Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.     

Estimation of phase center corrections for GLONASS-M satellite antennas

Driven by the comprehensive modernization of the GLONASS space segment and the increased global availability of GLONASS-capable ground stations, an updated set of satellite-specific antenna phase center corrections for the current GLONASS-M constellation is determined by processing 84 weeks of dual-frequency data collected between January 2008 and August 2009 by a worldwide network of 227 GPS-only and 115 combined GPS/GLONASS tracking stations. The analysis is performed according to a rigorous combined multi-system processing scheme providing full consistency between the GPS and the GLONASS system. The solution is aligned to a realization of the International Terrestrial Reference Frame 2005. The estimated antenna parameters are compared with the model values currently used within the International GNSS Service (IGS). It is shown that the z-offset estimates are on average 7 cm smaller than the corresponding IGS model values and that the block-specific mean value perfectly agrees with the nominal GLONASS-M z-offset provided by the satellite manufacturer. The existence of azimuth-dependent phase center variations is investigated and uncertainties in the horizontal offset estimates due to mathematical correlations and yaw-attitude modeling problems during eclipse seasons are addressed. Finally, it is demonstrated that the orbit quality benefits from the updated GLONASS-M antenna phase center model and that a consistent set of satellite antenna z-offsets for GPS and GLONASS is imperative to obtain consistent GPS- and GLONASS-derived station heights.     

GBM快速轨道产品及非差模糊度固定对其精度的改进

GNSS是实时定位导航最重要的方法,精密卫星轨道钟差产品是GNSS高精度服务的前提。国际GNSS服务中心(IGS)及其分析中心长期致力于GNSS数据处理的研究及高精度轨道和钟差产品的提供。GFZ作为分析中心之一,提供GBM多系统快速产品。本文基于2015—2021年GBM提供的精密轨道产品,阐述了数据处理策略,分析了轨道的精度,介绍了非差模糊度固定的原理和对精密定轨的影响。结果表明:GBM快速产品中的GPS轨道精度与IGS后处理精密轨道相比的精度约为11~13 mm,轨道6 h预报精度约为6 cm;GLONASS预报精度约为12 cm,Galileo在该时期的精度均值为10 cm,但是在2016年底以后精度提升到5 cm左右;北斗系统的中轨卫星(medium earth orbit,MEO)在2020年以后预报精度约为10 cm;北斗的静止轨道卫星(geostationary earth orbit,GEO)卫星和QZSS卫星的预报精度在米级;卫星激光测距检核表明,Galileo、GLONASS、BDS-3 MEO卫星轨道精度分别为23、41、47 mm;此外,采用150 d观测值的试验结果表明,采用非差模糊度固定能显著改善MEO卫星轨道精度,对GPS、GLONASS、Galileo、BDS-2和BDS-3的MEO卫星的6 h时预报精度改善率分别为9%~15%、15%~18%、11%~13%、6%~17%和14%~25%。     

A computationally efficient approach for estimating high-rate satellite clock corrections in realtime

Realtime satellite clock corrections are usually estimated using undifferenced phase and range observations from a global network. Because a large number of ambiguity parameters must be estimated, the computation is time-consuming. Consequently, only a sparse global network of limited number of stations is processed by most IGS Realtime Analysis Centers with an update rate of 5 s. In addition, it is very desirable to build the capability to simultaneously estimate clock corrections for multi-GNSS constellations. Although the estimation can be sped up by epoch-differenced observations that eliminate ambiguities, the derived clocks can contain a satellite-specific bias that diminishes the contribution of range observations. We introduce a computationally efficient approach for realtime clock estimation. Both the epoch-differenced phase and undifferenced range observations are used together to estimate the epoch-differenced satellite clocks and the initial clock bias for each satellite and receiver. The biased clock corrections accumulated from the estimated epoch-differenced clocks are then aligned with the estimated clock biases and provided as the final clock corrections to users. The algorithm is incorporated into the EPOS-RT software developed at GFZ (GeoForschungsZentrum) and experimentally validated with the IGS global network. The comparison with the GFZ rapid products shows that the accuracy of the clock estimation with the new approach is comparable with that of the undifferenced approach, whereas the computation time is reduced to one-tenth. As a result, estimation of high-rate satellite clocks from a large reference network and tracking satellites of multi-GNSS constellations becomes achievable.     

