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2024 | Book

China Satellite Navigation Conference (CSNC 2024) Proceedings

Volume III

Editors: Changfeng Yang, Jun Xie

Publisher: Springer Nature Singapore

Book Series : Lecture Notes in Electrical Engineering


About this book

This book presents selected research papers from China Satellite Navigation Conference (CSNC) 2024, held in Jinan, China, on 22–24 May 2024. These papers discuss the technologies and applications of the Global Navigation Satellite System (GNSS) and in particular the latest advances in the China BeiDou System (BDS). They are divided into 8 topics to match the corresponding sessions at CSNC 2024, which broadly covered key topics in GNSS. Readers learn about the BDS and keep abreast of the latest advances in GNSS technologies and applications.

Table of Contents


Satellite Orbit Determination and Precise Positioning

Performance Analysis of BDS-3 Klobuchar Model

Since July 2020, the global Beidou Navigation Satellite System (BDS-3) satellites provide new B1C and B2a public navigation service signals, as well as the legacy B1I and B3I signals. With the opening of BDS-3 global service, the service area of the broadcast Klobuchar model (BDSKlob) parameters expanded from China and parts of the Asia-Pacific region to the whole world. In this study, the differences between the GPS Klobuchar model (GPSKlob) and the BDSKlob is comprehensively analyzed. The data since the opening of the BDS-3 is collected, and the results show that: (1) the average correction accuracy of the BDSKlob model in global-scale is about 4.61–5.75 TECU; (2) the correction abnormalities of the modified BDSKlob model in high latitude region has been improved significantly; (3) the interchangeability between the BDSKlob and the GPSKlob model algorithm has been verified, is initially verified.

Yongxing Zhu, Gang Wan, Xianggao Yan
Analysis of the Impact of Tonga Volcano Eruption on Satellite Navigation Services

On January 15, 2022, the violent eruption of Tonga volcano in the South Pacific Ocean triggered tsunami waves and atmospheric gravity waves around the world, which had a significant impact on the Earth's magnetic field and atmosphere. Based on GNSS observations, this paper analyzes the impact of Tonga volcanic eruption on satellite navigation services from the aspects of signal propagation delay and user positioning. The results show that the troposphere over China has a short-term fluctuation of 2–3% due to the impact of atmospheric gravity waves triggered by Tonga volcanic eruption. For the middle and low latitudes, the ionosphere shows VTEC abnormal values from southeast to northwest, and the propagation speed of VTEC abnormal is basically equivalent to that of atmospheric gravity waves. The volcanic eruption caused obvious fluctuations in the up direction of positioning results. Dynamic PPP can be used for real-time monitoring of large-scale anomalies of satellite navigation services.

Jingyu Zhang, Bin Wang, Chao Xie, Junping Chen
Prediction of Satellite Solar Radiation Pressure Parameters Based on Recurrent Neural Network

The BeiDou Navigation Satellite System (BDS) has been put into operation. With the system's continuous operation, the data accumulated by the BDS has a growing trend. At the same time, the service is diversified and refined. Due to the huge system, operation and maintenance are increasingly difficult. To adapt to the high-quality and refined operation of the BDS, it is proposed to introduce artificial intelligence-related technologies to assist the BDS in achieving high-quality intelligent operation and maintenance. Based on the three network models of recurrent neural networks (RNN, LSTM, and GRU), this paper models and analyzes the BDS satellite's solar radiation pressure parameters. The optimal model and hyperparameters are obtained through data mining and analysis and model training, and the prediction model is used to verify the measured data. It is found that the prediction accuracy of the three recurrent neural network models is equivalent, the average accuracy is more than 90%, and the prediction accuracy from high to low is GRU, RNN, and LSTM. The prediction method based on the cyclic neural network adopted in this paper can be applied to the state prediction of time series data of the BDS and has certain reference significance for the construction of intelligent operation and maintenance of the BDS.

Jianbing Chen, Lei Chen, Shanshi Zhou, Shuai Huang
Real-Time Kinematic Orbit Determination of GEO Satellite with the Onboard GNSS Receiver

The spacecraft has widely used Global Navigation Satellite System (GNSS) in precise navigation, attitude determination, formation flight and time synchronization. For high earth orbit spacecraft, the space environment is very challenging for GNSS receivers to work. Taking the No. 2 Telecommunication Technology Test satellite (TTS-2) as an example, under both preprocessing strategies of the carrier phase smoothing pseudorange algorithm and single receiver fault detection algorithm based on residual, this paper analyzes the real-time kinematic orbit determination capability of Geostationary Earth Orbit (GEO) satellite by standard point positioning (SPP) and kinematic precise positioning (KPP). The experimental results show that the 3D error of the SPP kinematic orbit is about 100 m, and that of the KPP kinematic orbit is about 20 m. Carrier phase smoothing pseudorange and single receiver fault detection algorithm based on residual are used to preprocess the onboard GPS data, they reduce the 3D error of the SPP kinematic orbit to 49.4 m and radial error to 46.4 m, which decreased by 45%. And they reduce the 3D error of the KPP kinematic orbit to 16 m, a reduction of 23%, and the radial error to 10 m, a reduction of 34%. The kinematic orbit is convenient to implement the hardware and software of the onboard GNSS receiver, and the real-time and high-precision position provides favorable conditions for the accurate orbit control of the spacecraft. This paper’s research work and conclusion have important reference value and significance for the application of high-orbit GNSS, and will promote the development of space-borne GNSS application.

Xinglong Zhao, Xiaogong Hu, Shaojun Bi, Huichao Zhou, Zheng Song, Qiuli Chen, Meng Wang, Shanshi Zhou, Chengbin Kang, Haihong Wang, Gong Zhang
Analysis of the Contributions of ISL to the Precise Orbit Determination of BDS-3 Satellites

The 3rd generation of the Chinese Beidou Navigation Satellite System (BDS-3) is the first GNSS deployed with Inter-Satellite Link (ISL) payloads within the whole constellation. A series of Precise Orbit Determination (POD) experiments have been conducted to investigate the contributions of ISL to the orbits of BDS-3 satellites in cases of different ground tracking coverage. Results show that the improvement in orbit precisions is most significant when only a regional ground network is available. When integrating with ISL observations, the single-day solution from a regional network is good enough to meet the performance requirement. For a globally distributed sparse tracking network, additional ISL measurements also better the orbit precision by 51% from the point of view of orbit Day Boundary Discontinuity (DBD) 1D RMS, the average of which decreases from 8.22 cm to 4.05 cm. Surprisingly, benefits of integrating ISL with ground tracking are still visible even with a denser global network. In this case, an average reduction of ~28% in orbit DBD 1D RMS can be observed after integrating ISL measurements, decreasing from 5.12 cm to 3.59 cm. In addition to range measurements, the profit of ISL clock measurements is also explored. It shows that combining ISL clock measurements with ground tracking reduces the orbit 1D RMS by 19%. And the orbit radial component exhibits the most benefits from additional ISL clock observations, with a DBD RMS reduction from 4.02 cm to 2.44 cm. Results from this research indicate the great potential of the ISL of BDS-3, which can not only guarantee the performance of standard services under unfavorable conditions but also improve the high-precision service capability of BDS-3.

Hanbing Peng, Yu Xiang
BDS-3/GNSS Multi-frequency PPP Rapid Ambiguity Resolution

The four available civil frequencies of BDS-3 provide strong support for multi-frequency multi-system PPP-AR. It has been shown that multi-frequency improves the PPP-AR positioning performance of BDS-3/GNSS significantly, but most of the IGS station 30 s sampling rate observations are used to evaluate the positioning performance, while the high sampling rate is closer to the actual application scenario. To fill this gap, the multi-frequency multi-system BIAS product of CNES is used, combined with the 1 s sampling rate observations of the European EUREF station, to verify the multi-frequency BDS-3/GNSS is used to verify the possibility of achieving 1 s ambiguity resolution. The multi-frequency and multi-system single-epoch PPP-WAR is performed for smart driving applications with sub-metre positioning requirements, and the necessary conditions to meet the accuracy are analysed. Therefore, this paper analyses the stability differences between CNES BIAS phase fractional deviation product systems, between satellites and between frequencies; achieves fast convergence of the BDS-3/GNSS full-frequency PPP-AR by optimising the partial ambiguity fixation algorithm, and analyses the contribution of the number of wide lane fixes in the single-epoch PPP-WAR. The results show that the inter-system standard deviation of BIAS products: GPS < Galileo < BDS-3; the BDS-3 four-frequency PPP-AR imitates a dynamic mean convergence time of 15.32 min, with horizen and vertical accuracy of 4.3 cm and 5.3 cm; in the BDS-3/GNSS multi-frequency PPP-AR experiments, fast convergence within 3 min can be achieved with 90% confidence. In the BDS-3/GNSS multi-frequency PPP-AR experiment, the horizen and vertical accuracy can be 2.2 cm and 8.9 cm with 90% confidence, and some samples can be converged with 1 s fixation; in the single-epoch PPP-WAR, the horizen accuracy of 20 cm and vertical accuracy of 30 cm can be achieved when the number of WL fixation reaches 13.

