncertainty of 10 ns locally at the user, the accuracy of national time reproduction system is better than 5 ns within 2000 km. The above time reproduction system based on satellite common view time comparison is limited by baseline length, not suitable for long-distance users to provide time distribution services. Compared with the common view time comparison method, the all-in-view time comparison does not require that both sides have the same visual satellite at the same time. The precise clock and orbit products are used to precisely correct the clock error and ephemeris error. Therefore, the all-in-view time comparison can realize the time comparison between any two places in the global range. In this paper, a long baseline time recurrence method based on all-in-view time comparison is proposed, applying all-in-view time comparison method to time reproduction system, which can effectively solve the problem that the time service system based on the common view principle is limited by the baseline length. To improve the timing accuracy of this method, calculate all-in-view comparison of ultrafast prediction products respectively, and regard IGS comparison as the Vondrak filter value of the prediction time comparison, determining the best smoothing factor, and then filtering the prediction time comparison which is considered as the all-in-view clock to adjust the reproduction terminal constantly. This method can real-time reproduces Immediately better than 5 ns time frequency signal at super long distance.

Pan Du, Longxia Xu, Ya Liu, Xiaohui Li, Feng Zhu

Research on Time-Frequency Synchronization Technology of Multistatic Joint Observation

The multi-station joint detection of non-cooperative targets, such as high-dynamic space debris and aircraft, requires the synchronization of time, frequency and phase between stations, and the synchronization performance could affect the observation accuracy. In view of the requirement, the time, frequency synchronization requirements and resource conditions of space debris joint exploration platform has been analyzed in this paper. Based on the capability of satellite Common-View/All-View time transfer and time steering algorithm, a method of time-frequency signal remote synchronization which is not limited by distance and can be flexibly networking has been proposed. The time synchronization performance of three types of frequency references, including passive hydrogen clock, rubidium clock and crystal oscillator, which have been compared under the 300 km, 30 km and zero km baseline. The results show that the accuracy and stability of the frequency reference is directly proportional to the synchronization performance between stations. When the passive hydrogen maser or rubidium atomic clock is used as the frequency reference, the synchronization deviation between stations can be less than ±5 ns, and the frequency deviation is better than 5E−14. When the OCXO is used as the reference, the frequency deviation is less than 5E−12, which can meet the requirements of positioning of tens to several meters.

Ya Liu, Duo-sheng Fan, Jia-chen Wang, Rui-qiong Chen, Xiao-hui Li

Research on BDS/GPS Carrier Phase Time and Frequency Transfer

The model of BDS/GPS carrier phase time and frequency transfer is given in this paper, and the transformation method of time and coordinate reference are researched. Adopting precise satellite orbits and clocks provided by GFZ, data from MGEX are processed to analysis the performance of BDS/GPS carrier phase time and frequency transfer. The results show that the precision of BDS/GPS carrier phase time and frequency transfer is not better than the single system obviously when the visible satellites are more than 7. BDS convergence time is significantly longer than GPS and BDS/GPS, due to fewer MEO satellites. The influence for single system time and frequency transfer is more obvious than BDS/GPS under complex environment. When the elevation mask angle is over 30°, BDS have better performance than GPS due to BDS’s special constellation in asian-pacific region, and GPS time transfer results are nonsequence. When the elevation mask angle is over 40°, BDS time transfer is also nonsequence at sometime, and GPS cannot be used for time transfer, but BDS/GPS is still get the high precision results; the convergence speed and stability are better than the single system.

Xiang-lei Wang, Feng-feng Shi, Fang-jun Yan, Jia-min Fang

A Rubidium Clock Taming Algorithm Based on Modified Grey Model and PID Control

Aiming at the problems of unstable taming results and limited taming precision of the existing rubidium clock taming algorithm, a rubidium clock taming algorithm based on modified grey model and proportion integration differentiation (PID) control is proposed. Firstly, the algorithm uses the traditional GM(1,1) model to model the original rubidium clock bias, and then the quadratic polynomial model is used to fit the modeling residual of the grey model, and the modified GM(1,1) model is obtained by the corresponding addition of the two models. Finally, PID algorithm is used to tame the modeling result. The result shows that the modified GM(1,1) model can effectively eliminate the random jitter of rubidium clock bias caused by atomic clock noise and satellite measurement noise, so the prediction error within 10,000 s can reach less than 2 ns based on which the taming stability of PID algorithm is significantly improved. And the stability of the system is ensured even if the real-time clock bias data is not obtained. The result also shows that if the PID control interval is shortened from 960 s to 30 s, the taming accuracy can reach less than 0.2 ns.

