First use of IGEX precise ephemerides for intercontinental GLONASS P-code time transfer

 Until recently, the Global Positioning System (GPS) was the only operational means of distributing time to an arbitrary number of users and of synchronizing clocks over large distances with a high degree of precision and accuracy. Over the last few years it has been shown that similar performance can be achieved using the Russian Global Navigation Satellite System (GLONASS). GLONASS time transfer between continents was initially hampered by the lack of post-processed precise ephemerides. Results from the International GLONASS Experiment (IGEX) campaign are now available, however, and this paper reports on the first use of IGEX precise ephemerides for GLONASS P-code intercontinental time links. The results of GLONASS P-code and GPS C/A-code time transfer are compared under similar conditions. Received: 31 January 2000 / Accepted: 10 July 2000     

GPS-assisted GLONASS orbit determination

 Using 1 week of data from a network of GPS/GLONASS dual-tracking receivers, 15-cm accurate GLONASS orbit determination is demonstrated with an approach that combines GPS and GLONASS data. GPS data are used to define the reference frame, synchronize receiver clocks and determine troposphere delay for the GLONASS tracking network. GLONASS tracking data are then processed separately, with the GPS-defined parameters held fixed, to determine the GLONASS orbit. The quality of the GLONASS orbit determination is currently limited by the size and distribution of the tracking network, and by the unavailability of a sufficiently refined solar pressure model. Temporal variations in the differential clock bias of the dual-tracking receivers are found to have secondary impact on the orbit determination accuracy. Received: 5 January 2000 / Accepted: 15 February 2001     

QZSS L6E增强服务改正数支持的PPP性能评估

准天顶卫星系统目前利用QZS-2~QZS-43颗卫星播发L6E信号,为东亚和大洋洲地区用户提供实时的增强服务。该文分析了L6E信号结构及轨道和钟差的计算模型,研究了目前L6E信号的覆盖范围和可用性,评估了L6E改正数恢复的卫星轨道和钟差及其用于动态PPP的精度水平。结果表明:我国用户在使用15°截止高度角时L6E信号仍有100%的可用性;L6E改正数恢复的GPS和GLONASS卫星轨道的3D RMS平均值分别为5.3和13.9 cm,卫星钟差的STD平均值分别为0.14和0.22 ns,利用GPS卫星的轨道和钟差进行的动态PPP可以获得水平优于10 cm、高程优于15 cm的精度,在加入GLONASS卫星后,东方向和高程方向定位误差和收敛时间均有明显改善。     

顾及码频间偏差的GPS/GLONASS实时卫星钟差估计

在进行GPS/GLONASS联合卫星钟差估计时,GLONASS码频间偏差（inter-frequency bias,IFB）因卫星频率间的差异而无法被测站接收机钟差参数吸收,其一部分将进入GLONASS卫星钟差估值中。通过引入多个"时频偏差"参数（inter-system and inter-frequency bias,ISFB）及附加基准约束对测站GLONASS码IFB进行函数模型补偿,实现其与待估卫星钟差参数的有效分离,并对所估计实时卫星钟差和实时精度单点定位（real-time precise point positioning,RT-PPP）进行精度评估。结果表明,在卫星钟差估计观测方程中忽略码IFB,会明显降低GLONASS卫星钟差估值精度;新方法能有效避免码IFB对卫星钟差估值的影响,所获得GPS、GLONASS卫星钟差与ESA（European Space Agency）事后精密钟差产品偏差平均均方根值分别小于0.2 ns、0.3 ns。利用实时估计卫星钟差进行静态RT-PPP,当观测时段长为2 h时,GPS单系统、GPS/GLONASS组合系统的3D定位精度优于10 cm,GLONASS单系统3D定位精度约为15 cm;三种模式24 h单天解的3D定位精度均优于5 cm。     