Lijun Yang, Guofu Pan, Xiang Zuo, Jinsheng Zhang, Zhihao Yu
Effect of Troposphere Parameter Estimation on BDS PPP

To investigate the effect of the tropospheric wet delay parameter estimation on BDS precision point positioning (PPP), observations from 13 global MGEX stations are selected over 24 days for static PPP using four parameter estimation methods: Random walk (RW), Piecewise Constant estimation (PWC: 120/180/360, estimated every 120/180/360 min). The results of the tropospheric zenith delay (ZTD) and PPP positioning are evaluated using the ZTD product and the weekly solution product provided by IGS. The ZTD time series and ZTD accuracy of the four parameter estimation methods are analyzed, and the applicability of the four parameter estimation methods is further validated by the PPP positioning accuracy. The experiments show that RW and PWC:120 are suitable for the case of drastic overall ZTD variation, whereas PWC:180 and PWC:360 are suitable for the case of gentle overall ZTD variation; furthermore, it is observed that selecting a suitable parameter estimation method leads to an improvement in both ZTD accuracy and PPP positioning accuracy. According to those results, we recommend the following order of preference for the four parameter estimation methods: RW, PWC:120, PWC:180, and PWC:360, based on their respective strengths.

Zhimin Liu, Yan Xu, Xing Su, Junli Zhang, Jianhui Cui, Zeyv Ma, Qiang Li, Baopeng Xu
Comprehensive Analysis of the Cycle Slip Detection Threshold in Kinematic PPP During Geomagnetic Storms

Space weather events may affect the magnetosphere and ionosphere, and thus reduce the positioning capacity of global navigation satellite systems. The paper analyzes the BDS/GPS kinematic Precise Point Positioning (PPP) accuracy during the November 2021 geomagnetic storm to investigate the impact of the cycle slip (CS) detection on positioning accuracy under an active ionosphere. The results show that when using the conventional constant threshold of geometry-free (GF) CS detection, several stations in high latitudes present obvious accuracy anomalies and the maximum positioning error reaches 6 m. It is also found that the CS incidence increases significantly during the period of accuracy anomalies. When using the adaptive GF threshold, the kinematic PPP positioning accuracy and CS incidence return to the normal level, which proves that the underprivilege of conventional GF threshold that the geomagnetic storm could generate CS misjudgments and lead to an abnormal positioning accuracy. The average 3D positioning accuracies of 40 stations worldwide located at different latitudes show that the adaptive GF threshold could improve the average positioning accuracy of stations in high latitudes by 42.5%.

Qiang Li, Xing Su, Chunyan Tao, Junli Zhang, Zhimin Liu, Jianhui Cui, Zeyv Ma, Baopeng Xu, Yan Xu
Analysis of Rapid Re-initialization Performance of Precise Point Positioning for Low-Cost Receiver

The tracking loop performance of low-cost receiver is poor, and the risk of satellite signal loss increases, resulting in frequent carrier phase cycle slip. The conventional satellite-by-satellite cycle slip processing method initializes the carrier phase ambiguity with cycle slip, decreases precise point positioning performance, and may lead to re-initialization. To avoid the degradation of positioning performance and even PPP re-initialization caused by cycle slip processing of the low-cost receiver, we proposed a method of partial cycle slip fixing based on the time-differenced model for low-cost receiver. In this method, the cycle slip subset is selected by quality control, and then the cycle slip is estimated and fixed by the time-differenced observation. The proposed method is verified with collected BDS and GPS dual-frequency data using a u-blox low-cost receiver, and the results show that the method adopted in this paper can correctly fix the cycle slip and achieve rapid PPP re-initialization, and improve the continuity of PPP high-precision positioning results of the low-cost receiver.

Fenghua Luo, Lin Zhao, Fuxin Yang, Zhiguo Sun, Jie Zhang
Prototype of Real-Time Orbit Service for LEO Navigation Satellite System

With continuous deployment of Low Earth Orbit (LEO) satellites and development of inter-satellite links, LEO enhanced Global Navigation Satellite System (LeGNSS) brings new opportunities for future high-precision positioning, navigation, and timing (PNT) services. Real-time precise LEO orbit is the prerequisite for real-time precise positioning. In order to provide precise real-time LEO orbit and guarantee the normal operation of LeGNSS, a prototype of real-time orbit service for LEO navigation satellite system is proposed. We evaluate the accuracy of LEO orbit, and demonstrate the system infrastructure and working principle. In addition, two real-time LEO orbit broadcasting methods are designed: (1) using LEO orbit determined by RTS products as the fitting part to predict orbit, the prediction part is fitted by ephemeris parameters, which are injected into LEO and broadcasted to users. (2) differences between LEO orbits obtained by RTS products and the broadcast ephemeris are used to generate orbit corrections and broadcasted to users. Results show that LEO near-real-time orbit achieves centimeter-level accuracy, and the fitting errors of broadcast ephemeris are smaller than 10 cm in 20-min fitting arc. Moreover, the LEO broadcast ephemeris would obtain decimeter-level accuracy orbit, while the orbit corrections method would provide users with real-time centimeter-level LEO orbit.

Guanlong Meng, Haibo Ge, Bofeng Li
BDS3-Based Precise Orbit Determination for LEO Satellites with Single-Receiver Ambiguity Fixing

Single-receiver ambiguity fixing can enhance the observation geometric constraint, and improve the orbit accuracy of low Earth Orbit (LEO) satellites. We propose a single-receiver ambiguity fixing method by taking the carrier phase residual as the index to choose reference in the single-difference ambiguities. The ambiguity fixing performance and Precise Orbit Determination (POD) is verified by using the spaceborne BDS3 observation from Tianhui 02-02 satellites. The ambiguity fixing success rates for BDS3 wide- and narrow-lanes are 98% and 89%. Taking the GPS-based orbit with single-receiver ambiguity fixing as a reference, the orbit comparison shows that the accuracy of radial, tangential and normal directions of BDS3-based POD are improved by 26%, 42% and 52% with the single-receiver ambiguity fixing, and the three-dimensional RMS of orbit difference is improved from 2.5 cm to 1.4 cm. The baseline from the orbit difference is evaluate by comparing to the baseline derived from the double-difference GPS-based precise relative orbit determination. The radial, tangential and normal accuracy of baseline solution are improved by 27%, 45% and 46% when fixing ambiguity. The 3D RMS of baseline difference is reduced from 7.6 mm to 4.3 mm. The single-receiver ambiguity fixing can be performed by using our ambiguity fixing method, and the accuracy of BDS3-based POD and baseline can be improved.

Houzhe Zhang, Kai Shao, Xiaojun Duan
Assessment About Parameters Selection Strategy of ECOMC Solar Radiation Pressure Model for BDS-3 Satellites During the Earth Eclipsing Period

Solar radiation pressure perturbation is the dominant error of POD of navigation satellites, which is directly bound up with the attitude control strategy of satellites and the properties of surface materials. Because of the difference of satellite characteristics, the 5-parameter ECOM model is not completely suitable for BDS-3 satellites during the earth eclipsing period. The higher-order periodic terms of ECOMC model can effectively absorb errors such as thermal radiation that are not modeled during the earth shadow period. This paper studies the variation of D0, Y0 and B0 of ECOMC model with the sun elevation angle, proves that compared with the 5-parameter ECOM model, the ECOMC model is more accurate for navigation satellites POD. In order to solve the problem of excessive parameterization of ECOMC model, this paper analyzes the correlation between 13 solar radiation pressure parameters of ECOMC model. Based on the strong correlations, the 11-parameter ECOMC model for CAST satellites without estimating Bc and D4c parameters and the 12-parameter ECOMC model for SECM satellites without estimating Bc12 parameters are proposed respectively. The experimental results show that compared with the 5-parameter ECOM model, the 11-parameter ECOMC model of CAST satellites can improve the radial, along-track and cross-track accuracy by 74.0%, 65.5% and 61.3%, respectively, and the 1DRMS by 66.7% during the Earth Eclipsing period. The 12-parameter ECOMC model for SECM satellites can prove the radial, along-track and cross-track accuracy by 58.5%, 56.2% and 70.7%, respectively, and the 1DRMS accuracy by 60.0% during the Earth Eclipsing period.

Renlong Wang, Jianhua Cheng, Hui Li, Guojian Sun, Xitie Lu
Assessment of Solar Radiation Pressure Models for BDS-3 MEO Navigation Satellites

Precise orbit products of BeiDou Navigation Satellite System (BDS) are the primary prerequisite to provide high-quality positioning, navigation and timing services. As the dominating satellite type in BDS-3 constellation, the orbit accuracy of Medium Earth Orbit (MEO) satellite mainly depends on geometric observation conditions and the quality of dynamic models. In recent years, the growing number of global BDS monitoring stations greatly enhance the geometric pattern for BDS-3 MEO satellites. However, solar radiation pressure (SRP) of BDS-3 MEO satellites is still under investigation and the SRP models adopted by analysis centers in the International GNSS Service (IGS) are different from each other. Based on International GNSS Monitoring and Assessment System (iGMAS) BeiDou analysis center of Tongji University, this paper comprehensively evaluates six SRP models (e.g., ECOM1, ECOM2, ECOM1 with a prior Box-wing model, ECOM2 with a prior Box-wing model, ECOM1 with an empirical force model, ECOM2 with an empirical force model) that commonly used for BDS-3 MEO satellites. The results indicate that compared with ECOM1 model, ECOM2 model can reduce orbit overlap error by 5.02% when satellites are out of earth eclipse. Moreover, ECOM2 model can effectively reduce the orbit overlap error in spite of a low solar elevation angle. As for satellite laser ranging residuals of BeiDou-3 MEO satellites, ECOM1 model with an empirical force model performs better. The average orbit bias in radial direction is 0.63–2.51 cm and the standard deviation is 2.68–3.16 cm, which is decreased by 7.76%–26.97% comparing with other five models. Furthermore, the orbit products resolved by this paper is better than orbit products provided by GFZ and WUM in radial direction.