Jingyan Zhao, Xinyu Miao, Yaojun Qiao

The Method of BDS PPP Time Transfer Considering Clock Modeling

GPS Precise Point Positioning (PPP) time transfer has been applied to the international time comparison at BIPM, while BDS PPP time transfer has not been applied at BIPM. With the rapid development of China’s international GNSS continuous Monitoring and Assessment System (iGMAS), this work, supported by iGMAS products, has carried out the BDS PPP time transfer method and experimental research. The traditional PPP algorithm takes the receiver clock offset parameter as independent white noise, while ignoring the correlation of between-epoch clock offset. For this problem, this contribution proposed the BDS PPP time transfer method which is constrained by the receiver clock model. Using the final (ISC) precise orbit and clock products released by iGMAS, the paper selected the stations of the timing laboratories such as the National Timing Center (NTSC), the Physikalisch Technische Bundesanstalt (PTB) and the GNSS station with external hydrogen atomic clock, and forms 5 time-links with NTSC station as the center node to investigate the experiment. The GPS PPP solutions using IGS final products were regarded as the reference. The experimental results demonstrated that the standard deviation (STD) values of traditional BDS PPP time transfer based on iGMAS products is about 0.7 ns in Eurasian links, and about 0.5 ns in Asia-Pacific links. Compared with the traditional BDS PPP time transfer, the STD value of BDS PPP based on the between-epoch constraint model is reduced significantly, range from 1.53% to 16.6%, especially in the Eurasian links. In addition, the frequency stability of traditional BDS PPP based on iGMAS products is comparable to that of GPS PPP under good observation conditions. BDS PPP using clock model has been significantly improved in the Eurasian link, both in terms of long-term and short-term stability, and the max improvement is about 80%. In the Asia-Pacific region, short-term stability is significantly improved. The maximum stability at 120 s is increased to 57%, while the 15360 s stability is increased by 19%. At the same time, with the development of iGMAS global tracking station and BDS, BDS PPP time transfer performance can be further improved.

Yulong Ge, Shuo Ding, Peipei Dai, Xuhai Yang, WeiJin Qin, Ye Yu

The Long-Term Performance and Life Test of the Spaceborne Rubidium Atomic Clock Under Vacuum on the Ground

The spaceborne atomic clock is one of the core payloads of the Beidou III Global Navigation Satellite, which provides a highly stable time frequency reference for navigation satellites. At present, the Beidou III navigation satellites are equipped with the rubidium clock and the passive hydrogen clock. This paper presents the result of a long-term performance and life test of the spaceborne rubidium clock developed by Chinese Academy of Space Technology (Xi’an), for more than 430 days under vacuum condition on the ground. During the whole test, the rubidium clock is in the normal status, stable in performance and without any failure. The frequency stability of the clock reaches 5.31 × 10−15/100000 s (with drift removed), and the frequency drift rate tends to zero with the increase of working time and reaches −9.8 × 10−15/day before the end of the test. Data fitting of telemetry parameters of the rubidium clock has been performed, the result shows that there would be no significant performance degradation of the spaceborne rubidium clock during the 12-year mission period of the Beidou III navigation satellite.

