Initial results of precise orbit and clock determination for COMPASS navigation satellite system

The development of the COMPASS satellite system is introduced, and the regional tracking network and data availability are described. The precise orbit determination strategy of COMPASS satellites is presented. Data of June 2012 are processed. The obtained orbits are evaluated by analysis of post-fit residuals, orbit overlap comparison and SLR (satellite laser ranging) validation. The RMS (root mean square) values of post-fit residuals for one month’s data are smaller than 2.0 cm for ionosphere-free phase measurements and 2.6 m for ionosphere-free code observations. The 48-h orbit overlap comparison shows that the RMS values of differences in the radial component are much smaller than 10 cm and those of the cross-track component are smaller than 20 cm. The SLR validation shows that the overall RMS of observed minus computed residuals is 68.5 cm for G01 and 10.8 cm for I03. The static and kinematic PPP solutions are produced to further evaluate the accuracy of COMPASS orbit and clock products. The static daily COMPASS PPP solutions achieve an accuracy of better than 1 cm in horizontal and 3 cm in vertical. The accuracy of the COMPASS kinematic PPP solutions is within 1–2 cm in the horizontal and 4–7 cm in the vertical. In addition, we find that the COMPASS kinematic solutions are generally better than the GPS ones for the selected location. Furthermore, the COMPASS/GPS combinations significantly improve the accuracy of GPS only PPP solutions. The RMS values are basically smaller than 1 cm in the horizontal components and 3–4 cm in the vertical component.     

Performance of GPS and GPS/SINS navigation in the CE-5T1 skip re-entry mission

A CE-5T1 spacecraft completed a high-speed skip re-entry to the earth after a circumlunar flight on October 31, 2014. In addition to the strapdown inertial navigation system (SINS), a lightweight GPS receiver with rapid acquisition was developed as a navigation sensor in the re-entry capsule. The GPS receiver effectively solved the poor accuracy problem of long-term navigation using only the SINS. In contrast to ground users and low-earth-orbit spacecraft, numerous factors, including high altitude and kinetic characteristics in high-speed skip re-entry, are important for GPS positioning feasibility and were presented in accordance with the flight data. GPS solutions started at nearly 4900 km orbital altitude during the phases of re-entry process. These solutions were combined by an inertial measurement unit in a loosely coupled integrated navigation method and SINS navigation initialization. A simplified GPS/SINS navigation filter for limited resources was effectively developed and implemented on board for spacecraft application. Flight data estimation analyses, including trajectory, attitude, position distribution of GPS satellite, and navigation accuracy, were presented. The estimated accuracy of position was better than 42 m, and the accuracy of velocity was better than 0.1 m/s.     

北斗系统在南极中山站地区的基本定位性能评估

对北斗区域卫星导航系统（BDS）正式运行后在南极中山站地区的基本导航定位性能进行了评估,包括卫星可用性、位置精度因子（PDOP）、伪距观测值质量、电离层模型精度及单频伪距导航定位性能等方面。对南极中山站地区实测数据分析的结果表明,首先,北斗卫星导航系统的可用性与伪距观测值质量在总体上与GPS处于同一水平,并已初步具备了全天导航定位的能力,但存在卫星分布不够均匀、GEO卫星高度角较低、电离层模型精度较差等问题。其次,北斗单频伪距单点定位北、东方向的精度分别优于22 m和9 m,高程方向优于25 m;超短基线的单频伪距差分定位在北、东、高程三个方向的精度分别为3.6 m、2.3 m和3.3 m;总体而言与GPS相比有一定差距。最后,北斗/GPS组合定位相对于单一的GPS定位不仅增加了系统的可靠性,还对定位的精度有明显改善,对于单频伪距单点定位、伪距差分定位的三维点位精度可分别提高10%、22%。     