Leitong Yuan, Bofeng Li, Weiguang Gao, Haibo Ge
Combined Processing of Outlier and Multipath in GNSS Precise Point Positioning

The Global Navigation Satellite System (GNSS) precise point positioning (PPP) technology is inevitably affected by outlier and multipath, especially under complex environments. Based on the idea of robust estimation and multipath detection, a combined processing method considering the outlier and multipath simultaneously is proposed for GNSS PPP in this study. The GNSS observations in real complex environments were used to conduct the kinematic PPP experiment. Besides, the PPP positioning performance is carefully compared and analyzed among without the outlier and multipath processing, the traditional outlier processing, and the combined outlier and multipath processing. The results show that the proposed processing method can improve the positioning performance for GNSS PPP. Compared with the traditional outlier processing, the positioning accuracy of the proposed method is improved by 20.3%, 49.2% and 13.6% in E, N, and U directions, respectively. Hence, the proposed method considering both the outlier and multipath can effectively improve the PPP positioning performance, especially under complex environments.

Haijun Yuan, Xiufeng He, Zhetao Zhang
Polar Motion Prediction Based on the Combination of Weighted Least Squares and Vector Autoregressive Models

This paper presents the application of weighted least squares (WLS) extrapolation and vector autoregressive (VAR) modelling in polar motion prediction. The simultaneous predictions of pole coordinates $$x_{{\text{p}}}$$ x p , $$y_{{\text{p}}}$$ y p are generated by the combination of (1) WLS extrapolation of harmonic models for the linear trend, Chandler and annual wobbles, and (2) VAR stochastic prediction of the WLS residuals (WLS+VAR). For WLS fit the weights are computed by a power function to accurately extract the Chandler and annual wobbles. Moreover, the VAR technology is used to model and predict the WLS residuals of pole coordinates $$x_{{\text{p}}}$$ x p , $$y_{{\text{p}}}$$ y p together considering the correlation between $$x_{{\text{p}}}$$ x p and $$y_{{\text{p}}}$$ y p . . The results show that the accuracy of the ultra short-term predictions up to 10 days into the future obtained by WLS+VAR is equal to or slightly better than that by LS+AR, whilst the predictions out 10 days are substantially more accurate than those by LS+AR. Furthermore, the medium-term predictions beyond 90 days can be improved by WLS+VAR in comparison with the prediction values provided by the IERS Bulletin A. The improvement in the prediction accuracy can reach up to 20%.

Yu Lei, Danning Zhao
Precise Orbit and Clock Offset Determination of LEO Navigation Satellites Based on Multi-constellation and Multi-frequency Spaceborne GNSS Data

With massive low earth orbit (LEO) satellites, LEO navigation enhancement system is important to improve the service performance of GNSS system. The high precision orbit and clock offset calculation of LEO satellites is one key to establish the stable and reliable space-time reference. Based on GPS/BDS/GALILEO data measured by LEO navigation satellites, this paper determines the precise LEO orbit and clock offset, and evaluates the precision of LEO orbit and clock offset solution. The orbit determination accuracy using GPS (L1/L2), GPS (L1/L5), BDS (B1C/B2a), and GALILEO (E1/E5a) combination is 2.42, 2.93, 2.67, and 2.87 cm, respectively. The clock offset solution accuracy using the above four combination is 0.167, 0.194, 0.186, and 0.180 ns, respectively. These results can provide high-quality product for navigation enhancement system services.

Junjun Yuan, Ertao Liang, Liqian Zhao, Kai Li, Chengpan Tang, Shanshi Zhou, Xiaogong Hu
GNSS Carrier Phase Heading Determination with a Single Array Antenna

In the field of global navigation satellite system (GNSS), low-cost anti-jamming array antennas are seldom adopted for precise heading determination. In this contribution, we propose a method for carrier phase heading determination with a single array antenna. Using a centimeter-level very-short baseline composed of two antenna elements in the array, the GNSS observations of a single epoch are iteratively solved to remove the impact of antenna-induced phase biases on heading solutions. To improve the accuracy and availability of heading solutions, the baseline constrained LAMBDA method (C-LAMBDA) is adopted to perform the ambiguity resolution (AR). By simulating a set of GNSS observations for very-short baselines of 10 cm, the proposed method is simulated under single-frequency, single-epoch conditions. Simulation results indicate that the proposed method can achieve heading solutions with root mean square errors (RMSE) of about 2°. The impact of the number of iterations and C-LAMBDA on heading solutions are also analyzed.

Wenxin Jin, Wenfei Gong, Tianwei Hou, Xin Sun, Hao Ma
Performance Evaluation of BDS-3 Satellite Clocks Based on Inter-Satellite Link and Satellite-Ground Observations

The onboard atomic clock is responsible for the generation and maintenance of the time and frequency reference signal on the satellite, and its performance directly affects the service performance of the navigation system. Accurate and reliable satellite clock offsets are the basic data source for the performance evaluation of onboard clocks. Based on the satellite clock offsets measured by the Ka-band inter-satellite links (ISL) and the L-band satellite-ground precise orbit determination and time synchronization (ODTS), the performance of BDS-3 onboard rubidium clocks and hydrogen clocks, including the frequency accuracy, the frequency drift rate and the frequency stability are compared and analyzed in this paper. The research results based on the experimental data show that the frequency accuracy and frequency drift rate of the BDS-3 satellite clocks evaluated by the Ka-band ISLs and the L-band ODTS are basically consistent, and the frequency accuracy and drift rate of the hydrogen clock are better than rubidium clock. For the evaluation of frequency stability, the stabilities of BDS-3 satellite clocks for the averaging time of 1000 s and one day reach 2.5 × 10–14 and 2.5 × 10–15, respectively. The results of hydrogen clocks are also better than those of rubidium clocks. In addition, the satellite clock stability evaluation using the L-band ODTS and Ka-band ISL have their respective advantages. The evaluation results based on the ODTS clock offsets show better short-term stability. When the averaging time of the Allen variance is greater than 5000 s, the ISL clock offsets show better medium and long-term stability. In addition, compared with the ODTS clock offsets, the ISL clock offsets are not affected by the orbit errors, and the frequency stability of IGSO/GEO satellites obtained based on the ISL is significantly better than the ODTS clock. Therefore, the ISL is more suitable for evaluating the frequency stability of the BDS-3 IGSO/GEO satellites.

Yinan Meng, Xin Xie, Hongliang Cai, Chao Zhang, Rui Jiang, Xia Guo, Jun Lu
Global Mapping of Ionospheric ROTI Index and Its Preliminary Application in Analysis of Precise Positioning Degradation

The Rate Of change of total electron content (TEC) Index (ROTI), derived from the GNSS dual-frequency carrier phase combination, has been widely used as a key indicator of ionospheric disturbances. In this paper, we propose an ordinary kriging approach to generating ionospheric ROTI maps with the aim of characterizing ionospheric irregularities and assessing their impacts on precise point positioning (PPP) at a global scale. In the kriging-based mapping of the ROTI index, we exploit three semi-variogram models (i.e., Gaussian, Spherical and Exponential) and evaluate their performance during the September 6–9, 2017 geomagnetic storm by taking advantage of more than 500 GNSS stations. Results suggest that (1) The overall RMSE of kriging cross-validation for all three models is generally less than 0.4 TECu/min, and the spherical semi-variogram performs best by analyzing the semi-variogram fitting and interpolation accuracy. (2) The ROTI maps can effectively represent the spatial-temporal evolution and intensity of global ionospheric irregularities during the geomagnetic storm. (3) There is a strong positive correlation between the PPP errors and ROTI values. The maximum, average and RMS of 3D positioning errors are 0.33 m, 0.14 m and 0.40 m, respectively, with the level of ROTI values less than 0.5 TECu/min, while they can reach 7.06 m, 2.80 m and 3.63 m, respectively, when the ROTI increases above 2.5 TECu/min. The ground positioning risk derived from the ROTI maps can effectively indicate the degradation of positioning performance.

Haoyang Jia, Zhe Yang, Bofeng Li
Precise Point Positioning Ambiguity Resolution with Multi-frequency Ionosphere-Reduced Combination

Precise point positioning (PPP) with ambiguity resolution can improve positioning accuracy and reliability. In conventional dual-frequency ionosphere-free (IF) PPP (IFPPP), the IF ambiguity loses its integer property, so the fixing process needs to be decomposed into a two-step way of fixing wide-lane (WL) and narrow-lane (NL) ambiguity separately. Only when both are fixed at the same time, can a reliable positioning solution be obtained. In order to take full advantages of multi-frequency signals and simplify the ambiguity resolution process, by proper selecting the combination coefficients, a PPP ambiguity resolution method based on ionosphere-reduced (IR) combination is proposed in this paper. The proposed IRPPP model hardly needs to consider the effect of ionosphere, while has the equivalent wavelength and observation noise compared with conventional IFPPP. In addition, the combined IR ambiguity maintains its integer solvability, thus only one-step of directly fixing the IR ambiguity is need to achieve positioning performance comparable to conventional IFPPP. The model is further evaluated globally, and the results show that the IRPPP is superior to the conventional IFPPP in terms of the number of available NL ambiguity and the time to first fix (TTFF), and the average TTFF can be shortened by 22.6%. As for positioning accuracy, both models are basically the same with centimeter-level accuracy.