Feng Xu, Jia Yu Hu, Ke Liang He, Min Cheng, Ruo Feng Cao, Wei Zhang, Chang Liu, Tao Yang, Chun Bo Zhao, Er Wang Du, Yu Ling He

Discrete GM (1,1) Based on Sequence of Stepwise Ratio in the Application of the BDS Satellite Clock Bias Prediction

Aiming at the problem that the fitting sequence of the traditional gray system forecasting model can not reflect the dynamic change of the stepwise ratio of modeling data sequence, proposed to target the stepwise ratio sequence of the sequence of modeling data, a discrete gray model that reflects the trend of the modeling data sequence level is established, the specific steps of the method applied to satellite clock error prediction are given. Firstly, a corresponding step ratio sequence is generated for the modeling clock sequence; then, the step ratio sequence is modeled and predicted by the discrete gray model; finally, the relationship between the stepwise ratio and the modeled clock stepwise ratio sequence is used. The forecast results are restored to obtain the corresponding clock ratio prediction value. In order to avoid the influence of the initial deviation, the reliability of the prediction model is improved by fitting the last data of the last five epochs in the modeling data. The post-precision clock data provided by iGMAS was used for single-day and continuous multi-day forecasting experiments, and compared with the polynomial model and the traditional gray model forecast results. The results show that in the continuous multi-day forecasting experiment, the average accuracy of the forecast products obtained by the method is higher than the quadratic polynomial model, GEO satellite, IGSO satellite and MEO satellite increased by 59.45%, 37.79% and 47.60%, compared to the traditional gray model, increased 59.51%, 44.60%, and 48.46%, respectively.

Changsong Mei, Yufeng Yang, Chenxin Qing, Lei Xia, Xiong Pan

Progress Towards a Miniaturized Mercury Ion Clock for Space Application

A compact mercury ion microwave clock prototype using sealed vacuum system has been developed in Wuhan institute of Physics and Mathematics (WIPM) since 2018. In this letter, we report the recent progress on this small prototype. After one year’s sealed-off, the ion trapping time in sealed vacuum tube is measured to ~73 h. It is much longer than the trapping time in previous turbo pumped vacuum system. By optimizing the time sequence of the clock operation and bias magnetic field intensity, the signal to noise ratio (SNR) of the clock transition is significantly enhanced. A short-term frequency stability of 4.5 × 10−13/τ1/2 (τ = 4–104 s) has been achieved.

Hao Liu, Yihe Chen, Bibo Yan, Ge Liu, Lei She

Research on a New On-orbit Control Strategy of Onboard Atomic Clock of Navigation Satellite

Onboard atomic clock is mainly used for the generation of time and frequency signals of navigation satellite. It is one of the core devices that determine the service performance of navigation satellite. Due to the limitation of its performance and the number of bits in navigation message, the onboard clock usually needs to be controlled and adjusted many times in its life cycle. Based on the analysis of the onboard clock performance characteristics and control methods in current satellite navigation system, a new on-orbit control strategy of the onboard clock is proposed, first of which is to maximize the control period and the second is to avoid impacting service of the satellite when the control is necessary. Theoretical analysis and simulation experiment are carried out, and the results show that the strategy is feasible. This paper is of great significance to the precious operations and service ability promotion of the satellite navigation system.

Maolei Wang, Jun Lu, Shenghong Xiao, Shichao Wang, Sijia Yang

BDS PPP Ambiguity Resolution and Its Application on Time and Frequency Transfer

Time and frequency transfer using precise point positioning (PPP) ambiguity resolution is the hot topic in the time community. The Bureau International des Poids et Mesures (BIPM) applies the GPS observations and phase clock products of the Centre National d’Etudes Spatiales (CNES) to implement time and frequency transfer based on GPS PPP ambiguity resolution. In this contribution, we apply the BDS observations and phase bias products of the CNES to study the contribution of BDS PPP ambiguity resolution (PPP-AR hereafter) on time and frequency transfer. At first, the quality of phase bias product and the performance of ambiguity resolution are assessed. Then, four time links are formed in the common clock experiment and the remote time transfer experiment. The experimental results demonstrate that, compared with the results using PPP technique, the standard deviation (STD) values of PPP-AR time transfer are decreased by 15.6–26.9%. The modified Allan deviations (MDEV) of the PPP-AR results at the most averaging times are smaller than those of the PPP. In the common-clock experiment, the MDEV values of the PPP-AR results at 38400 and 76800 s averaging time are decreased by 16.8% and 42.9%, respectively.