偏航姿态对GPS和GLONASS精密轨道和钟差的影响

利用全球约110个国际GNSS服务（International GNSS Service,IGS）测站2013年全年观测数据,分析和研究了GPS和全球卫星导航系统（global navigation satellite system,GLONASS）卫星偏航姿态对其精密轨道和钟差的影响。结果表明,偏航姿态对不同型号GPS卫星轨道和钟差的影响程度不同,当采用偏航姿态改正后地影期的BLOCK ⅡA型卫星轨道改善可达17 mm,BLOCK ⅡF为近5 mm,而BLOCK ⅡR几乎不受影响。由于偏航姿态对GLONASS-M卫星定轨精度影响较大,因此,当改正偏航姿态后所有GLONASS卫星相对于IGS最终轨道平均一维差异提高10 mm,相对于德国地学中心（German Research Center for Geosciences,GFZ）最终钟差平均标准差提升0.034 ns。     

Homogeneous reprocessing of GPS,GLONASS and SLR observations

The International GNSS Service (IGS) provides operational products for the GPS and GLONASS constellation. Homogeneously processed time series of parameters from the IGS are only available for GPS. Reprocessed GLONASS series are provided only by individual Analysis Centers (i. e. CODE and ESA), making it difficult to fully include the GLONASS system into a rigorous GNSS analysis. In view of the increasing number of active GLONASS satellites and a steadily growing number of GPS+GLONASS-tracking stations available over the past few years, Technische Universität Dresden, Technische Universität München, Universität Bern and Eidgenössische Technische Hochschule Zürich performed a combined reprocessing of GPS and GLONASS observations. Also, SLR observations to GPS and GLONASS are included in this reprocessing effort. Here, we show only SLR results from a GNSS orbit validation. In total, 18 years of data (1994–2011) have been processed from altogether 340 GNSS and 70 SLR stations. The use of GLONASS observations in addition to GPS has no impact on the estimated linear terrestrial reference frame parameters. However, daily station positions show an RMS reduction of 0.3 mm on average for the height component when additional GLONASS observations can be used for the time series determination. Analyzing satellite orbit overlaps, the rigorous combination of GPS and GLONASS neither improves nor degrades the GPS orbit precision. For GLONASS, however, the quality of the microwave-derived GLONASS orbits improves due to the combination. These findings are confirmed using independent SLR observations for a GNSS orbit validation. In comparison to previous studies, mean SLR biases for satellites GPS-35 and GPS-36 could be reduced in magnitude from \(-35\) and \(-38\)  mm to \(-12\) and \(-13\)  mm, respectively. Our results show that remaining SLR biases depend on the satellite type and the use of coated or uncoated retro-reflectors. For Earth rotation parameters, the increasing number of GLONASS satellites and tracking stations over the past few years leads to differences between GPS-only and GPS+GLONASS combined solutions which are most pronounced in the pole rate estimates with maximum 0.2 mas/day in magnitude. At the same time, the difference between GLONASS-only and combined solutions decreases. Derived GNSS orbits are used to estimate combined GPS+GLONASS satellite clocks, with first results presented in this paper. Phase observation residuals from a precise point positioning are at the level of 2 mm and particularly reveal poorly modeled yaw maneuver periods.     

顾及卫星姿态的多系统精密钟差产品综合

国际GNSS服务(IGS)提供的GPS综合产品被广泛应用于各种高精度科学研究中. 随着各国卫星导航系统的发展,亟需研究针对多系统全球卫星导航系统(GNSS)产品的综合策略. 由于卫星姿态与钟差相互耦合,综合钟差时额外考虑姿态改正将进一步提高综合产品精度,因此研究了一种顾及卫星姿态的GNSS钟差综合策略,改正姿态后GPS综合残差最大可减小80%. 对142个IGS测站进行精密单点定位(PPP)解算发现,综合产品比单个分析中心产品更加稳定,东(E)、北(N)、高(U)方向的动态定位精度最大可提升22.7%、16.7%和18.3%. 相对于未顾及姿态改正的综合产品,顾及姿态改正的综合产品的动态定位精度最大可提升65.3%.      

多模全球导航卫星系统融合精密定轨

基于武汉大学自主研制的卫星导航系统综合处理软件(PANDA),利用全球实测的GPS/GLONASS、GPS/Gali-leo试验卫星(GIOVE)多模接收机数据进行GPS、GLONASS、GIOVE卫星的融合精密定轨理论与方法研究。通过与IGS提供的GPS与GLONASS卫星精密轨道比较、轨道重叠弧段互差以及SLR观测数据检核等多种方法对融合计算的精密轨道精度进行了评定。     