Time Transfer Experiments Using GLONASS P-code Measurements from RINEX Files

We have used GLONASS P-code measurements from different geodetic GPS/GLONASS receivers involved in the IGEX campaign to perform frequency/time transfer between remote clocks. GLONASS time transfer is commonly based on the clock differences between GLONASS system time and the local clock computed by a time transfer receiver. We choose to analyze the raw P-code data available in the RINEX files. This also allows working with the data from geodetic receivers involved in the IGEX campaign. As a first point, we show that the handling of the external frequency in some of the IGEX receivers is not suited for time transfer applications. We also point out that the GLONASS broadcast ephemerides give rise to a considerable number of outliers in the time transfer, compared to the precise IGEX ephemerides. Due to receiver clock resets at day boundaries, which is a characteristic of the R100 receivers from 3S-Navigation, continuous data sets exceeding one day are not available. Invthis context, it is therefore impossible to perform RINEX-based precise frequency transfer with GLONASS P-codes on a time scale longer than one day. Because the frequencies used by GLONASS satellites are different, the time transfer results must be corrected for the different receiver hardware delays. After this correction, the final precision of our time transfer results corresponds to a root-mean-square (rms) of 1.8 nanoseconds (ns) (maximum difference of 11.8 ns) compared to a rms of about 4.4 ns (maximum difference of 31.9 ns) for time transfer based on GPS C/A code observations. ? 2001 John Wiley & Sons, Inc.     

Combined processing of the IGS and the IGEX network

 Since the beginning of the International Global Navigation Satellite System (GLONASS) Experiment, IGEX, in October 1998, the Center for Orbit Determination in Europe (CODE) has acted as an analysis center providing precise GLONASS orbits on a regular basis. In CODE's IGEX routine analysis the Global Positioning System (GPS) orbits and Earth rotation parameters are introduced as known quantities into the GLONASS processing. A new approach is studied, where data from the IGEX network are combined with GPS observations from the International GPS Service (IGS) network and all parameters (GPS and GLONASS orbits, Earth rotation parameters, and site coordinates) are estimated in one processing step. The influence of different solar radiation pressure parameterizations on the GLONASS orbits is studied using different parameter subsets of the extended CODE orbit model. Parameterization with three constant terms in the three orthogonal directions, D, Y, and X (D = direction satellite–Sun, Y = direction of the satellite's solar panel axis), and two periodic terms in the X-direction, proves to be adequate for GLONASS satellites. As a result of the processing it is found that the solar radiation pressure effect for the GLONASS satellites is significantly different in the Y-direction from that for the GPS satellites, and an extensive analysis is carried out to investigate the effect in detail. SLR observations from the ILRS network are used as an independent check on the quality of the GLONASS orbital solutions. Both processing aspects, combining the two networks and changing the orbit parameterization, significantly improve the quality of the determined GLONASS orbits compared to the orbits stemming from CODE's IGEX routine processing. Received: 10 May 2000 / Accepted: 9 October 2000     

Fehlertheoretische Maxwell-Boltzmann-Verteilung

Summary The probability to find an error vector in multiples of the Helmert-Maxwell-Boltzmann point error σ² δ_ij(δ_ij Kronecker symbol) is calculated. It is found that the probability is for σ39%, for2 σ86% and for3 σ99% in two dimensions, for σ20%, for2 σ74% and for3 σ97% in three dimensions. The fundamental Maxwell-Boltzmann-distribution is tabulated0,02 (0,02) 4,50.      

On the existence of solutions for the method of Bjerhammar in the continuous case

The method of Bjerhammar is studied in the continuous case for a sphere. By varying the kernel function, different types of unknowns (u^*) are obtained at the internal sphere (the Bjerhammar sphere). It is shown that a necessary condition for the existence of u^* is that the degree variances (σ _n ² ) of the observations are of an order less than n⁻². According to Kaula’s rule this condition is not satisfied for the earth’s gravity anomaly field (σ _n ² =n⁻¹) but well for the geopotential (σ _n ² =n⁻³).     