Daqian Lv, Fangling Zeng, Yijing Han, Xiaofeng Ouyang

Satellite Navigation Augmentation Technology

Frontmatter

Non-Gaussian Carrier-Derived Doppler Integrity FDE for Multiple GNSS Satellites

In this paper, a real-time multi-satellite non-Gaussian carrier-derived Doppler integrity fault detection and elimination (FDE) method is proposed for the abnormal jump of user clock drift estimation caused by satellite switching for low-earth orbit (LEO) global navigation satellite system (GNSS) users. The carrier-derived Doppler integrity faults of multiple GNSS satellites under non-Gaussian distribution are detected and eliminated by using the nearest neighbor principle of user clock drift constraint. Multiple carrier-derived Doppler faults caused by multiple satellite handoffs can be eliminated and the corresponding abnormal jumps in the user clock drifts are removed. Estimation accuracy and integrity of user clock drift are improved for LEO GNSS clock discipline. The analysis of the measured data shows that the stability of the user clock drift with broadcast ephemeris is improved to 5E-13-2E-12 except that the stability of the user clock with 64-10,000 s is not worse than 5E-13 before 64 s. The abnormal jumps in the user clock drift series estimated with non-Gaussian carrier-derived Doppler can be effectively suppressed for multiple GNSS satellites.

Wenying Lei, Hong Han, Wenshan Liu, Fei Ling, Yansong Meng

Analysis of Ionospheric Grid Model Performance for China Area

Special characteristics of regional ionosphere generally impact the grid model of SBAS most seriously. Performance of grid model is analyzed for stormy ionosphere conditions with GNSS data in the year of 2011–2017 for China area. It is demonstrated that grid model is more accuracy in north of China than in south of China. Equatorial Ionization Anomaly (EIA) in south of China and storm are the main factors degrading grid model. Steep ionospheric delay gradient arising from EIA exists in the areas of 20oN–30oN, leading to error over-bound of the model. In general, impact of EIA begins at noon at local time, and lasts until night at local time. Disturbing period indicated by Dst index is not consistent with the interval of time when grid model is impacted most seriously, making Dst not an effective indicator for storm events.

Dun Liu, Xiao Yu, Liang Chen, Weimin Zhen

Type B Fault Integrity Monitoring for BDS Broadcast Ephemeris

The integrity and continuity of aircraft precision approach are the most significant performance requirements for aviation users. To ensure positioning integrity of users, it is necessary to detect type B ephemeris fault one of the main integrity risk sources of precision approach. Based on the repeatability of satellite motion period, the Yesterday’s Ephemeris minus Today’s Ephemeris (YE-TE) method is implemented to detect type B fault monitoring for Global Positioning System (GPS). But it is not suitable for BeiDou Navigation Satellite System (BDS) due to the significant differences between BDS and GPS’s orbital period and satellite type. Based on the sensitivity of satellite position error to variations in the broadcast ephemeris parameters, a Predict Ephemeris minus Today’s Ephemeris (PE-TE) method is proposed. It utilizes the extrapolation of different orders polynomials to acquire more accurate prediction parameter. The test statistics and the minimum detectable error (MDE) are constructed which reflect satellite position error. The results show that the test statistics and the MDE satisfy the continuity and integrity risk requirements of precision approach. Type B fault for BDS broadcast ephemeris can be effectively monitored by the proposed PE-TE method.

Liang Li, Yuanyuan Liu, Chun Cheng, Hui Li

Design and Analysis of Beidou Global Integrity System Based on LEO Augmentation

In view of the problem that ground-based monitoring in China is difficult to distribute stations around the world, the global integrity service of Beidou is limited. This paper proposes a Beidou global integrity monitoring system based on the LEO constellation. The global integrity service of Beidou is provided through the monitoring and redundancy voting of the high-precision monitoring receiver and the inter-satellite link of real-time transmission on the LEO satellite. In terms of integrity monitoring methods, the types of satellite on-board faults and monitoring methods based on pseudorange and carrier phase observation measurements are analyzed. The simulation of Spirent GSS9000 simulator verifies the feasibility of the monitoring method. The results show that the pseudorange and carrier phase monitoring methods proposed in this paper can complete the integrity monitoring of the orbit and clock bias. 24 LEO satellites can meet the global triple coverage of Beidou satellites. Through LEO redundant voting, the integrity risk can meet the requirements of CAT I.

