Time synchronization of new-generation BDS satellites using inter-satellite link measurements

Autonomous satellite navigation is based on the ability of a Global Navigation Satellite System (GNSS), such as Beidou, to estimate orbits and clock parameters onboard satellites using Inter-Satellite Link (ISL) measurements instead of tracking data from a ground monitoring network. This paper focuses on the time synchronization of new-generation Beidou Navigation Satellite System (BDS) satellites equipped with an ISL payload. Two modes of Ka-band ISL measurements, Time Division Multiple Access (TDMA) mode and the continuous link mode, were used onboard these BDS satellites. Using a mathematical formulation for each measurement mode along with a derivation of the satellite clock offsets, geometric ranges from the dual one-way measurements were introduced. Then, pseudoranges and clock offsets were evaluated for the new-generation BDS satellites. The evaluation shows that the ranging accuracies of TDMA ISL and the continuous link are approximately 4?cm and 1?cm (root mean square, RMS), respectively. Both lead to ISL clock offset residuals of less than 0.3?ns (RMS). For further validation, time synchronization between these satellites to a ground control station keeping the systematic time in BDT was conducted using L-band Two-way Satellite Time Frequency Transfer (TWSTFT). System errors in the ISL measurements were calibrated by comparing the derived clock offsets with the TWSTFT. The standard deviations of the estimated ISL system errors are less than 0.3?ns, and the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. For the regional BDS network, the addition of ISL measurements for medium orbit (MEO) BDS satellites increased the clock tracking coverage by more than 40% for each orbital revolution. As a result, the clock predicting error for the satellite M1S was improved from 3.59 to 0.86?ns (RMS), and the predicting error of the satellite M2S was improved from 1.94 to 0.57?ns (RMS), which is a significant improvement by a factor of 3–4.     

Design and experiment of onboard laser time transfer in Chinese Beidou navigation satellites

High-precision time synchronization between satellites and ground stations plays the vital role in satellite navigation system. Laser time transfer (LTT) technology is widely recognized as the highest accuracy way to achieve time synchronization derived from satellite laser ranging (SLR) technology. Onboard LTT payload has been designed and developed by Shanghai Astronomical Observatory, and successfully applied to Chinese Beidou navigation satellites. By using the SLR system, with strictly controlling laser firing time and developing LTT data processing system on ground, the high precise onboard laser time transfer experiment has been first performed for satellite navigation system in the world. The clock difference and relative frequency difference between the ground hydrogen maser and space rubidium clocks have been obtained, with the precision of approximately 300 ps and relative frequency stability of 10E−14. This article describes the development of onboard LTT payload, introduces the principle, system composition, applications and LTT measuring results for Chinese satellite navigation system.     

Early analysis of precise orbit and clock offset determination for the satellites of the global BeiDou-3 system

Eight new-generation BeiDou satellites (BeiDou-3) have been launched into Medium Earth Orbit (MEO), allowing for global coverage since March 2018, and they are equipped with new hydrogen atomic clocks and updated rubidium clocks. Firstly, we analyzed the signals for the carrier-to-noise-density ratio (C/N0) and pseudorange multipath (MP) by using international GNSS (Global Navigation Satellite System) Monitoring and Assessment System (iGMAS) station data, and found that B1C has a lower C/N0, and B2a has the same level of C/N0 as the B1I and B3I signals. For pseudorange multipath, compared with the BeiDou-2 satellites, the obvious systematic variation of MP scatters related to the elevation angle is greatly improved for the BeiDou-3 and BeiDou-3e satellites signals. For the signals of the BeiDou-3 satellites, the order of the Root Mean Square (RMS) values of multipath and noise is B3I?<?B1I?<?B2a?<?B1C. Then, the comparison of the precise orbit determination and clock offset determination for the BeiDou-2, BeiDou-3, and BeiDou-3 experimental (BeiDou-3e) satellites was done by using 10 stations from iGMAS. The 3D precision of the 24?h orbit overlap is 24.55, 25.61, and 23.35?cm for the BeiDou-3, BeiDou-3e, and BeiDou-2 satellites, respectively. BeiDou-3 satellite has a comparable precision to that of the BeiDou-2 satellite. For the precision of clock offset estimation, the Standard Deviation (STD) of the BeiDou-3 MEO satellite is 0.350?ns, which is an improvement of 0.042?ns over that of the BeiDou-2 MEO satellite. The stabilities of the BeiDou-3 and BeiDou-3e onboard clocks are better than those of BeiDou-2 by factors of 2.84 and 1.61 at an averaging time of 1000 and 10,000?s, respectively.     