Qing Zhao, Shuguo Pan, Wang Gao, Ji Liu, Yin Lu, Peng Zhang
Simulation Study on Real-Time Orbit Determination Based on GNSS for LEO Satellite Considering the Effect of Electric Propulsion

The traditional GNSS pseudo-range based Real-Time Orbit Determination(RTOD) cannot meet the requirements for high-precision and reliable orbit determination of LEO satellite with electric propulsion in the whole process, this paper conducts mathematical modeling of electric thrust based on the magnitude, direction and satellite attitude of electric thrust, improves the traditional GNSS pseudo-range based RTOD algorithm, and takes into account the impact of inertial system acceleration generated by electric thrust during the Kalman time update process of RTOD, A new RTOD algorithm based on GNSS pseudo-range considering the influence of electric propulsion is proposed. Then, based on GNSS signal simulator and space-borne GPS/BDS receiver, the simulation scenarios of single electric thruster and dual electric thruster are designed and simulation GPS/BDS data are collected. Using the independently developed RTOD software SATODS, offline simulation RTOD data processing tests are conducted on the collected simulation data. The test results show that the new RTOD algorithm based on GNSS pseudo-range considering the influence of electric propulsion proposed in this paper is not affected by the electric thrust, which verifies the adaptability of the improved RTOD algorithm to the orbit determination of orbital maneuver conditions with the electric propulsion.

Jiapeng Wu, Wanwei Zhang, Fuhong Wang, Meng Wang, Chengxiang Yin
Analysis of the Performance of Broadcast Ionospheric Model for Anti-disturbance Capability

Magnetic storms and solar flares cause anomalous changes in ionospheric electron content, during which the performance of the broadcast ionospheric model correction decreases. In this paper, we use the CODE GIM (Center for Orbit Determination in Europe global ionosphere maps) product as a reference to evaluate the BDGIM (BeiDou global ionospheric correction model) BDS Klobuchar (BKlob), GPS Klobuchar (GKlob), and NeQuick G models in terms of its correction performance and the adaptability to magnetic storm and flare events. The analysis of the measured data shows that (1) during the magnetic storm, the BDGIM model does not show significant changes at low and mid-latitudes, while the correction rate is less than 20.0% at high latitudes; the BKlob and GKlob models show fluctuations at mid and high latitudes. The fluctuation range is roughly 20.0–40.0% in mid-latitudes and the correction rate is less than 20.0% in high latitudes; the NeQuick G model decreases the correction rate to about 20.0% at mid and high latitudes in the southern hemisphere during the outbreak of higher-grade magnetic storms. (2) During solar flares, the BDGIM model shows no significant change in the correction performance in the Northern Hemisphere and globally, and fluctuations in the Southern Hemisphere; the BKlob and GKlob models show fluctuations in the Southern Hemisphere at mid-latitudes, and the correction rate in the Southern Hemisphere at high latitudes is less than 20.0%; the NeQuick G model shows a decrease in all regions, and the correction rate ranges from 20.0% to 40.0%. (3) The BDGIM model has better adaptation to flares, and the NeQuick G model has better adaptation to magnetic storms; the BKlob and GKlob models have comparable adaptation to both, with differences in individual latitudinal bands.

Xianggao Yan, Xiaolin Jia, Yongxing Zhu, Jialong Liu, Zhichao Zhang
Global Instantaneous Centimeter-Level Multi-constellation and Multi-frequency Precise Point Positioning with Cascading Ambiguity Resolution

With the progresses of Global Navigation Satellite System (GNSS), a number of satellites transmitting multi-frequency signals contribute precise point positioning (PPP). Global instantaneous or single-epoch centimeter-level PPP may be reached because global single-epoch narrow-lane (NL) ambiguity resolution (AR) may be possible with many wide-lane (WL) ambiguities being fixed instantaneously, which can improve the accuracy of the instant NL ambiguities. In this article, the cascading AR (CAR) method was extended to the GPS, Galileo, and BDS-3 all-frequency signals. The performance of instantaneous PPP was investigated with global public stations. The results showed that attributed to the additional frequency observations, the instant positioning accuracy improved substantially. On a global scale, the instant horizontal and up positioning accuracy improved from about 20 and 60 cm, respectively, for the dual-frequency PPP-CAR to about 6 and 20 cm, respectively, for the multi-frequency PPP-CARs. These results are quite encouraging for global autonomous driving cars because better positioning accuracy is expected once the multi-constellation and multi-frequency signals are integrated with inertial sensors.

Lizhong Qu, Luping Wang, Haoyu Wang, Wei Jiang, Yiwei Du

Time Frequencies and Precision Timing

High-Performance Microwave Frequency Standard Systems Based on the Ground-State Hyperfine Splitting of 171Yb+ and 113Cd+ Ions

Microwave frequency standards based on laser-cooled 171Yb+ and 113Cd+ ions have achieved excellent results. The fractional frequency uncertainties of ground-state hyperfine splitting frequency of 171Yb+ and 113Cd+ were $$1.8\times {10}^{-14}$$ 1.8 × 10 - 14 and $$6.33\times {10}^{-14}$$ 6.33 × 10 - 14 , respectively. The short-term stabilities of 171Yb+ microwave frequency standard and 113Cd+ microwave frequency standard are promoted to a new record level. Based on these experiment results, some defects of the system are discussed and corresponding schemes are proposed to improve the frequency accuracy. Sympathetic cooling is introduced to improve the performance of microwave frequency standard.

Ying Zheng, Yiting Chen, Nongchao Xin, Shengnan Miao, Haoran Qin, Jianwei Zhang, Lijun Wang
Precision Analysis of Clock Products Data from iGMAS Analysis Centers

With the full accessibility to the BeiDou navigation satellite system (BDS) and the further development of the international GNSS monitoring & assessment system (iGMAS), it is of great significance to study the satellite atomic clock related technology with the iGMAS clock bias data. Presently, the analysis focuses on global positioning system (GPS), but the iGMAS rapid/ultra-rapid clock bias products have not been comprehensively evaluated. Thus the clock bias precision analysis strategy and precision assessment index were devised. The final precise clock bias data were taken from the international GNSS service analysis center (IGS) and three analysis centers under the programs of the multi-GNSS experiment (MGEX). The data were then comprehensively assessed in terms of precision using the median-based two-step gross error detection method and the second difference eliminating system bias method. The precision index of the iGMAS rapid/ultra-rapid clock bias products was further analyzed. As revealed in the test results, the iGMAS final precise clock bias products were as accurate as indicated by the data from the MGEX analysis centers. The observed-half precision of rapid and ultra-rapid clock bias products was in hundred-picoseconds, while the predicted-half precision of ultra-rapid clock products was within two nanoseconds. In the end, the miss rate of data regarding the iGMAS clock bias products is discussed to provide reference for practical applications.

Yifeng Liang, Jiangning Xu, Miao Wu, Yundong Shang
The Research on BeiDou Time Transfer via Precise Point Positioning based on Raw Observations

The Precise Point Positioning (PPP) technique has been widely applied in the field of satellite navigation and precise positioning. In the field of time transfer, the PPP technique is able to achieve high-precision BeiDou timing thanks to precise carrier phase observations and error correction models. Moreover the PPP technique can achieve time transfer which is independent of the baseline length globally due to the fact that the positioning of single station doesn’t involve the interaction with other stations. However the dual-frequency ionosphere-free linear combination method is usually carried out for the regular PPP method, in which the integrality property of the ambiguity parameters would be ruined and the precision of the combined observations is degraded by a factor which depends on the combined frequencies. On this basis, this article proposes a BeiDou PPP time transfer model based on the raw observation approach which implements the least-squared estimation for PPP network solution using the raw pseudorange and carrier phase observations of globally distributed stations to determine the clock offset of the receivers. Due to the unification of the bias parameters (e.g. the carrier phase bias of satellites) and the VTEC parameters of ionosphere, the estimated clock offsets of multiple stations can be unified within the same bias framework, which eliminates the influence of different GNSS products, different estimation strategies and the transfer and absorption of error between bias parameters and clock offsets and maintains the estimated clock offsets within the station network self-consistent to each other on the basis of the precision improvement.