Evaluation of COMPASS ionospheric grid

As an important component of the augmentation service, the ionospheric grid contributes to improving single-frequency positioning accuracy. The ionospheric delay corrections are broadcast as vertical delay estimates at specified ionospheric grid points (IGPs) for most satellite-based augmentation system, where the IGPs are predefined with a resolution of 5° and 5° in latitude and longitude. Different from the general strategy, the COMPASS IGPs are predefined with a resolution of 2.5° and 5° in latitude and longitude. The need for this special IGPs distribution is investigated with experiments using real data. The performance of the COMPASS ionospheric grid is analyzed in terms of accuracy and availability. Comparing the performance of the special IGPs distribution with that of 5° × 5° IGPs, the results show that the ionospheric correction improves by 0.2 m and the 3D positioning accuracy improves by 1 m in middle-low latitude regions. The RMS of the COMPASS grid ionospheric correction accuracy is better than 0.5 m in most regions of the China mainland, and the availability is better than 95 % except in the northeast, northwest and outside China. In addition, we investigated the performance of the method that combined the inverse distance weighted and spherical harmonics grid modeling algorithm. Simulations show that the new method clearly improves grid availability. The mean availability in the mainland is better than 99 %.     

SBAS orbit and satellite clock corrections for precise point positioning

The quality of real-time GPS positions based on the method of precise point positioning (PPP) heavily depends on the availability and accuracy of GPS satellite orbits and satellite clock corrections. Satellite-based augmentation systems (SBAS) provide such corrections but they are actually intended to be used for wide area differential GPS with positioning results on the 1-m accuracy level. Nevertheless, carrier phase-based PPP is able to achieve much more accurate results with the same correction values. We applied SBAS corrections for dual-frequency PPP and compared the results with PPP obtained using other real-time correction data streams, for example, the GPS broadcast message and precise corrections from the French Centre National d’Etudes Spatiales and the German Deutsches Zentrum für Luft- und Raumfahrt. Among the three existing SBAS, the best results were achieved for the North American wide area augmentation system (WAAS): horizontal and vertical position accuracies were considerably smaller than 10 cm for static 24-h observation data sets and smaller than 30 cm for epoch-by-epoch solutions with 2 h of continuous observations. The European geostationary navigation overlay service and the Japanese multi-functional satellite augmentation system yield positioning results with biases of several tens of centimeters and variations larger by factors of 2–4 as compared to WAAS.     

星载GPS 伪距观测量重建及定轨精度分析

讨论了如何从星上下传的卫星位置数据中重建星载GPS 伪距观测量, 分析了重建伪距数据事后动力学 定轨精度及该方法对提高LEO 卫星位置精度的贡献。GRACE-A 卫星2008 年3 月1 日—14 日实测数据计算结果表明: 重建数据事后动力学定轨能显著提高地面主控站接收到的LEO 卫星实时位置精度; 其中由C/A 码伪距和广播星历 实时单点定位得到的卫星位置精度约为15m, 重建伪距事后动力学定轨得到的卫星位置精度约为2m。     

A new coarse-time GPS positioning algorithm using combined Doppler and code-phase measurements

A new coarse-time Global Positioning System (GPS) positioning algorithm based on the use of Doppler and code-phase measurements is proposed and described. The proposed method was demonstrated to be essential for reducing the time to first fix and the power consumption in a GPS receiver. Only 1 ms of data is required to obtain a positioning fix with accuracy comparable to that of the traditional GPS navigation algorithm. The algorithm is divided into two parts. In the first part, the Doppler measurement of the GPS signal is used to determine the coarse user position. With proper constraints, the required time accuracy for the Doppler measurements can be relaxed to be as long as 12 h. In the second part of the algorithm, the accurate user position is calculated by means of the 1 ms code-phase data. The traditional tracking process is no longer necessary in the proposed algorithm. Using the acquired 1-ms code-phase measurement, the positioning accuracy was determined to be approximately a few tens of meters in our experimental results. However, if the data length is extended to 10 ms, the positioning accuracy can be improved to within 10–20 m, which is similar to that of the traditional GPS positioning method. Various experiments were conducted to verify the usefulness of the proposed algorithm.     