Yizhe Jia, Lang Bian, Yueling Cao, Yansong Meng, Lixin Zhang

Method of GNSS Security Augmentation Based on LEO Satellite

In order to improve the service performance of the global navigation satellite system (GNSS), a variety of augmentation systems have been developed, including satellite-based and ground-based augmentation methods. The purpose of augmentation systems usually includes integrity augmentation, accuracy augmentation and availability augmentation. With the emerging user fields, especially those related to life safety or economic debt, more dependence on GNSS, leads to a high demand for the robustness and security of GNSS civil signals. The received power of GNSS signal on ground is weak and the civil signal structure is open, which is easy to become the target of jamming and spoofing. Therefore, it has become a trend to enhance the security of GNSS civil signals. At present, there are two ways to enhance the security. One is to introduce security authentication features into civil signals, including navigation message authentication and spread spectrum code authentication. This method has little effect on non-authenticated users, but the security authentication is not real time. The other method is based on the location authentication of LEO satellite multi spot-beam features represented by iridium next satellite. The method has high real-time performance, but the accuracy is limited by the beam pattern. In this paper, a GNSS security augmentation method based on LEO satellite is proposed. Using the credible ranging signal broadcasted by LEO satellite, the positioning result of GNSS civil signal is authenticated to achieve security augmentation. This proposed method has the advantages of high real-time performance and high precision. Theoretical analysis shows the effectiveness and feasibility of this method.

Tao Yan, Ying Wang, Xiao Liu, Lang Bian, Yansong Meng

Performance Analysis of a Navigation System Combining BeiDou with LEO Communication Constellation

In recent years, LEO communication constellation shows a blowout development trend. The number of satellites in each constellation varies from tens to tens of thousands. If the general navigation payload is loaded on these satellites, the performance of the system will be greatly improved, and more accurate and reliable navigation and positioning services will be provided for the future mass high-precision users, intelligent driving, unmanned platform, and other users. Given this situation, based on analyzing the characteristics of the current LEO communication constellation, this paper proposes a navigation system architecture supported by combining BDS with LEO constellation. Through simulation analysis, the quantitative improvement of DOP (Dilution of Precision) and the positioning performance of the system is analyzed. The research results can provide a reference for the development of the PNT architecture and the next generation BeiDou system.

Xing Li, Xia Guo, Bing Zhu, Shumin Geng

Error Modeling and Integrity Risk Analysis in SPP

With the popularity and development of GNSS, the concept of integrity is proposed in order to ensure the safety of navigation and positioning. In some related fields such as civil aviation and lifesaving, the requirements for the integrity are becoming stricter, making the Integrity Monitoring a hot issue to be solved urgently. However, the existing methods for this problem are theoretically imperfect and the error model used can’t accurately describe the actual error distribution. In this article, we will first present a model for the observation error in single point positioning. Considering that the actual observation errors always have thick tails, a binormal error model has been raised. Next, based on the previous error model, we use the Robust Parameter Estimation (RPE) method based on predicted residual with single iteration to detect and exclude the fault observation values, and then calculate the positioning result. Finally, we derive a method for conservatively estimating the integrity risk in the position by segmenting and magnifying the test-passing domain. The experimental results show that compared with the single normal error model, our binormal error model can describe the actual error distribution better and is conservative in the tail. The RPE method based on predicted residual with single iteration has a good effect of detecting and excluding fault observations and has a small positioning error. When the theoretical risk is less than the risk threshold, the statistical integrity risk obtained from the data is also less than the threshold. In addition, in the case of a worse error distribution with larger fault probability and larger fault error variance, the integrity risk evaluation results are still credible, indicating our method has better robustness.