Yifan Wu, Qianyi Ren, Xinying Lu, Yongshan Dai, Yuan Shen
An Engineered High Performance Optically Pumped Compact Cesium Atomic Clock

As a primary frequency standard, the cesium atomic clock has a wide range of military and civilian applications. The cesium atomic clock realized by the optical pumping principle has a high atom utilization rate and has the potential to achieve higher performance. Our team focuses on the research and development of the optically pumped compact cesium atomic clock, and explores the advantages of optical pumping technology on the basis of the currently commercialized optically pumped compact cesium atomic clock. The mature cat-eye structure was used to further narrow the laser linewidth and realize the laser output with a linewidth less than 350kHz. The short-term and medium-term stability of the optically pumped compact cesium atomic clock was increased by more than 3 times to reach the level of 3.88 × 10−12τ−1/2. The high-stability constant current source realized by high-stability constant current source technology is combined with C field servo technology to make C field stability less than 1 × 10–4 level. At the same time, the mature liquid crystal phase retarder solution was used to stabilize the laser power amplitude, and the Allan deviation of the power stability test reached the level of 1 × 10–5/s. The long-term stability of the optically pumped compact cesium atomic clock was improved by improving the C field stability and laser power. Through testing, the long-term stability of the optically pumped compact cesium atomic clock has entered the level of less than 1 × 10–14/day. The frequency stability of the solution is increased 3 times higher than that of the 5071A high-performance product. Based on the technology and production of the existing commercial optically pumped compact cesium atomic clock, an engineering prototype has been realized, and now it has entered the stage of small batch trial production.

Qiang Wei, Yu-ao Li, Dong-xu Li, Zhi-bin Wang, Xing-wen Zhao
Ultra-thin Rubidium Atomic Clock

The traditional rubidium clock is the most widely used in engineering, and its height is an important factor to be considered in many applications (such as the board-card-type device). Through the design of the ultra-miniature waveguide microwave cavity and separated spectrum lamp, our team has realized a kind of ultra-thin (with a height of 17.7mm), miniaturized, and high-performance traditional rubidium atomic clock. The physical size of the rubidium atomic clock is 76mm × 76mm × 17.7mm. This atomic clock is powered by the low voltage power of + 12V, the locking time is less than 3 min, the frequency stability is better than 3 × 10−11/ $$\sqrt {\tau }$$ τ , the phase noise is better than −100dBc@10Hz, −140dBc@100Hz, −145dBc@1kHz, and −150dBc@10kHz, the frequency-temperature characteristic is better than 3 × 10−10 (under the ambient temperature range of −40°C to + 60°C), the frequency drift rate is better than 5 × 10−12/day. The product can be used in highly limited board-card-type time-frequency and synchronization devices.

Fang-fang An, Hu-jun Zhang, Peng Wang, Cheng-yong Liu, Tao Peng, Xing-wen Zhao
A Method for Establishing Elastic Time-Frequency Reference for Navigation Constellation

The time synchronization accuracy of navigation constellations determines the performance of navigation positioning and timing, while the reliability of satellite time and frequency determines the safety of system navigation positioning and timing services. In order to further improve the accuracy of navigation con-stellation time and frequency and the reliability of constellation time and frequency system operation, the article proposes the establishment and maintenance technology of navigation constellation elastic time and frequency reference, pro-vides the basic concept of navigation constellation elastic time and frequency reference establishment and maintenance technology, and describes the frame-work of navigation satellite and constellation elastic time and frequency reference composition. Starting from three aspects of the elastic combination of spaceborne time clock sources, the elastic measurement of time-frequency transmission link, and the elastic International Atomic Time algorithm, this paper focuses on the noise characteristics of the atomic clock taking into account the environmental impact, the clock difference correction model adapted to different atomic clocks, and the elastic integrated International Atomic Time algorithm. The analysis of the impact of random noise and colored noise on time frequency transmission links shows that if we want to achieve frequency signal transmission with a 10000 s stability better than 1 × 10–14, the observation noise of the link should be less than 0.05 ns, and the colored noise of the link should be less than 0.1 ns. Finally, the article conducted simulation analysis on typical scenarios of navigation satellite elastic time-frequency reference operation based on the data of the Beidou-3 satellite in orbit atomic clock. Under the working conditions of a clock group consisting of only 9 satellite hydrogen clocks, the 2-h clock deviation prediction error is less than 0.05 ns, and the 24-h clock deviation prediction error is less than 0.1 ns. As the failure rate de-creases, the error of clock deviation prediction will further decrease, effectively improving the accuracy of satellite clock deviation prediction.

Richang Dong, Jun Lu, Chengpan Tang, Yinan Meng, Chengeng Su
Research on Time Transfer Method Based on Un-Differenced Combination Model Between Stations

Time is an indispensable element in daily production and life, and accurate time information plays an irreplaceable role in basic scientific research and national defense construction. Taking advantage of GNSS measurement accuracy and wide coverage, long-distance time transfer can be performed. In view of the problems of high accuracy requirements for long-distance time transfer and the difficulty of accurately predicting satellite clock offset, we proposed a carrier phase time transfer method based on the un-differenced combination model between stations, which does not require high-precision satellite clock offset products and can complete time transfer only by using satellite orbit products. Based on the ultra-fast satellite orbit products provided by the International GNSS Service (IGS), the data from the IGS Observatory are used for time transfer experiments. The results showed that sub-nanosecond accuracy can be achieved by using this model in real-time long-distance time transfer, and the transfer accuracy and stability are better than the traditional PPP model, indicating that the model has good applicability and stability in long-distance time transfer.

Dong LV, Genyou Liu, Run Wang
An Improved Method for PPP Time Transfer with Forecast Clock Model and Performance Evaluation

In traditional PPP time transfer, the receiver clock offset is estimated as white noise (WN) and the atomic clock frequency characteristics are ignored, which is challenging to meet the needs of current high precision time-frequency users. To improve the accuracy and frequency stability of the current PPP time transfer method, a PPP time transfer based on the forecast clock (FC) model is proposed in this paper. Relevant experiments were conducted for the model and the experimental results showed that: (1) The selection of sliding window size in the FC model is recommended to be set between 0.5 and 1 h. (2) The time transfer accuracy and frequency stability of the FC model are both improved compared to the WN model. For time transfer accuracy, the FC model is more than 20% better than the WN model; For frequency stability, the FC model not only improves up to 54% compared to the WN model but also improves more than 8% overall, and the short-term and long-term stability is better than IGS final products.

Jinyang Han, Jie Zhang, Shiming Zhong, Runmin Lu, Bibo Peng
Research on PPP Time Transfer Method Based on Observable-Specific Signal Bias

Precision time transfer is an integral part of precision time systems, ensuring that multiple clocks maintain high-precision time synchronization. Currently, the GNSS carrier phase time transfer technology mainly uses PPP (Precise Point Positioning) technology, which has the advantages of global, all-weather, high precision and low cost. However, the traditional PPP time transfer technology has the problems of long initial time, low accuracy and reliability. If the ambiguity can be fixed correctly, the accuracy and reliability of PPP time transfer can be greatly improved. The key to realizing the fixed ambiguity is to effectively separate the initial phase and hardware delay deviation of the satellite end, and then restore the integer characteristics of the ambiguity. In the multi-frequency and multi-system environment, with the increase of navigation system, signal and receiver type, increasing types of signal delay deviation are generated, the rich signal resources cause various and complex problems in the combination form of deviation, and difficult to achieve a unified and convenient ambiguity fixed PPP time transfer method for phase deviation correction. This paper using a simple and uniform code/phase absolute deviation product of the observations, correcting the absolute deviation to the observations, and implementing ambiguity fixed PPP time transfer method considering the deviation correction of the observations. Experimental results show that: the time transfer accuracy of static mode is 0.02ns, and that of multi-system time is 0.017ns, the single system time transfer of dynamic mode is 0.06ns, which is superior than the traditional PPP time transfer.

Pan Du, Feng Shen, Dingjie Xu, Juan Yin, Peipei Dai, Qi Li, Yuqing Zhao
Application of Improved GPS Satellite Clock Error Prediction Model in Real-Time Precise Point Positioning

High-precision real-time GNSS precision point positioning (PPP) is based on precision satellite clock error and orbit estimation and its service. The prediction accuracy of IGS ultra-rapid orbit products has reached the requirements of real-time PPP. Thus, the estimation of high-precision satellite clock error and real-time service (RTS) are important factors restricting the application of PPP. The current IGS RTS relies on good network communication, and the clock corrections is broadcast frequently. Once communication is interrupted, the satellite clock corrections cannot be obtained, and PPP users will not be able to perform high-precision positioning. Under this concern, the manuscript considers the stable and significant periodic characteristics of satellite atomic clock, a satellite clock error prediction model combined polynomial with multi-periodic harmonic-based function is proposed, analyzing the accuracy of different order polynomial plus multi-periodic harmonic-based function to model the clock error of different arc length, and uses the model coefficients to extrapolate the satellite clock corrections, therefore, high-precision real-time satellite clock error would be recovered with broadcast ephemeris satellite clock error. The experimental results indicate that the higher the polynomial order is, the higher the modeling accuracy of clock error is. Combining with harmonic-based function can further improve the accuracy of modeling performance, and the 8-th harmonic function is better than 4-th harmonic-based function. When the communication is interrupted for several minutes, the higher-order polynomial would be limited on the clock error extrapolation accuracy. The clock error extrapolation model using low-order polynomial plus harmonic function, and 0.5 h arc length saved satellite clock corrections, the extrapolated clock corrections can meet the millimeter level static positioning accuracy and centimeter level kinematic positioning accuracy, which providing a feasible reference scheme for the user to maintain stable and high-precision positioning when communication is suddenly interrupted for several minutes, and also be meaningful for the modeling of BDS satellite clock error and its real-time clock error service.