GPS/GLONASS组合精密单点定位研究

讨论了GPS/GLONASS组合精密单点定位的数学模型,并以IRKJ跟踪站的观测数据为例,分别利用GPS和GPS/GLONASS组合两种方式进行精密单点定位解算。计算结果表明,当GPS观测卫星数较多(9~10颗)时,组合GPS/GLONASS较单系统GPS的精密单点定位精度及收敛速度有一定改善,但效果不明显。当GPS卫星数较少(4~5颗)时,引入GLONASS卫星进行GPS/GLONASS组合精密单点定位,其定位精度及收敛速度较单系统GPS精密单点均有显著改善。     

顾及频率间偏差的GPS/GLONASS卫星钟差实时估计

GPS/GLONASS卫星钟差联合估计过程中，由于GLONASS系统采用频分多址技术区分卫星信号，因而会产生频率间偏差（IFB）^[1]。本文在GPS/GLONASS卫星定轨过程中的IFB参数特性分析的基础上，引入IFB参数，实现顾及频率间偏差的GPS/GLONASS卫星钟差实时估计。同时，为解决实时估计中待估参数过多导致的实时性较弱等问题，基于非差伪距观测值和历元间差分相位观测值改进实时估计数学模型，实现多系统卫星钟差的联合快速估计。结果表明：GPS/GLONASS联合估计时需引入IFB参数并优化其估计策略，采用MGEX和iGMAS跟踪站的实测数据进行实时钟差解算，快速估计方法可实现1.6 s逐历元快速、高精度估计，与GBM提供的最终精密卫星钟差相比，GPS卫星钟差实时精度约为0.210 ns，GLONASS卫星约为0.298 ns。     

Multiple transit times and least squares for gyroscopic azimuth

Principles of North determination using suspended gyrocompasses are reviewed. Accuracy is evaluated and a procedure with two series of measurements symmetrical with respect to the zero torsion tape position is mathematically proven to be the “best” (minimum variance). Our purpose is to prove that a 20″ accuracy (1 σ) instrument was brought to a level of accuracy four times better by using multiple transit times and least squares fit. Over a total of 15 North determinations based on more than a thousand transit times, an external standard error of 4″.4 was obtained using a WildGAK-1.     

Relativistic Time Transformations in GPS

Since Selective Availability was permanently switched off on 7 May 2000, most of the GPS satellite clocks have been well behaved. During a 24-h period precise satellite clock solutions, corrected for GPS conventional relativistic corrections, follow straight lines within a few nanoseconds. The linear clock fit RMS for the best satellite clocks are well below the 1-ns level, which is consistent with the nominal stability of the GPS frequency standards. Typically, the GPS satellite clocks show an Allan variance at or below one part in 10¹¹/100 s for the Cesium frequency standards and a few parts in 10¹²/100 s for the Rubidium frequency standards. These results correspond to clock RMSs for 15-min sampling at or below 3 and 0.3 ns, respectively. This already confirms experimentally that the conventional periodic relativity correction of the GPS system, also adopted for all the IGS clock solution products, is precise and correct to 0.6 ns or better. To establish the precision limits of the GPS conventional relativity treatment, the relativistic time transformations of GPS satellite frequency and clocks are critically reviewed, taking into account all the contributions larger than the 10⁻¹⁸ (or 0.001 ns). The conventional GPS relativity treatment was found to be accurate, i. e., correctly modeling the actual relativistic frequency (clock rate) effects of GPS satellites at about the 10⁻¹⁴ level. However, it is also affected by small periodic errors of the same magnitude. The integration of these small periodic frequency relativistic errors gives the approximation errors of the conventional periodic relativistic clock correction with amplitudes of about 0.1 ns and a predominant period equal to a half of the orbital period (∼ 6 h). These approximation errors of the conventional GPS relativistic clock correction are at about the same level as the current precision of the IGS clock solutions. ? 2002 Wiley Periodicals, Inc.     