Yuan Song, Qingsong Li, Yi Dong, Wanli Jian, Dingjie Wang, Jie Wu

Research on Software Defined Payload Reconstruction Technology Scheme

Software-defined payload system architectures typically consist of a modular, generalized, reconfigurable hardware platform and a variety of reconfigurable task software. Software-defined payload support system functions are re-constructed on demand, and can flexibly respond to various spatial mission requirements, which is an important development direction of future satellite payload systems. In this paper, combined with the current in-orbit navigation satellite payload single-star or constellation reconstruction time is too long, the re-construction efficiency is too low, etc. for the new requirements of payload reconstruction function, based on the software-defined payload system architecture, a fast response is proposed. Satellite payload reconstruction solution, including dynamic Reconfiguration Design of Load Task Migration application, software task level reconstruction design, FPGA configuration data ground compression and on-board decompression design, and star-star payload based on inter-satellite link design. The reconfiguration scheme can realize the rapid reconstruction of the single-star software defined load by the ground station and the fast reconstruction of the entire constellation through inter-satellite link, suitable for rapid reconstruction of wartime load functions, and greatly shortening or eliminate the abnormal interruption time of spacecraft caused by payload reconstruction, and the scheme has good engineering application value.

Guochun Wu, Lei Wang, Fei Ling

Sparse Reconstruction of Regional Ionospheric Tomography Based on Beidou Ground Based Augmentation System

Real-time and accurate modeling of three-dimensional (3D) electron density in the ionosphere is important for space navigation and communication technology as well as space weather. This paper investigates ionospheric tomography based on compressive sensing (CS) to achieve high resolution with sparse observation. This methodology includes the slant electron density (STEC) extraction by the un-difference and un-combined precise point positioning algorithm (UPPP), VTEC mapping based on basis function and compressive sensing reconstruction. The validation of the sparse sensing methods have been tested in both simulation and real navigation data in Yunnan from Beidou Ground Based Augmentation System (GBAS) by Qianxun Spatial Intelligence Inc. The constructed electron density by compressive sensing based on real GBAS navigation data agrees well with incoherent scatter radar (ISR) and ionosonde data in Qujing, Yunnan. The sparse sensing method shows 50% accuracy improvement in comparison to traditional ART method. In conclusion, the CS method can effectively reconstruct the three-dimensional electron density of the regional ionosphere by only relying on sparse observation, which can be used for real-time ionospheric tomography.

Yun Sui, Haiyang Fu, Denghui Wang, Shaojun Feng, Zonghua Ding, Feng Xu, Yaqiu Jin

Un-difference PPP Method and Performance Assessment Based on Regional Ionospheric Model

In the field of global navigation satellite system (GNSS), the delay error caused by the ionosphere can reach several meters to several hundred meters, which is the most uncertain error source in GNSS navigation and positioning. The ionospheric delay error seriously affects the GNSS positioning effect and service performance. The real-time and accurate ionospheric model is very important for improving positioning accuracy and shortening convergence time. The high-density GNSS reference station data lays a foundation for constructing the real-time and accurate ionospheric model. In this paper, the VTEC model and the STEC model in Yunnan were realized based on the Beidou ground-based augmentation system date which is constructed and operated by Qianxun Position. The ionospheric model is added to the un-difference and un-combined PPP algorithm. The results of positioning accuracy and convergence time of the ionospheric VTEC and STEC constrained PPP models are analyzed. The results show that the convergence time of the ionospheric constrained un-difference PPP models is improved.

Han Wang, Yun Sui, Denghui Wang, Haiyang Fu, Shaojun Feng

Online Integrity Alert Limit Determination Method for Autonomous Vehicle Navigation

Integrity is the critical performance indicator for navigation in safety-critical applications such as autonomous vehicles. Alert limit is one of the representative parameter in integrity which defines the maximum tolerable positioning error for an operation to safely proceed. However the integrity requirements for GNSS assessment are quite different from those for autonomous vehicles. For autonomous vehicles, a reasonable alert limit needs to ensure the vehicle security and take full advantage of the space between vehicle and lane as much as possible. Based on the analysis of differences from civil aviation to autonomous vehicles, an improved alert limit determination method is proposed in this paper. The kinematic model is firstly introduced into the online determination of alert limit. The integrity risk on two sides are allocated optimally respect to the road geometry and kinematic model. The fixed cuboid bounding box is replaced by a subversive fan-shaped bounding box which is more reasonable to cover the safe-critical areas. The experiment test results compared with those of the Ford model also verified the superiority of the proposed method. Finally the paper also gives the alert limits calculated based on the Chinese standards and hopefully it could provide some references.