Xiaoming Li, Haojun Li
Research on Phase/Frequency Consistent Adjusting Method for Main/Backup Signals

In order to ensure the continuity and stability of the time/frequency signal, the time-keeping system outputs signals use the way of redundant backup of the main-backup signals, and make the backup signal traceable to the main signal. The signal generation system is set up, which uses UTCr and jointed atomic time scale (TA) to adjust the main signal, and adjusts the backup signal based on the historical data. Experiments show that the time deviation of TA is between −0.68 ns and 0.52 ns. The time synchronization precision of main-backup signals is less than 0.18 ns, the phase deviation of master-backup signals switching is 0.10ns, and the frequency deviation is 1.1E-15. These results fully prove that the signal generation system can realize smooth switching.

Guitao Fu, Zhaonan Li, Baoguo Yu
Frequency Performance Evaluation of BeiDou-3 Satellite Clocks

The satellite navigation system is a positioning, navigation and timing system based on time measurement. The performance of its satellite clocks determines its service accuracy. With the BeiDou-3 satellite clock operating successfully in orbit, it is providing a stable time-frequency reference for the space segment. In this work, the frequency performance evaluation system of BeiDou-3 satellite clocks is established. Frequency accuracy is evaluated by the average frequency deviation through hourly fitting. Considering that any clock product will introduce method errors which will affect the accurate evaluation of clock performance, the Combined Overlapping Hadamard deviation (COHDEV) is proposed as the frequency stability index based on the error characteristics of different products. The evaluation results show that the frequency accuracy of the BeiDou-3 satellite clock is better than 10–11, the frequency drift of the passive hydrogen maser (PHM) is better than 10–15/day, and the stability reaches 10–15/day. In contrast, the rubidium clock has obvious frequency drift, and the long-term frequency stability is worse than that of PHMs.

Leyuan Sun, Xiangwei Chang, Wende Huang, Liwen Guo, Bo Liu, Long Guan
Engineering Optical Clocks for GNSS Timing Reference Applications

Optical clocks are atomic clocks referenced to the atomic optical band jump frequencies, which are 4–5 orders of magnitude higher than microwave clocks. For achieving the same order of magnitude clock jump linewidth measurements, optical clocks have the advantage of improved cross-order of magnitude performance compared to microwave clocks. However, optical clocks are limited by a complex system architecture, rigorous operating environment, and low operating rate, which constrains their engineering applications. For the future needs of an integrated space-time service system, optical clocks engineering and application in timekeeping can significantly improve the accuracy and long-term stability of the existing microwave timekeeping system. Optical clocks suppress the long-term time deviation of the microwave timekeeping system and enhance the autonomous timekeeping capability of the joint system. This has become a research hotspot in the field of basic research and engineering demonstration of time frequency applications in recent years. Based on different reference atomic systems, optical clocks are categorized into two categories: ion optical clocks and atomic optical lattice clocks. Globally, among the ion optical clock systems whose uncertainty and stability are at the 10–18 scale, calcium ion optical clock has a relatively simple atomic energy level structure and fewer lasers. Their wavelengths can be achieved by mature semiconductor lasers with an outstanding engineering potential. The integrated calcium ion optical clock developed by our team so far has achieved long-distance transport at the kilometer level with uncertainty up to the small factor 10–17 level, which meets the time reference accuracy requirements of GNSS (Global Navigation Satellite System) and other systems for a certain period of time in the future. This paper focuses on the further engineering progress of the calcium ion optical clock, involving the miniaturization and modularization research of core components such as ion trap and vacuum system, laser system, optical path, and control system. It can further reduce the volume, weight, and power consumption of the optical clock to 1 m3, 100 kg, and 1 kW, respectively. It improves the operational reliability and environmental adaptability. The development of the engineering optical clock is of great significance for building a more accurate and robust GNSS time reference system and supporting the construction of a more ubiquitous, convergent, and intelligent GNSS time and frequency technology and service system in the future.

Yuan Qian, Huaqing Zhang, Mengyan Zeng, Bin Wang, Yanmei Hao, Lijun Du, Jun Lu, Yuzhuo Wang, Maolei Wang, Yao Huang, Hua Guan, Jun Xie, Keling Gao
A Small High-Temperature Rubidium Frequency Standard

The rubidium frequency standard is widely used in many fields because of its small size, reliable performance, and economical application. However, the current mainstream commercial rubidium frequency standard has a working temperature range of −45 ℃ to +70 ℃, which cannot meet the long-term use requirements of high temperature environments above +70 ℃.The operating temperature of the physical package of the rubidium frequency standard is improved by changing the parameters such as the type of buffer gas, gas pressure, and type of rubidium filling in the rubidium bulb and rubidium absorption cell. The operating temperature range of the small high-temperature rubidium frequency standard is expanded to −45 ℃ ~ +80 ℃, and the volume is compressed to 100 mm × 100 mm × 25 mm. The test data shows that the frequency stability of the small high-temperature rubidium frequency standard is better than 3E-11/ $$\sqrt{\uptau }$$ τ (τ:1 s ~ 1000 s), the temperature frequency characteristic is better than 5E-9 in the range of −45 ℃ ~ +80 ℃, and it can remain locked at the ambient temperature of +85 ℃.

Yuxi Li, Shiguang Li, Tongmin Yang, Nina Ma, Zhaohua Liu, Weili Wang, Liang Wang
Accuracy Analysis of BeiDou-3/GPS Real-Time Precise Common View Time Transfer Based on Carrier-Phase

The accuracy of GNSS timing through standard service could not meet the requirements of new-generation mobile communication, distributed cooperative observation, deep space exploration, and many other fields. The performance of BeiDou-3 Navigation Satellite System (BDS-3)/GPS Precise Common View (PCV) time transfer based on carrier-phase is investigated to address this issue. Using 33-day consecutive observations of 11 stations from the tracking network of the international GNSS Monitoring and Assessment System and the International GNSS Service, long baseline PCV time transfer experiments were carried out from several aspects, including different signals, different orbit products, and real-time and post-processing. The accuracy of PCV time transfer results is evaluated by comparing them with the results produced by PPP time transfer. For the real-time PCV time transfer based on broadcast ephemeris, the accuracy of results with BDS-3 is within 0.2 ns for baselines up to 3000 km, which is better than that with GPS. In the aspect of real-time and post-processing PCV time transfer based on precise ephemeris, while it is hard to get a regular solution with GPS-only observations for baselines over 7000 km, it is still better than 0.6 ns with BDS-only observations. For baselines of 3000 km and less, GPS and BDS-3 PCV results with precise ephemeris are of comparable accuracy. Based on precise ephemeris, the accuracy of real-time PCV time transfer is close to post-processing PCV. From the experiment results, one can find that PCV time transfer is unaffected by the differential code bias at the satellite end and is immune to the day-boundary discontinuities caused by the clock products. The results show that the carrier-phase-based BeiDou-3 PCV time transfer can achieve sub-nanosecond accuracy in post-processing and real-time mode for baselines as long as 7000 km.

Hongyuan Zhou, Baoqi Sun, Lingyang Sun, Lihua Zhao, Zhe Zhang, Ge Wang, Kan Wang, Xuhai Yang

System Intelligent Operation and Autonomous Navigation

3D Small Object Detection from Cameras and Point Clouds Using Five-Head Attention in a Fusion Method

In this paper, we focus on 3D point clouds, multimodal data fusion, and attention mechanisms. Through a survey of related research on 3D object detection based on multimodal data fusion, we identified three problems: (1) the detection accuracy of small objects, such as pedestrians and bicycles, is unsatisfactory; (2) the fusion training of two different models cannot match the efficiency of single model training; and (3) when there are long-range objects in the pseudo-image generated by the features, existing methods cannot maintain the original high accuracy, and the generalization ability of the model is weak. To solve these problems and improve the detection performance of single-modal based detectors, this paper introduces a new fusion network that mainly consists of a five-head attention module and a posterior decision fusion (CPFN) module. The five-head module suppresses noise interference by jointly considering channel, spatial, point, and voxel attention, while enhancing the understanding of key information about the object. Additionally, CPFNet uses a PointPillars network with an attention mechanism for decision fusion with a CascadeR-CNN network. Experimental results on the validation set of the KITTI dataset show that our proposed method far outperforms existing methods in the small sample category, whether compared to state-of-the-art fusion-based methods or point cloud neural networks.hods or point cloud neural networks.