TJS-2 geostationary satellite orbit determination using onboard GPS measurements

This study analyzes the quality of onboard data of tracking signals from GPS satellites on the far side of the earth and determines the orbit of the geostationary satellite using code and carrier phase observations with 30-h and 3-day orbit arc length. According to the analysis results, the onboard receiver can track 6–8 GPS satellites, and the minimum and maximum carrier to noise spectral densities were 24 and 45 dB-Hz, respectively. For a GPS receiver on a high-altitude platform above the navigation constellations, the blocking of the earth and a weak signal strength usually cause a piece-wise GPS signal tracking and an increase in the number of ambiguity parameters. Individual GPS satellites may be continuously tracked for as little as several minutes and as long as 3 h. Moreover, considering the negative sign of elevation angles reflects the fact that GPS satellites are tracked below the receiver in the study. GPS satellites appear mainly in the elevation angle range of ??53° to ??83°, and dilution of precision values could reach ten or one hundred and more. Also, it is observed that when a signal suffers from atmospheric refraction, other GPS signals tracked simultaneously by the receiver experience strong systematic errors in the code observations. Based on single-frequency code and carrier phase measurements, the mean 3D root mean square (RMS) value of the overlap comparisons between 30-h orbit determination arcs is 2.14 m. However, we found that there were also some biases in the carrier phase residuals, which contributed to poor orbit accuracy. To eliminate the effects of the biases, we established a correction sequence for each GPS satellite. After corrections, the mean 3D RMS was reduced to 0.99 m, representing a 53% improvement.     

New jump trajectory determination method using low-cost MEMS sensor fusion and augmented observations for GPS/INS integration

Objective information on athletic maneuvers for performance evaluation has become highly desired in sports such as skiing, snowboarding, and mountain biking. Body-mounted devices, incorporating low-cost microelectromechanical, inertial navigation units, and global positioning system (GPS) receivers, to calculate sport-specific key performance variables (KPVs) and provide real-time feedback, are now commercially available. However, algorithms implemented for such purposes still lack accuracy and power efficiency. A new GPS/INS (inertial navigation system) integration algorithm is proposed to determine the trajectory of an athlete executing jumps while skiing, snowboarding, mountain biking etc. KPVs, such as jump horizontal distance, vertical height, and drop, are calculated from the trajectory. A new sensor error compensation scheme is developed using sensor fusion and linear Kalman filters (LKF). The LKF parameters are varied to address the fluctuating dynamics of the athlete during a jump. The extended Kalman filter used for GPS/INS integration has an observation vector augmented with sensor error measurements derived from sensor fusion. The performance of the proposed algorithm is evaluated through experimental field tests. For the determination of jump horizontal distance, height, and drop, the proposed algorithm has errors of 14.3 cm (5.5 %), 1.6 cm (38 %), and 6.7 cm (9.4 %), respectively. Errors in KPVs for a set of jumps were first determined with respect to the true KPVs, and then the errors for all the jumps were averaged to calculate the absolute and percentage errors. The accuracy achieved is deemed to fulfill the expectations of both recreational and professional athletes.     

Multi-GNSS precise point positioning (MGPPP) using raw observations

A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays.     

COMPASS与GPS兼容定位算法及性能分析

多卫星导航系统间实现互用是提高导航定位性能的重要途径,目前已成为全球卫星导航领域关注的热点和发展方向。我国正在建设新一代卫星导航系统,为保护国家利益,获得世界认同与支持,COMPASS必须走与其他导航系统的兼容之路。本文分析了我国新一代卫星导航系统与GPS系统兼容定位算法和性能,并利用实测数据计算得到了COMPASS-M1与GPS兼容定位结果,验证了COMPASS与GPS兼容定位的可能性。     

Real-time kinematic positioning of LEO satellites using a single-frequency GPS receiver