Wide-angle airborne laser range data analysis for relative height determination of ground-based benchmarks

 A wide-angle airborne laser ranging system has been developed for the determination of relative heights of ground-based benchmarks in regional-scale networks (typically 100 laser reflectors spread over 100 km²). A first prototype demonstrated a 1–2 mm accuracy in radial distance measurement in a ground-based experiment in 1995. The first aircraft experiment was conducted in 1998, over a small area (1 km²) equipped with a network of 64 benchmarks. The instrument was modified before that experiment, in order to minimize echo superimposition due to the high density of benchmarks. New data processing algorithms have been developed, for the deconvolution of strongly overlapped echoes and a high a priori uncertainty in the aircraft flight path, and for the estimation of benchmark coordinates. A special methodology has been developed for the parameterization of these algorithms and of outlier detection tests. From a total of 2×10⁴ pseudo-range measurements, that have been acquired from two flights composed of 30 legs each, only 3×10³ remain after outlier detection. A positioning accuracy of 1.5 cm in the vertical coordinate (2.1 cm in the difference between the two flights) has been achieved. It is shown that the errors are normally distributed, with a nearly zero mean, and are consistent with the a posteriori uncertainty. It is also shown that the accuracy is limited mainly by the sensitivity of the photodetector used for this experiment (due to reduced response time). Another limiting factor is the effect of aircraft attitude changes during the measurements, which produces additional uncertainties in absolute distance measurements. It is planned to test new photodetectors with high internal gains. These should provide, in future experiments with smaller benchmark density, an improvement in signal-to-noise ratio of a factor of 5–10, leading to sub-centimeter vertical positioning accuracy. Received: 19 June 2001 / Accepted: 3 January 2002     

GNSS receiver autonomous integrity monitoring (RAIM) performance analysis

The availability of GPS signals is a major concern for many existing and potential applications. Fortunately, with the development of Galileo by the European Commission (EC) and European Space Agency (ESA) and new funding for the restoration of the Russian GLONASS announced by the Russian Federation (Revnivykh et al., in European Navigation Conference 2005, Munich, Germany, July 19–22), the future for satellite-based positioning and navigation applications is extremely promising. With the complete cooperation from all these global navigation satellite systems (GNSS), greater levels of satellite visibility and therefore integrity can be expected. In this paper, a receiver autonomous integrity monitoring (RAIM) scheme along with reliability and separability measures are used to assess integrity performance levels of standalone GPS and integrated GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo systems where the clock offsets for each of the additional systems are estimated. It is shown, herein, that a minimum of three satellites must be visible in an additional system in order to provide a full integrity contribution when the system’s clock offset is to be estimated within the adjustment. A comparison of the integrity results obtained via system clock offsets estimated in the adjustment versus the case where the offsets are known and the measurements are corrected prior to the adjustment is also made for a high elevation mask scenario. Global simulation results for combined GPS/GLONASS/Galileo show that, theoretically, for the time of simulation and for any point on the globe, an outlier of 20 m can be detected with 80% probability at the 0.5% significance level and then separated from any other measurement with 90% probability. Corresponding values for the GPS only and combined GPS/GLONASS and GPS/Galileo systems, respectively, are approximately 435, 110 and 28 m, respectively, for the maximum MSBs and 312, 50 and 26 m, respectively, for the maximum MDBs. Temporal 24 h simulations for the GPS/GLONASS/Galileo scenario delivered agreeable results with the global snapshots for a 15° elevation mask. For the case where system clock offsets are estimated within the adjustment, it was shown that only the reliability measure was available for 100% of the time, with horizontal external reliability values of no more than about 12 m when a 30° masking angle was used. By assuming the clock offsets were determined and corrected for prior to the adjustment, the separability measure was markedly improved and was also available 100% of the time.     