Haogang Mao, Jichao Jiao, Jialun Li, Yang Fuxing
Research on Autonomous Orbit Determination Based on BeiDou Navigation Satellite System Inter-Satellite Link

The BeiDou navigation satellite system (BDS) is a global navigation satellite system independently developed by China. The user's high-precision positioning relies on the precise orbit determination (POD) of the BeiDou satellites. The traditional POD mainly uses the observation data of ground monitoring stations, and the POD results are greatly affected by the global distribution of observation stations and atmospheric time delay. The autonomous POD using inter-satellite link (ISL) data can reduce the dependence of the BDS on ground station and avoid the impact of the atmosphere on observation. In this paper, batch processing method is used to process the ISL data to determine the orbit of BeiDou satellites. Epoch reduction is performed, the clock difference and the geometric range can be obtained by subtracting and summing the dual one-way ranging data. The preliminary results of autonomous BDS POD are: the root mean square of the positional deviation is about 0.50 m compared with the precise ephemeris published by iGMAS (Mean value of all satellites), the mean value of ISL residuals is 0.09 m, the mean value of the User Range Error (URE) is 0.12 m (Mean value of all satellites). Then, we studied the influences to POD precision from the initial error of the reference satellite and the changing of reference satellite respectively. The result shows that the error is proportional to the product of the orbital semimajor axes of satellites in the constellation and the initial rotation angle of the reference satellite, the precision can also be improved when the satellite with a higher initial precision is selected as the reference satellite. We also studied the POD result without EOP coefficients and the result shows that setting the EOP coefficients to zeros will not influence the precision significantly but reduce the convergence speed of iteration.

Songhua Hu, Jingshi Tang, Haihong Wang
Robust Alignment Base on IKF for SINS/DVL Integrated Navigation System

SINS is the main navigation means for AUV, which is mainly composed of SINS, DVL and acoustic transponder. Due to the advantages of strong autonomy, high accuracy and strong stabilization of velocity measurement with time, DVL can realize all-time and all-weather autonomous navigation when being integrated with SINS. In SINS/ DVL integrated autonomous navigation underwater, the measured data of DVL are easily polluted by non-Gaussian noise such as outliers. The priori information of state quantity is usually unknown and the value is also hard to estimate accuracy enough, which will lead performance of alignment to decline or even divergent. To solve the above problems, a RIKF alignment method based on Mahalanobis distance (MD) with an expansion factor weighting is proposed in this paper. The effectiveness of the proposed RIKF is verified by the data measured from the SINS/DVL on board. Initial alignment experiments are carried out by traditional KF, IKF and RIKF algorithm respectively under the conditions of DVL being polluted by outliers noise. Compared with KF and IKF, the results show that the proposed RIKF algorithm have a better performance with the measured data polluted by outliers, and RIKF algorithm is feasible and effective to be applied to the dynamic initial alignment of SINS/DVL integrated system.

Jingshu Li, Bing Zhu, Ge Tian, Zuohu Li, De Jiang, Xia Guo
Multi-UUVs Cooperative Localization in Asymmetric Large Configuration

Multi-Underwater unmanned vehicles (UUVs) can make up for the defects of a single platform with the advantages of low cost, small size and large number, achieve the extension of time-space benchmark of the global navigation satellite system, and complete large-scale underwater search and rescue, submarine resource exploration, coordinated attack and other difficult and highly complex tasks. Aiming at the problem that the former work focuses on the symmetric configuration of single slave UUV and the task requirements of multi-UUVs formation configuration, a novel multi-UUVs cooperative localization method in asymmetric large configuration is proposed. Based on the nonlinear Lie derivative theory, the relationship between the system observability and the rate of direction and distance between UUV in adjacent time is derived, and the variation rule of the UUVs cooperative localization in asymmetric configuration is demonstrated. By adjusting the cooperative communication strategy, the multi-UUVs cooperative localization method in asymmetric large configuration is established. The sound velocity profile in Nankai trough (Japan) is selected, and multi-UUVs on the underwater and surface are simulated for verification. The experimental results show that the proposed method can significantly improve the accuracy of cooperative localization by increasing the underwater baseline constraint.

Zhenqiang Du, Hongzhou Chai, Minzhi Xiang, Fan Zhang, Jun Hui, Zhaoying Wang
Research on Autonomous Detection and Recovery Technology of Satellite Clock Anomaly During the Autonomous Navigation of BDS-3 Constellation

During BDS-3’s autonomous navigation period, the on-board atomic clocks may experience frequency-hopping and phase-hopping anomalies, which cause the abnormal clock deviating from the constellation’s unified time. This paper propose an on-board clock anomaly detection and recovery algorithm for the BDS-3 constellation. The anomaly detector is implemented with an O-C value (also known as innovation) detector in Kalman filtering. The recovery algorithm reconstructs the filter starting parameters of the abnormal clock and reconnect the clock to the constellation’s autonomous time synchronization algorithm. The simulation results based on the in-orbit data of BD-3 show that the algorithm provided in this paper can achieve the phase jump anomaly detection accuracy of 3ns and frequency jump anomaly detection accuracy of 2E-11 under the condition that the false alarm probability is less than 1E-6.

Shaojun Bi, Guodong Zhang, Haihong Wang, Zhaofeng Zhong
Research on Life Prediction of Navigation Satellite Based on Bayesian Network

Navigation satellite is composed of three types of products with different failure mechanisms: random, loss and consumption. In order to solve the problems that the failure data of random product is too little and the actual internal and external structure is not considered, based on the comprehensive consideration some factors, such as product redundant backups, common-cause failure, functional backup, this paper uses Bayesian network to build the navigation satellite life prediction model based on random failure product, and present a method of predicting the remaining life of navigation satellite due to sudden failure. Combined with the life prediction results of loss and consumption failure product, the research on the navigation satellite life prediction is completed. The case shows that the accuracy and credibility of the navigation satellite life prediction can be improved by considering the redundancy backup of product, common-cause failure and functional backup.

Hongliang Cai, Ru Feng, Yinan Meng, Bo Zhou, Heng Zheng, Zongsheng Xie
Research on the Constellation Rotation Mechanism and Suppression Method of Distributed Autonomous Orbit Determination

This paper comprehensively combs the constellation rotation in autonomous navigation, summarizes and compares the rotation correction methods and their principle differences proposed by researchers, analyzes in detail the dynamic characteristics and error characteristics of long-term predicted ephemeris on the ground, and then analyzes and gives the dynamic mechanism of the rotation of distributed autonomous orbit determination constellation, A calculation method for restraining constellation rotation error is derived. Through processing, analysis and comparison of actual measured data, the following conclusions are drawn: (1) Due to the imperfection of force model, the coordinate frame represented by satellite long-term prediction ephemeris has different degrees of rotation relative to the reference frame, and the size and direction of the rotation angle are inconsistent, the maximum rotation angle is 52.62 arcsec, and the minimum rotation angle is −6.88 arcsec, There is no significant rotation consistency feature. Therefore, the long-term prediction ephemeris of any satellite is not suitable for use as a spatial reference, nor can it be independently used for the orbital plane direction constraint of the autonomous orbit determination filter product. (2) In the classical distributed autonomous orbit determination filtering algorithm, the orbital plane direction parameter prediction error in one-step orbit prediction contains two components. The constraints of inter satellite ranging on the orbital plane direction information are rank deficient, and it is impossible to establish an effective observation equation for the consistent mean part of the constellation with prediction errors. The prediction errors cannot be corrected in time and accumulated. Autonomous orbit determination shows a global rotation, which is the dynamic mechanism of the rotation of the classical distributed autonomous orbit determination constellation. (3) In this paper, a global rotation suppression method for distributed autonomous orbit determination constellation is proposed, which can significantly suppress the overall rotation angle of the constellation around the three coordinate axes of the spatial reference, reducing 1–2 orders of magnitude; It can constrain the consistency of filtering results of satellites in the three orbital planes, and eliminate the significant differences and independent grouping problems of satellites in the three orbital planes rotating around the z-axis.

Haihong Wang, Wei Zhou, Xu Zhang, Songhua Hu, Shanshi Zhou, Qiuli Chen, Jingshi Tang, Hongliang Cai, Jingang Wang, Fengyu Xia
Integrity Monitoring for GNSS/INS Integrated Navigation Based on Improved AIME

Integrity is an indispensable requirement for the application of high-precision GNSS/INS integrated navigation related to life safety. Integrated navigation is threatened by multiple risk sources in urban envirenments. The classical Autonomous Integrity Monitoring Extrapolation (AIME) algorithm is based on sliding window with fixed averaging time length. It is difficult for the algorithm to satisfy the response time and sensitivity of integrity monitoring for different types of risk sources An improved AIME algorithm based on the residual chi-square test method (RCTM) and the classical AIME method is proposed in this paper. This method combines RCTM and AIME with non-fixed averaging time to construct test statistics, which is used to adjust detection sensitivity and response time for different types of failures. Compared with the classical AIME algorithm, the proposed method can effectively detect multiple failures, improve the monitoring response time by at least 11%, and reduce the horizontal protection level by about 9.4%.

Qiwei Ye, Yu Gu, Liang Li, Fengze Du, Ruijie Li
Research on Visual Inertia SLAM Technology with Additional Point and Line Features

With the rapid development of GNSS jamming technology, GNSS is facing increasingly severe challenges. Under the condition of GNSS rejection in complex electromagnetic environment, many devices cannot accurately perceive the surrounding environment and thus cannot work normally. Therefore, exploring autonomous navigation under the condition of GNSS rejection is one of the hot topics in the future research. With the rapid development of computer vision, visual inertial odometer (VIO), which is closely coupled with camera and inertial measurement unit (IMU), can obtain high precision local pose results in unknown environments, and is widely concerned for its low cost and miniaturization. In complex and changeable structured scenes, sparse and structured features are still the bottleneck of restricting the performance of visual navigation. In this paper, LSD line segment extraction algorithm is added on the basis of visual inertial odometer to extract more line features of environmental structure, and the sliding window strategy is used to achieve state optimization. In order to verify the effectiveness of this algorithm, this paper tests the proposed method using the open data set. The test results show that the proposed method can effectively provide position and attitude estimation when GNSS refuses. In the test, the error mean value of 0.119 m, the minimum error of 0.015 m, and the maximum error of 0.259 m can be achieved. Compared with the traditional point feature VIO, the precision is improved by 50.6%, and has strong real-time and robustness.