Due to their low cost and low power consumption, single-frequency GPS receivers are considered suitable for low-cost space applications such as small satellite missions. Recently, requirements have emerged for real-time accurate orbit determination at sub-meter level in order to carry out onboard geocoding of high-resolution imagery, open-loop operation of altimeters and radio occultation. This study proposes an improved real-time kinematic positioning method for LEO satellites using single-frequency receivers. The C/A code and L1 phase are combined to eliminate ionospheric effects. The epoch-differenced carrier phase measurements are utilized to acquire receiver position changes which are further used to smooth the absolute positions. A kinematic Kalman filter is developed to implement kinematic orbit determination. Actual flight data from China’s small satellite SJ-9A are used to test the navigation performance. Results show that the proposed method outperforms traditional kinematic positioning method in terms of accuracy. A 3D position accuracy of 0.72 and 0.79 m has been achieved using the predicted portion of IGS ultra-rapid products and broadcast ephemerides, respectively.     

GPS/Galileo long baseline computation: method and performance analyses

Modernized GPS and Galileo will provide triple-frequency signals for civil use, generating a high interest to examine the improvement of positioning performance using the triple-frequency signals from both constellations over baselines up to hundreds or thousands of kilometers. This study adopts a generalized GPS/Galileo long-range approach to process the mutually compatible GPS and Galileo triple-frequency measurements for high-precision long baseline determination. The generalized approach has the flexibility to deal with GPS and Galileo constellations separately or jointly, and also the capability to handle dual or triple-frequency measurements. We compared the generalized long-range approach with the Bernese v5.0 software on two test baselines located in East Asia and obtained highly compatible computational results. Further, in order to assess possible improvement of GPS/Galileo long baseline determination compared with the current dual-frequency (L1/L2) GPS, we simulated GPS and Galileo measurements of the test baselines. It is shown that the current level of accuracy of daily baseline solutions can be improved by using the additional Galileo constellation. Both the additional constellation and the triple-frequency measurements can improve ambiguity resolution performance, but single-constellation triple-frequency ambiguity resolution is more resistant to the influences of code noise and multipath than dual-constellation dual-frequency ambiguity resolution. Therefore, in environments where large code noise or multipath is present, the use of triple-frequency measurements is the main factor for improving ambiguity resolution performance.     

北斗与GPS在桥梁变形监测中的对比分析

目前我国北斗导航系统已经完成第二阶段区域系统的建设,利用北斗导航定位技术进行桥梁变形监测是今后发展的必然趋势。本文分析了北斗定位技术在桥梁变形监测中的的优势,并与GPS定位技术作对比分析,结果表明:在监测区域内,北斗二号的可见卫星数要略多于GPS可见卫星数,卫星几何精度因子略低于GPS,数据质量与GPS相当,相对定位精度略优于GPS,平面定位精度在1~2 cm,水平定位精度在5~6 cm。     

基于抗差估计的GPS／CoMPASS组合实时差分定位算法

在GPS／cOMPASS组合差分定位基础上,引入抗差估计方法,通过降权调整合有粗差观测值对定位的影响,利用路测试验,对比RTK的厘米级定位,结果表明：抗差GPS／COMPASS组合实时差分定位优于非抗差定位,平面精度在2．0m左右。     

Calculation and accuracy evaluation of TGD from IFB for BDS

With the development of new global navigation satellite system applications, the demand of high accurate positioning navigation timing (PNT) service becomes urgent. For precise PNT, the timing group delay (TGD) is regarded as an important parameter in the satellite navigation message. Instead of using the absolute receiver hardware delay, a method based on receiver inter-frequency bias (IFB, i.e., differential receiver hardware delay between different frequencies) calibration is presented to deal with the rank deficiency of a calculation matrix and to reduce jumps in TGD solutions in BDS. The double-differenced pseudorange obtained from a pair of zero baseline receivers is used to evaluate the IFB calibration accuracy. The estimated precision of TGD is evaluated and compared with GPS TGD provided by IGS. In order to ensure the quality of assessment, a method based on the difference of dual-frequency ionospheric delay is proposed to compare the accuracy of the estimated TGD and broadcast TGD. Finally, the effect of TGD on the user equivalent range error is analyzed. The analysis result shows that for BDS IGSO satellites, the precision of TGD1, which is the differential hardware delay between B1 (1561.098 MHz) and B3 (1268.52 MHz) frequencies, is better than 0.5 ns, and for GEO and MEO satellites the TGD1 is better than 1 and 2 ns, respectively. The precision of TGD2 of all satellites, which is the differential hardware delay between B2 (1207.14 MHz) and B3 frequencies, is better than 0.5 ns. The accuracy analysis result reveals that the proposed TGD estimation method can provide better results when compared with the broadcast data.     