Carrier-phase inter-frequency biases of GLONASS receivers

The frequency division multiplexing of the GLONASS signals causes inter-frequency biases in the receiving equipment. These biases vary considerably for receivers from different manufacturers and thus complicate or prevent carrier-phase ambiguity fixing. Complete and reliable ambiguity fixing requires a priori information of the carrier-phase inter-frequency bias differences of the receivers involved. GLONASS carrier-phase inter-frequency biases were estimated for 133 individual receivers from 9 manufacturers. In general, receivers of the same type and even receivers from the same manufacturer show similar biases, whereas the differences among manufacturers can reach up to 0.2 ns (more than 5 cm) for adjacent frequencies and thus up to 2.4 ns (73 cm) for the complete L1 or L2 frequency bands. A few individual receivers were identified whose inter-frequency biases behave differently as compared to other receivers of the same type or whose biases vary with time.     

The international GLONASS experiment: products, progress and prospects

 In October 1998 the IGEX field campaign, the first coordinated international effort to monitor GLONASS satellites on global basis, was started. Currently about 40 institutions worldwide support this effort either by providing GLONASS tracking data or in operating related data and analysis centers. The increasing quality and consistency of the calculated GLONASS orbits (about 25 cm early in 2000), even after the end of the official IGEX field campaign, are shown. Particular attention is drawn to the combination of precise ephemerides in order to generate a robust, reliable and complete IGEX orbits product. Some problems in modeling the effect of solar radiation pressure on GLONASS satellites are demonstrated. Finally, the expected benefits and prospects of the upcoming International GLOnass Service-Pilot Project (IGLOS-PP) of the International GPS Service (IGS) are discussed in more detail. Received: 17 August 2000 / Accepted: 12 April 2001     

Improved antenna phase center models for GLONASS

Thanks to the increasing number of active GLONASS satellites and the increasing number of multi-GNSS tracking stations in the network of the International GNSS Service (IGS), the quality of the GLONASS orbits has become significantly better over the last few years. By the end of 2008, the orbit RMS error had reached a level of 3–4 cm. Nevertheless, the strategy to process GLONASS observations still has deficiencies: one simplification, as applied within the IGS today, is the use of phase center models for receiver antennas for the GLONASS observations, which were derived from GPS measurements only, by ignoring the different frequency range. Geo++ GmbH calibrates GNSS receiver antennas using a robot in the field. This procedure yields now separate corrections for the receiver antenna phase centers for each navigation satellite system, provided its constellation is sufficiently populated. With a limited set of GLONASS calibrations, it is possible to assess the impact of GNSS-specific receiver antenna corrections that are ignored within the IGS so far. The antenna phase center model for the GLONASS satellites was derived in early 2006, when the multi-GNSS tracking network of the IGS was much sparser than it is today. Furthermore, many satellites of the constellation at that time have in the meantime been replaced by the latest generation of GLONASS-M satellites. For that reason, this paper also provides an update and extension of the presently used correction tables for the GLONASS satellite antenna phase centers for the current constellation of GLONASS satellites. The updated GLONASS antenna phase center model helps to improve the orbit quality.     

北斗三号空间信号测距误差评估与对比分析

北斗三号作为我国自主建设的全球卫星导航系统,其本身性能水平以及与其他卫星导航系统的性能对比情况,对后续推广应用具有重要影响。为此,本文以空间信号测距误差（signal-in-space range error,SISRE）作为系统关键性能指标,以GFZ提供的多系统精密轨道钟差作为标准,给出了卫星轨道、卫星钟差、SISRE的比对评估方法,并以2020年1—3月共3个月的实测数据,验证了北斗三号相对北斗二号的精度改进情况,并重点分析了北斗三号与GPS、Galileo、GLONASS之间的性能对比关系。结果表明：无论是卫星轨道还是卫星钟差,北斗三号的精度水平相对北斗二号都有了明显提高;北斗三号卫星轨道在R、T、N方向精度分别达到0.07、0.30、0.26 m,在4个全球系统中处于最优水平;卫星钟差精度达到1.83 ns,基本与GPS系统持平,优于GLONASS,但还略差于Galileo;在空间信号测距误差方面,如果仅考虑轨道误差,北斗三号SISRE（orb）平均达到0.08 m,紧随其后,Galileo达到0.26 m,GPS达到0.57 m,GLONASS达到0.98 m。如果综合考虑轨道和钟差误差,北斗三号SISRE平均达到0.50 m,稍逊于Galileo的0.38 m,略优于GPS的0.58 m,明显好于GLONASS的2.35 m。     