Switching and performance variations of on-orbit BDS satellite clocks

The information of the satellite clock switching and performance variations on-orbit of Chinese BeiDou-2 Navigation System (BDS) is not available for the public. In order to detect the BDS satellite clock switching and performances variation, we analyzed the precise clock offset products with a total duration of 5?years every BDS satellite equipped four atomic clocks from four different manufactures from January 2013 to October 2017. Three important contributions are concluded as follows. (1) It is found that the average time of on-orbit operation for BDS satellite clocks is about 1–2?years. There have been 22 times of clock switching for BDS satellites, of which the C05 and C08 satellites have been switched to the fourth (last) atomic clock. (2) There are frequent phase adjustments for BDS on-orbit satellite clocks, and the frequency series is relatively stable. Furthermore, there are semi-annual sinusoid cycles in the frequency drift series of C06 and C09 satellites. (3) The performances of MEO satellite clocks perform better than the IGSO and GEO satellite clocks. The average ten-thousand frequency stability of BDS satellite clocks is about 1E-13, which is worse than that of GPS and Galileo but better than that of GLONASS.     

Quality variation of GPS satellite clocks on-orbit using IGS clock products

Over 60% clocks on board of the GPS satellites are working longer than their designed life. Therefore realizing their stabilities in a long time scales is essential to GPS navigation and positioning plus IGS time scale maintaining. IGS clock products from 2001 to 2010 are used to analyze the GPS satellite clock qualities such as frequency stabilities and clock noise level. We find out that for the clocks of Block IIA satellites the frequency stabilities and clock noise are 10 times worse than that of the Block IIR and IIR-M satellites. Moreover, the linear relationships between frequency stabilities and clock residuals have been deduced with an accuracy of better than 0.02 ns. Specially, it is noticed that the clock of the PRN27 is instable and the relationship between the frequency stability and residuals is at least a quadratic curve. Therefore, we suggested that GPS satellite clocks should be weighted by their quality levels in application, and the observations of the Block IIA should not be used for real-time positioning which required precision better than one meter.     

Analysis of GNSS clock prediction performance with different interrupt intervals and application to real-time kinematic precise point positioning

Continuous and timely real-time satellite orbit and clock products are mandatory for real-time precise point positioning (RT-PPP). Real-time high-precision satellite orbit and clock products should be predicted within a short time in case of communication delay or connection breakdown in practical applications. For prediction, historical data describing the characteristics of the real-time orbit and clock can be used as the basis for performing the prediction. When historical data are scarce, it is difficult for many existing models to perform precise predictions. In this paper, a linear regression model is used to predict clock products. Seven-day GeoForschungsZentrum (GFZ) final clock products sampled at 30 s are used to analyze the characteristics of GNSS clocks. It is shown that the linear regression model can be used as the prediction model for the satellite clock products. In addition, the accuracy of the clock prediction for different satellites are analyzed using historical data with different periods (such as 2 and 10 epochs). Experimental results show that the accuracy of the clock with the linear regression prediction model using historical data with 10 epochs is 1.0 ns within 900 s. This is higher accuracy than that achieved using historical data of 2 epochs. Finally, the performance analysis for real-time kinematic precise point positioning (PPP) is provided using GFZ final clock prediction results and state space representation (SSR) clock prediction results when communication delay or connection breakdown occur. Experimental results show that the positioning accuracy without prediction is better than that with prediction in general, whether using the final clock product or the SSR clock product. For the final clock product, the positioning accuracy in the north (N), east (E), and up (U) directions is better than 10.0 cm with all visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 15.0 cm to 7.0 cm. For the SSR clock product, the positioning accuracy of N, E, and U directions is better than 12.0 cm with visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 12.0 cm to 9.0 cm.     