Xiaoze Zheng, Chun Jia, Xiaohan Wang, Yang Li
An Adaptive and Robust Strategy for GPS/IMU/VO Integrated Navigation

The multi-sensor integrated navigation is critical for improving the continuity and accuracy of positioning for intelligent transport system (ITS) applications. Global Positioning System (GPS), inertial measurement unit (IMU) and visual odometry (VO) are commonly used sensors due to their complementarity. In complex urban environments, multipath interference (MI), non-line of sight (NLOS) and insufficient satellites degrade the positioning performance. Therefore, VO is required to correct the accumulated IMU errors and unreliable GPS positioning. Filter algorithms are commonly used in multi-sensor fusion. In the traditional Kalman filter, the measurement noise matrix and the fusion strategy of multi-sensors are usually fixed, which cannot adapt to the surrounding environment and the measurement quality of different sensors. To address this issue, we propose an adaptive and robust strategy for GPS/IMU/VO integrated navigation system. For the construction of the measurement vector, a dual GPS quality check method is proposed to realize adaptive switch of the filter. We also construct the robust factor weight matrix, so as to reduce the interference of gross errors on filter estimation. The field test in urban environment shows that the horizontal and 3D positioning accuracy of the proposed algorithm is 5.45 m and 5.83 m. Compared with the traditional GPS/IMU and GPS/IMU/VO fusion algorithm without adaptive and robust strategies, the 3D positioning accuracy has improvement of 69.49% and 44.64%, respectively.

Yeying Dai, Rui Sun
RGB-D SLAM Algorithm Based on Clustering and Geometric Residuals in Dynamic Environment

Most visual SLAMs, are with the assumption of static scene rigidity, without considering the adverse effects of dynamic objects in the scene, either feature point method or direct method. To solve this problem, this paper proposes a SLAM method in dynamic scenes. First, for coarse filtering and fine filtering of feature points, the scene is clustered with color information and depth information, and the image is divided into multiple cluster blocks. Then, the feature points are roughly filtered by the proportion of the feature points on each cluster block the geometric residuals of camera positions and corresponding points are calculated. Finally, dynamic feature points are obtained according to geometric residuals, and cluster blocks with large proportion or geometric residuals of dynamic feature points exceeding a certain threshold are defined as dynamic clusters, so that the feature points can be finely filtered. In this paper, experiments are carried out under the TUM RGB-D dataset. The experimental results show that the clustering time of a single image is about 0.08 s, which satisfies the real-time requirements of SLAM. At the same time, compared with ORB-SLAM2, the root mean square error of absolute trajectory error of the algorithm proposed in this paper is reduced by 10–90%. The improved method can effectively improve the estimation accuracy of camera posture in dynamic scene.

Jinjing Chen, Shuguo Pan, Wang Gao, Ji Liu, Yin Lu, Peng Zhang
Research on an Artificial Intelligence Based Diagnosis Algorithm of BDS Telemetry Anomaly

The traditional satellite telemetry data anomaly detection method based on threshold judgement and expert knowledge base has the characteristics of a wide diagnostic threshold range and large constraint by experience, and the accuracy of the detection results cannot fully meet the application requirements of high reliability of navigation satellites. Therefore, it is urgent to develop an automatic system for satellite anomaly detection. In this work, the Auto-Encoder algorithm (AE) and Prophet algorithm are applied to BDS telemetry anomaly detection and prediction for the first time, and typical satellite anomaly telemetry mode is selected for analysis and verification. The result shows that the satellite's abnormal fluctuation trend predicted by the Prophet algorithm is consistent with the actual data abnormal distribution. This algorithm can support accurate satellite anomaly detection, it can correctly predict the changing trend of satellite telemetry data and ensure the effectiveness of anomaly detection. It will be of great significance for the timely and effective diagnosis of satellite system telemetry data anomalies in the future.

Lu Wang, Lei Chen, Jian Wang, Huiyan Zhao, Bohao Cui, Yueyang Sun
Evaluation of Satellite Acceleration Determination Methods in GNSS/INS Deep Integration

Deep integration is a deep level integration of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS). One of the key steps in deep integration is to find out the motion dynamics between the receiver and satellite in line-of-sight direction and build the connection with the carrier tracking loop of the receiver. The carrier loops have high frequency of updating, while fragile to lose lock. As a result, timely and accurate satellite acceleration information is especially important in deep integration. Similar to the satellite velocity determination method, the derivative method can be applied to calculate satellite acceleration based on the second order derivative of the six orbital elements and corresponding correction terms, while the calculation formulas are relatively complex. The kinematic method and the difference method use the kinematic equations and velocity difference to solve the satellite acceleration respectively, which reduces the computation load significantly. Based solely on broadcast ephemeris, this paper implements three real-time satellite acceleration determination methods, namely derivative, kinematic, and difference method. All above methods are evaluated on calculation load, calculation accuracy, and application range with corresponding precise ephemeris as reference acceleration by Chebyshev interpolation. For the requirements of satellite acceleration determination in GNSS/INS deep integration, the method evaluation results in this paper can be used as an important reference for strategies selection under different scenarios.

Wei Gao, Xingqun Zhan, Rong Yang
Spatiotemporal Alignment and Measurement Accuracy Evaluation of New Point Cloud Devices in Autonomous Driving

Despite the increasing applications of point cloud, the measurement accuracy evaluation of point cloud devices is usually neglected, causing precision loss of missions. This paper is based on the synchronization and extrinsic calibration of different modalities of sensors, obtaining spatiotemporal alignment accuracy using the cumulative distribution function, and the measurement model for integrity monitoring. After spatial alignment, we proposed the static and dynamic measurement accuracy evaluation approaches. The static accuracy evaluation is based on standstill landmarks and sensors, using the ground truth obtained by integrated navigation to acquire measurements error. The dynamic accuracy evaluation requires the sensor moving with a trajectory, and establishing the surroundings’ map using SLAM process as the ground truth, then the sensor measurement error could be evaluated. Experiments of new point cloud devices such as high-resolution solid-state LiDAR and low resolution 4D radar demonstrate the effectiveness of our method.

Jiahui Liu, Xin Zhang, Xingqun Zhan
Calibration Method for LiDAR Cameras in Natural Dynamic Environments

The external calibration of sensors has a crucial impact on the accuracy of subsequent integrated navigation. In this paper, an automatic calibration method for a lidar/RGB camera system is proposed under dynamic environmental disturbances without any target present. The theoretical analysis focuses on the characteristics and limitations of edge features, as well as their influence on calibration accuracy. In terms of implementation, the measurement principles of the lidar and camera are analyzed. A projection-based method for dynamic point rejection of the lidar is proposed, and the external calibration of the sensor is achieved using a Bundle Adjustment optimization method based on the edge extraction results of point clouds and images. Since edge features are abundant in natural scenes, the proposed method is evaluated in an indoor scene with dynamic environmental disturbances. The results demonstrate that the proposed method has higher robustness and accuracy than conventional algorithms, achieving good calibration results in the presence of dynamic environmental disturbances.

Sheng Hong, Qinghua Zeng, Yineng Li, Xiaorong Sun, Jizhou Lai
Pedestrian Navigation Algorithm Based on EKF Combined with ZUPT + ZARU + Attitude Self-observation

In order to solve the problem of low positioning accuracy due to the influence of accumulated IMU errors in inertial pedestrian navigation, this paper proposes an EKF-based nonlinear error filtering combined with ZUPT/ZARU/Attitude self-observation positioning method. Firstly, in order to reduce the false rate of determining zero-speed state, a multi-conditional zero velocity detection determination method is proposed. Secondly, to solve the problem of incomplete error correction due to the small dimensionality of the error state vector value observations, the ZUPT/ZARU/Attitude self-observation is introduced to expand the dimensionality of the observations. The core of the attitude angle self-observation is giving a definition of a special attitude angle observation. The attitude angle self-observation mainly takes the pitch and roll angles obtained from the gravity component, the solved values of heading angles to the frame, and the heading angles obtained from the magnetometer as the source of the actual observed attitude angles, and then takes the difference of the currently solved attitude angles and the observed values as the observed error state value The method has solved the problem of large error in the positioning solution due to the relatively small number of error observation dimensions in ZUPT, ZUPT/ZARU and other correction schemes. The positioning error results of this method, single ZUPT and ZUPT/ZARU are compared and analyzed after pedestrian inertial guidance positioning experiments. The experimental analysis shows that this method has a good improvement in positioning accuracy compared with the single ZUPT algorithm and ZUPT/ZARU algorithm.

Chen Zhu, Hang Guo, Jian Xiong, Yujie Wang
China Satellite Navigation Conference (CSNC 2024) Proceedings
Changfeng Yang
Jun Xie
Copyright Year
Springer Nature Singapore
Electronic ISBN
Print ISBN