Interferometric Baseline Performance Estimations for Multistatic Synthetic Aperture Radar Configurations Derived from GRACE GPS Observations

Recent studies have demonstrated the usefulness of global positioning system (GPS) receivers for relative positioning of formation-flying satellites using dual-frequency carrier-phase observations. The accurate determination of distances or baselines between satellites flying in formation can provide significant benefits to a wide area of geodetic studies. For spaceborne radar interferometry in particular, such measurements will improve the accuracy of interferometric products such as digital elevation models (DEM) or surface deformation maps. The aim of this study is to analyze the impact of relative position errors on the interferometric baseline performance of multistatic synthetic aperture radar (SAR) satellites flying in such a formation. Based on accuracy results obtained from differential GPS (DGPS) observations between the twin gravity recovery and climate experiment (GRACE) satellites, baseline uncertainties are derived for three interferometric scenarios of a dedicated SAR mission. For cross-track interferometry in a bistatic operational mode, a mean 2D baseline error (1σ) of 1.4 mm is derived, whereas baseline estimates necessary for a monostatic acquisition mode with a 50 km along-track separation reveal a 2D uncertainty of approximately 1.7 mm. Absolute orbit solutions based on reduced dynamic orbit determination techniques using GRACE GPS code and carrier-phase data allows a repeat-pass baseline estimation with an accuracy down to 4 cm (2D 1σ). To assess the accuracy with respect to quality requirements of high-resolution DEMs, topographic height errors are derived from the estimated baseline uncertainties. Taking the monostatic pursuit flight configuration as the worst case for baseline performance, the analysis reveals that the induced low-frequency modulation (height bias) fulfills the relative vertical accuracy requirement (σ<1 m linear point-to-point error) according to the digital terrain elevation data level 3 (DTED-3) specifications for most of the baseline constellations. The use of a GPS-based reduced dynamic orbit determination technique improves the baseline performance for repeat-pass interferometry. The problem of fulfilling the DTED-3 horizontal accuracy requirements is still an issue to be investigated. DGPS can be used as an operational navigation tool for high-precision baseline estimation if a geodetic-grade dual-frequency spaceborne GPS receiver is assumed to be the primary instrument onboard the SAR satellites. The possibility of using only single-frequency receivers, however, requires further research effort.Deutsche Forschungsgemeinschaft (DFG) research fellow until Sept. 2004 at the Microwaves and Radar Institute, Deutsche Zentrum für Luft- und Raumfahrt (DLR) e.V., 82234 Weßling, Germany     

基于DREAMNET的GPS/BDS/GLONASS多系统网络RTK定位性能分析

随着BDS系统完成亚太地区组网、GLONASS系统再次实现满星座部署以及GPS系统的现代化,多系统集成已逐步成为网络RTK技术的发展趋势。本文结合笔者所在课题组自主研发的网络RTK数据处理系统DREAMNET,对不同卫星系统组合模式下的定位精度进行比较分析。试验结果表明,GPS/BDS/GLONASS网络RTK和GPS/BDS网络RTK的定位精度最高,GPS、BDS单系统网络RTK次之。此外,随着高度角的增加,GPS单系统网络RTK的可用性显著降低,而GPS/BDS/GLONASS网络RTK在高度角为40°时依然可以在99.84%的时间里提供水平精度0.01 m、高程精度0.025 m的定位服务。最后,对15 d的定位结果进行统计,包括不依赖GPS系统的BDS和BDS/GLONASS在内的6种组合方式皆可达到水平0.01 m、高程0.025 m的定位精度,其中GPS/BDS/GLONASS网络RTK则可以得到水平0.006 m、高程0.015 m的定位精度,证明DREAMNET的定位精度和稳定性完全可以满足测绘作业的需要。