“北斗二号”导航定位系统与GPS伪距单点定位性能对比研究

对GPS系统、北斗二号系统以及GPS/北斗组合系统伪距单点定位的关键技术进行研究,分析了3种导航系统的DOP值。单一系统随卫星高度角的增加,DOP值增大,定位精度下降。GPS伪距单点定位的精度达到2 m,北斗伪距单点定位的精度在5 m以内,GPS/北斗联合定位的精度和GPS相差不大。     

GPS-based precise orbit determination of Low Earth Orbiters with limited resources

The combination of GPS measurements and high-fidelity dynamic models via a Kalman filter/smoother, known as the reduced dynamic technique, allows 3D positioning of Low Earth Orbiters to the sub-decimeter level. Such accuracies can only be achieved if the GPS data are nearly continuous, post-processed and a dual-frequency receiver is utilized. The focus of this study is to quantitatively analyze the degradations in position accuracy in the presence of various limitations or constraints, which can be brought on by mission hardware limitations, for example, on micro- or nanosatellites. The constraints explored in this study are as follows: the use of single-frequency data only; real-time processing; limited dynamic modeling due to computing capabilities; and non-continuous GPS receiver operation due to power limits. The experiments are conducted with 6-h data arcs for 7 separate days using data from the CHAllenging Mini-Satellite Payload. A 3D root mean square (rms) error of 15 cm is observed in the best-case solution, in which dual-frequency data are post-processed with all available data. Various levels of accuracy degradations are observed as constraints are placed on this best-case solution. The 3D rms error of the post-processed, single-frequency solution is 68 cm and 1.3 m for the real-time, dual-frequency solution. In very challenging environments, for example, with the receiver on for only 10 min of a 90-min orbit, the 3D rms increases to 350 m.     

Sub-daily noise in horizontal GPS kinematic time series due to thermal tilt of GPS monuments

The sub-daily noise in horizontal global positioning system (GPS) kinematic time series arising from monument tilts is quantitatively evaluated using tiltmeter data at GPS stations from the Japanese nationwide global navigation satellite system network. The estimated tilt-induced monument displacements show characteristics that are typical of those caused by thermal tilts of the monuments. The root mean square of the displacements is typically a few millimetres, with notable inter-seasonal variations. The stacked amplitude spectra of the monument displacements have peaks at the tidal bands S1 and S2, and their higher tones. The peaks at the S1 and S2 bands in the amplitude spectra are reduced by 41 and 43 % for the north–south component and 36 and 53 % for the east–west component, respectively, after correcting for the monument displacements. The monument displacements due to the thermal tilts of the monuments may also be a favourable candidate for sub-daily noise at the S1 and S2 bands found in other GPS networks.     

Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system

An initial characterization and performance assessment of the COMPASS/BeiDou-2 regional navigation system is presented. Code and carrier phase measurements on up to three frequencies have been collected in March 2012 with a small regional network of monitoring stations. The signal and measurement quality are analyzed and compared with the Japanese Quasi Zenith Satellite System. A high level of stability is demonstrated for the inter-frequency carrier phase biases, which will facilitate the application of triple-frequency undifferenced ambiguity resolution techniques in future precise point positioning applications. The performance of the onboard Rubidium frequency standards is evaluated in comparison to ground-based hydrogen masers and shown to be well competitive with other GNSS satellite clocks. Precise orbit and clock solutions obtained in post-processing are used to study the presently achievable point positioning accuracy in COMPASS/BeiDou-2-only navigation. Finally, the benefit of triple-frequency measurements and extra-wide-lane ambiguity resolution is illustrated for relative positioning on a short baseline.