Qian Meng, Li-Ta Hsu, Shaojun Feng

Analysis of GBAS Integrity Requirements Based on Single Frequency Beidou Supporting CAT III

GNSS ground-based augmentation systems (GBAS) can be capable of supporting precision approach and landing operations for A/C. The existing GBAS system supports CAT I operation and the GBAS system supporting CAT III operations has been developed. The GBAS requirements for supporting CAT III are more stringent than those for supporting CAT I, especially for integrity. The allocation and derivation of integrity requirements of GBAS system supporting CAT III is difficult to follow the approach of CAT I. The international standard for GBAS systems based on GPS single frequency supporting CAT III has been established. The GBAS supporting CAT III is being actively researched in China, and GBAS technical standard based on Beidou supporting CAT III is in dispute, which makes the development, testing and application of related equipment lack the necessary basis. Therefore, it is necessary to study the allocation and derivation of GBAS system integrity, and carry out top level requirements research on the integrity of Beidou based GBAS system. This paper analyses the integrity requirements of GBAS system based on the single frequency Beidou system supporting CAT III. The integrity requirements of GBAS system supporting CAT III originate from aircraft’s automatic landing requirements. The requirements analysis starts from the landing performance requirements, focusing on the navigation system error (NSE) closely related to GBAS system. Combined with necessary hypothesis, integrity requirements of GBAS system under limit case and malfunction case required by the landing safety are deduced, the ground monitoring probability of missed detection of a ranging domain error due to a ranging source fault is obtained, and a preliminary discussion of airborne guarantee method for integrity is made. This paper provides a valuable reference to establishing top-level requirements of GBAS system based on Beidou system supporting CAT III.

Congbing Su, Anshi Wang, Bin Li

Analysis of the Spatial Correlation of Ionosphere in the Middle Latitude Region

Due to the influence of solar activity, geographical distribution and other factors, the change of total ionospheric electron content has rich space-time characteristics. Therefore, in GNSS relative positioning, with the increase of baseline distance, the ionospheric space-time correlation is weakened, and the double difference operation is difficult to eliminate the influence of ionospheric delay. In order to analyse the ionospheric temporal spatial correlation of the long baseline observation network and provide the fast solution of the global long baseline, this paper first analysed the correlation of double difference ionospheric delay with sunspot number (SSN) and solar F10.7 index. The results show that there is a strong correlation between the double difference ionospheric delay and the sun F10.7 index. Then the CORS data of the national geodetic survey of the United States was used as experimental data. Using the residual statistics of linear interpolation model (LIM) to analyse the correlation of ionospheric observation network range, solar activity state and other factors in detail, and finally obtains the empirical rule of statistics.

Zheng Yuan, Letao Zhou, Yinghao Zhao, Huchao Xu

Derivation of Integrity Allocation for Satellite Based Augmentation System Ionosphere Monitors

Integrity design, including fault node design, node probability allocation and fault elimination method design, has been the focus of Satellite Based Augmentation System. At present, most of the researches on integrity allocation are aimed at the range error caused by satellite signal fault. In contrast, fault from delay measurement of the Ionosphere Pierce Point does not directly affect the range, but indirectly affects the delay of IGPs. This may lead to some difference in MERR calculations. In addition, the test statistics of ionosphere anomalies are usually in chi-square form, so the traditional linear hypothesis is no longer valid. In this paper, the above problems are analyzed and the ionosphere related integrity allocation is studied. Taking the Feared Event with a “shift” of the distribution as an example, we first analyze the relationship between protection level integrity risk and the “shift” amount with the concept of Maximum-allowable ERror in Range (MERR). Then according to the Minimum Detectable Error (MDE), the monitor threshold and the expression of missed detection risk are obtained for the chi-square detection. Finally, the relationship between integrity risk and variance is analyzed, and the general methods to be followed in integrity design are given. The conclusions given in this paper can guide the BD SBAS integrity design.