基于GNSS的高轨卫星定位技术研究

利用全球卫星导航系统(GNSS)进行导航定位具有全球、全天候、实时和高精度的优点,应用于高地球轨道(HEO)卫星的定位,能够提供精确的轨道和姿态确定,并且可以克服目前主要利用地面测控系统对HEO卫星进行定位的设备复杂、投资高等缺点,使得自主导航成为可能.本文对利用GNSS的高轨卫星定位相关技术进行了研究,分析了单一GNSS系统和多个GNSS组合系统的卫星可见性、动态性和几何精度因子(GDOP).通过仿真分析表明,利用组合GNSS系统并通过提高GNSS接收机灵敏度的方法,可以解决GNSS进行HEO卫星定位的相关问题,并能保证HEO卫星定位精度的要求.      

Low-cost precise measurement of oscillator frequency instability based on GNSS carrier observation

Global navigation satellite systems (GNSS) receivers can be used in time and frequency metrology by exploiting stable GNSS time scales. This paper proposes a low-cost method for precise measurement of oscillator frequency instability using a single-frequency software GNSS receiver. The only required hardware is a common radio frequency (RF) data collection device driven by the oscillator under test (OUT). The receiver solves the oscillator frequency error in high time resolution using the carrier Doppler observation and the broadcast ephemeris from one of the available satellites employing the onboard reference atomic frequency standard that is more stable than the OUT. Considering the non-stable and non-Gaussian properties of the frequency error measurement, an unbiased finite impulse response (FIR) filter is employed to obtain robust estimation and filter out measurement noise. The effects of different filter orders and convolution lengths are further discussed. The frequency error of an oven controlled oscillator (OCXO) is measured using live Beidou-2/Compass signals. The results are compared with the synchronous measurement using a specialized phase comparator with the standard coordinated universal time (UTC) signal from the master clock H226 in the national time service center (NTSC) of China as its reference. The Allan deviation (ADEV) estimates using the two methods have a 99.9% correlation coefficient and a 0.6% mean relative difference over 1–1000 s intervals. The experiment demonstrates the effectiveness and high precision of the software receiver method.     

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

The GLONASS-M satellite yaw-attitude model

The proper modeling of the satellites’ yaw-attitude is a prerequisite for high-precision Global Navigation Satellite System (GNSS) positioning and poses a particular challenge during periods when the satellite orbital planes are partially eclipsed. Whereas a lot of effort has been put in to examine the yaw-attitude control of GPS satellites that are in eclipsing orbits, hardly anything is known about the yaw-attitude behavior of eclipsing GLONASS-M satellites. However, systematic variations of the carrier phase observation residuals in the vicinity of the orbit’s noon and midnight points of up to ±27 cm indicate significant attitude-related modeling issues. In order to explore the GLONASS-M attitude laws during eclipse seasons, we have studied the evolution of the horizontal satellite antenna offset estimates during orbit noon and orbit midnight using a technique that we refer to as “reverse kinematic precise point positioning”. In this approach, we keep all relevant global geodetic parameters fixed and estimate the satellite clock and antenna phase center positions epoch-by-epoch using 30-second observation and clock data from a global multi-GNSS ground station network. The estimated horizontal antenna phase center offsets implicitly provide the spacecraft’s yaw-attitude. The insights gained from studying the yaw angle behavior have led to the development of the very first yaw-attitude model for eclipsing GLONASS-M satellites. The derived yaw-attitude model proves to be much better than the nominal yaw-attitude model commonly being used by today’s GLONASS-capable GNSS software packages as it reduces the observation residuals of eclipsing satellites down to the normal level of non-eclipsing satellites and thereby prevents a multitude of measurements from being incorrectly identified as outliers. It facilitates continuous satellite clock estimation during eclipse and improves in particular the results of kinematic precise point positioning of ground-based receivers.     

GNSS receiver clock modeling when using high-precision oscillators and its impact on PPP

Processing data from Global Navigation Satellite Systems (GNSS) always requires time synchronization between transmitter and receiver clocks. Due to the limited stability of the receiver’s internal oscillator, the offset of the receiver clock with respect to the system time has to be estimated for every observation epoch or eliminated by processing differences between simultaneous observations. If, in contrast, the internal oscillator of the receiver is replaced by a stable atomic clock one can try to model the receiver clock offset, instead of estimating it on an epoch-by-epoch basis. In view of the progress made in the field of high-precision frequency standards we will investigate the technical requirements for GNSS receiver clock modeling at the carrier phase level and analyze its impact on the precision of the position estimates.     