Yan Zhang, Xiaomei Tang, Yangbo Huang, Long Huang, Gang Ou

A Statistical Study of the Ionospheric Anomalies Affecting SBAS Safety Detected over China Area in 2015

Ionospheric anomaly is the greatest risk affecting the integrity of the Satellite-Based Augmentation System (SBAS). The frequent occurrence of ionospheric anomalies in the low latitude area of China will degrade the accuracy of SBAS grid models severely. Moreover, it will influence Single-frequency SBAS service performance and threaten the safety of aviation users. In 2020, the Beidou global navigation system will be fully completed. For the safety problem of the BeiDou Satellite-Based Augmentation System (BDSBAS) caused by the ionospheric anomaly, it is necessary to carry out statistical research on the SBAS ionospheric anomaly in China. Based on a large volume of observation data from the Crustal Movement Observation Network of China (CMONOC). For the first time, this paper conducts long-term and large-scale research on the nature of SBAS ionospheric anomaly events as type, impact area and occurrence time over China area in 2015, which was the most active year for geomagnetic activity in the 24th solar cycle. In addition, solar activity is strong in 2015. The research shows that apart from the SBAS ionospheric anomaly events caused by Equatorial Ionization Anomaly (EIA), there are the SBAS ionospheric anomaly events caused by the Regional Ionospheric Disturbance (RID). Both happen frequently in China, and the area and time are relatively regular, which can be regarded as “daily anomaly”. It is greatly affected by solar activity and has the characteristics of obvious seasonal variation. The occurrence frequency and activity intensity are high in Spring and Autumn, but low in Summer and Winter. The impact of the ionospheric storm on SABS is random and sporadic. There is no SBAS ionospheric anomaly event caused by typical mid-latitude ionospheric storms in the data of 2015. It mainly affects the EIA over China area, which can be regarded as “abnormal anomaly”. The results of this study will provide data support for the research studies of the integrity of the ionospheric anomaly during the construction of the BDSBAS in China.

Yaxi Liu, Rui Li, Junjie Bao, Yutong Liu

Applicability Analysis of Kriging Methodology for China

A non-nominal condition of ionosphere likely makes the largest threat for aviation service of the Single Frequency (SF) Satellite-Based Augmentation System (SBAS). The Wide Area Augmentation System (WAAS) located in the mid-latitude region has updated the ionospheric grid correction technology from the Inverse Distance Weight (IDW) method to the Kriging methodology that was made primarily to improve system service availability and ensure system service integrity. The implementation of the Kriging methodology utilizes a dynamic fit domain to select a set of measurements and constructs two terms representing the threat of inaccurate model assumptions and the threat of spatial variations, respectively. The advantage of this methodology is that it not only reduces the dependence of the ionospheric augmentation information calculation on the distribution of reference stations but also improves system service performance. However, the BDSBAS (BeiDou Satellite-Based Augmentation System) service area, except for the terrain restricted the distribution of reference stations, has a larger latitude span. It has mid-latitude and low-latitude ionosphere characteristics, especially the irregularity of the low-latitude ionosphere will seriously affect the BDSBAS SF service performance. This paper analyzes the applicability of the Kriging methodology over China and constructs the quantitative relationship of observability between ionospheric measurements and the estimated location to solve the problem. The results show that the Kriging methodology can be used to calculate ionospheric delay augmentation information in the BDSBAS SF augmentation service. The search parameters of the dynamic fit domain in the Kriging can keep unchanged. The research of algorithm for China should focus on the analysis and modeling of ionospheric irregularities, develops the study of error uncertainty to meet the integrity requirements for aviation and improves the services of the system. Additionally, if there is no reference station in the overseas area, it is still difficult to implement effective monitoring of the integrity risk of edge grids caused by ionospheric irregularities, even under the conditions of multi-constellation.

Junjie Bao, Rui Li, Zhigang Huang

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