Carrier phase prediction method for GNSS precise positioning in challenging environment

Since the signals of global navigation satellite system (GNSS) are blocked frequently in challenging environments, the discontinuous carrier phases seriously affect the application of GNSS precise positioning. To improve the carrier phase continuity, this paper proposes a carrier phase prediction method based on carrier open-loop tracking. In the open-loop tracking mode, the carrier numerically controlled oscillator (NCO) is controlled by the predicted Doppler, but not by the loop filter output. To improve the phase prediction effective time, accurate receiver clock drift estimation is studied in the prediction method. The phase prediction performance is tested on GNSS software receiver. In the phase prediction effective time tests, open-loop processes were set for the tested channel. The test results show that, when some satellite signals are blocked in 15?s, the probability of carrier phase error less than quarter cycles is more than 94%. In the real time kinematic (RTK) positioning tests, some satellite signals are blocked in 10–15?s repeatedly. The test results show that, the carrier phase continuity is basically not affected by the signal interruption, and the RTK can almost keep continuous centimeter-level positioning accuracy without re-fixing the integer ambiguity.     

Inter-satellite links for satellite autonomous integrity monitoring

A new integrity monitoring mechanisms to be implemented on-board on a GNSS taking advantage of inter-satellite links has been introduced. This is based on accurate range and Doppler measurements not affected neither by atmospheric delays nor ground local degradation (multipath and interference). By a linear combination of the Inter-Satellite Links Observables, appropriate observables for both satellite orbits and clock monitoring are obtained and by the proposed algorithms it is possible to reduce the time-to-alarm and the probability of undetected satellite anomalies.     

北斗卫星导航系统实时定轨与钟差处理策略

目前鲜有对北斗卫星导航系统（BeiDouNavigationSatelliteSystem,BDS）实时精密定轨与钟差确定的研究,文章提出了BDS实时轨道与实时钟差处理策略,包括了观测与动力学模型、实时轨道与实时钟差处理流程与评估方法。尤其对于实时钟差,为了提高计算效率,联合使用两个独立并行的线程估计非差绝对钟差和历元间相对钟差。利用多模全球卫星导航系统试验(MGEX)与全球连续检测评估系统（iGMAS）实测数据进行了北斗实时轨道与钟差解算,BDS实时轨道径向平均精度对于GEO卫星优于20cm,对于IGSO与MEO一般优于10cm;钟差精度对于GEO卫星为0.5~4.5ns,对于IGSO／MEO为0.2~2.0ns。基于目前的轨道与钟差结果,实时精密单点定位（PrecisePointPositioning,PPP）结果可以达到分米量级。     

基于帝国竞争优化的双目标综合决策选星算法

全球卫星导航系统（GNSS）的应用前景已经得到世界各国的普遍承认，其应用领域也趋于多样化，在此背景下，卫星接收机也要求其具有更快的解算速度和可靠的精度。针对目前多数接收机的选星算法都是固定选星数目从而限制算法机动性的问题，提出基于帝国竞争优化算法（ICA）的双目标综合决策选星算法。为了更好获取几何构型较好的卫星星座，引入可见卫星的卫星仰角和方向角先验信息，进行先验性约束，通过构建几何精度因子（GDOP）以及选星数目2个目标，进行综合决策的快速选星，提高了选星的灵活度，并且在满足用户精度的要求下减轻了多星座卫星接收机的计算负担。通过仿真实验和实测数据对双目标综合决策选星算法验证的结果表明:所提算法在高度截止角5°下引入先验性约束条件后平均选星数目在仿真数据和实测数据中缩减率分别为51.8%和45.4%，平均GDOP值较无约束下分别减少0.209 2和0.248 4。同时，所提算法单次选星平均耗时分别为0.168 4 s和0.303 1 s，与遍历法的选星耗时4 s相比，提高了95.79%和92.42%。      

A new stochastic model considering satellite clock interpolation errors in precise point positioning

Precise clock products are typically interpolated based on the sampling interval of the observational data when they are used for in precise point positioning. However, due to the occurrence of white noise in atomic clocks, a residual component of such noise will inevitable reside within the observations when clock errors are interpolated, and such noise will affect the resolution of the positioning results. In this paper, which is based on a twenty-one-week analysis of the atomic clock noise characteristics of numerous satellites, a new stochastic observation model that considers satellite clock interpolation errors is proposed. First, the systematic error of each satellite in the IGR clock product was extracted using a wavelet de-noising method to obtain the empirical characteristics of atomic clock noise within each clock product. Then, based on those empirical characteristics, a stochastic observation model was structured that considered the satellite clock interpolation errors. Subsequently, the IGR and IGS clock products at different time intervals were used for experimental validation. A verification using 179 stations worldwide from the IGS showed that, compared with the conventional model, the convergence times using the stochastic model proposed in this study were respectively shortened by 4.8% and 4.0% when the IGR and IGS 300-s-interval clock products were used and by 19.1% and 19.4% when the 900-s-interval clock products were used. Furthermore, the disturbances during the initial phase of the calculation were also effectively improved.     

Performance improvement of real-time PPP ambiguity resolution using a regional integer clock

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.     

基于实时SSR数据的LEO卫星精密单点定位研究

对目前低轨卫星实时定位的方法进行了研究,现在通常采用GPS定位,使用广播星历和普通晶振,实时定位精度一般在10m以内,不能满足高精度实时定位的需求。IGS组织在全球范围内对GPS跟踪分析,生成精密星历、精密钟差产品、按SSR格式的广播星历和钟差修正产品并在网上发布。对这些IGS产品进行了调查,提出在现有测控支持情况下,可以通过高密度上注SSR信息流实现在轨高精度定位。以某型号低轨微小卫星在轨导航增强载荷为应用背景,用IGS03产品中的1057和1058数据对双频GPS接收机的星历和钟差进行修正,采用递推最小二乘估计和LAMDA模糊度固定过对载波相位和伪距信息进行处理,在短时间内获得亚米级定位结果。     

The impact of orbital errors on the estimation of satellite clock errors and PPP

Precise satellite orbit and clocks are essential for providing high accuracy real-time PPP (Precise Point Positioning) service. However, by treating the predicted orbits as fixed, the orbital errors may be partially assimilated by the estimated satellite clock and hence impact the positioning solutions. This paper presents the impact analysis of errors in radial and tangential orbital components on the estimation of satellite clocks and PPP through theoretical study and experimental evaluation. The relationship between the compensation of the orbital errors by the satellite clocks and the satellite-station geometry is discussed in details. Based on the satellite clocks estimated with regional station networks of different sizes (∼100, ∼300, ∼500 and ∼700 km in radius), results indicated that the orbital errors compensated by the satellite clock estimates reduce as the size of the network increases. An interesting regional PPP mode based on the broadcast ephemeris and the corresponding estimated satellite clocks is proposed and evaluated through the numerical study. The impact of orbital errors in the broadcast ephemeris has shown to be negligible for PPP users in a regional network of a radius of ∼300 km, with positioning RMS of about 1.4, 1.4 and 3.7 cm for east, north and up component in the post-mission kinematic mode, comparable with 1.3, 1.3 and 3.6 cm using the precise orbits and the corresponding estimated clocks. Compared with the DGPS and RTK positioning, only the estimated satellite clocks are needed to be disseminated to PPP users for this approach. It can significantly alleviate the communication burdens and therefore can be beneficial to the real time applications.     

Time Transfer by Laser Link: Data analysis and validation to the ps level

The Time Transfer by Laser Link (T2L2) is a very high resolution time transfer technique based on the recording of arrival times of laser pulses at the satellite. T2L2 was designed to achieve time stability in the range of 1 ps over 1000 s and an accuracy better than 100 ps. The project is in operation onboard the Jason-2 satellite since June 2008. The principle is based on the Satellite Laser Ranging (SLR) technology; it uses the input of 20–25 SLR stations of the international laser network which participate in the tracking. This paper focuses on the data reduction process which was developed specifically to transform the raw information given by both space instrument and ground network: first to identify the triplets (ground and onboard epochs and time of flight of the laser pulse), second to estimate a usable product in terms of ground-to-space time transfer (including instrumental corrections), and thirdly to produce synchronization between any pair of remote ground clocks. In describing the validation of time synchronizations, the paper opens a way for monitoring the time difference between ultra-stable clocks thanks to a laser link at a few ps level for Common View passes. It highlights however that without accurately characterizing the onboard oscillator of Jason-2 and knowing the unavailability of time calibrations of SLR stations generally, time transfer over intercontinental distances remain difficult to be accurately estimated.