Precise orbit determination of BeiDou constellation: method comparison

Chinese BeiDou navigation satellite system is in official service as a regional constellation with five geostationary earth orbit (GEO) satellites, five inclined geosynchronous satellite orbit (IGSO) satellites and four medium earth orbit (MEO) satellites. There are mainly two methods for precise orbit determination of the BeiDou constellation found in the current literatures. One is the independent single-system method, where only BeiDou observations are used without help from other GNSS systems. The other is the two-step GPS-assisted method where in the first step, GPS data are used to resolve some common parameters, such as station coordinates, receiver clocks and zenith tropospheric delay parameters, which are then introduced as known quantities in BeiDou processing in the second step. We conduct a thorough performance comparison between the two methods. Observations from the BeiDou experimental tracking stations and the IGS Multi-GNSS Experiment network from January 1 to March 31, 2013, are processed with the Positioning and Navigation Data Analyst (PANDA) software. The results show that for BeiDou IGSO and MEO satellites, the two-step GPS-assisted method outperforms the independent single-system method in both internal orbit overlap precision and external satellite laser ranging validation. For BeiDou GEO satellites, the two methods show close performances. Zenith tropospheric delays estimated from the first method are very close to those estimated from GPS precise point positioning in the second method, with differences of several millimeters. Satellite clock estimates from the two methods show similar performances when assessing the stability of the BeiDou on board clocks.     

Combination of GNSS and SLR observations using satellite co-locations

Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and allows the estimation of SLR station coordinates at the level of 1–2 cm. The SLR observations to GNSS satellites provide the scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119 mm and −13 mm on average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in the range of a few centimeters up to 5 cm. Scale differences of 0.9 ppb are seen between GNSS and SLR.     

多模GNSS精密卫星钟差估计与分析

对基于历元间差分相位和非差伪距观测值的混合差分卫星钟差估计方法进行了改进,实现了多模全球导航卫星系统（Global Navigation Satellite System,GNSS）卫星钟差联合快速估计。选择了全球分布的50个跟踪站进行实验,对卫星钟差精度进行了分析和精密单点定位（Precise Point Positioning,PPP）验证。结果表明:多模卫星钟差与武汉大学提供的最终精密卫星钟差互差优于0.2 ns,精密单点定位结果与武汉大学发布的最终精密卫星轨道和钟差产品的定位精度相当。     

Improving BeiDou precise orbit determination using observations of onboard MEO satellite receivers

In recent years, the precise orbit determination (POD) of the regional Chinese BeiDou Navigation Satellite System (BDS) has been a hot spot because of its special constellation consisting of five geostationary earth orbit (GEO) satellites and five inclined geosynchronous satellite orbit (IGSO) satellites besides four medium earth orbit (MEO) satellites since the end of 2012. GEO and IGSO satellites play an important role in regional BDS applications. However, this brings a great challenge to the POD, especially for the GEO satellites due to their geostationary orbiting. Though a number of studies have been carried out to improve the POD performance of GEO satellites, the result is still much worse than that of IGSO and MEO, particularly in the along-track direction. The major reason is that the geostationary characteristic of a GEO satellite results in a bad geometry with respect to the ground tracking network. In order to improve the tracking geometry of the GEO satellites, a possible strategy is to mount global navigation satellite system (GNSS) receivers on MEO satellites to collect the signals from GEO/IGSO GNSS satellites so as that these observations can be used to improve GEO/IGSO POD. We extended our POD software package to simulate all the related observations and to assimilate the MEO-onboard GNSS observations in orbit determination. Based on GPS and BDS constellations, simulated studies are undertaken for various tracking scenarios. The impact of the onboard GNSS observations is investigated carefully and presented in detail. The results show that MEO-onboard observations can significantly improve the orbit precision of GEO satellites from metres to decimetres, especially in the along-track direction. The POD results of IGSO satellites also benefit from the MEO-onboard data and the precision can be improved by more than 50% in 3D direction.     

四大GNSS广播星历精度评估与对比分析

分析了 目前广播星历精度评估中存在的问题,详细论述了广播星历精度评估过程中对精密星历进行天线相位中心改正的取值方法,提出了利用单颗星单日钟差均值作二次差对广播星历钟差的系统性偏差进行改正的方法.选取2019-09-01-2019-11-01 共计62天的多模 GNSS 实验(multi-GNSS experiment,...     

GPS天线相位中心改正方法研究

由于天线本身的特性及机械加工等原因,GPS卫星和接收机天线相位中心与其几何中心不重合,从而产生相位中心偏差。某些类型的天线该偏差甚至可达数cm,直接影响高精度GPS测量的精确可靠性[1]。讨论了GAMIT软件在高精度GPS数据处理中进行天线相位中心改正的原理、方法和策略,结合美国IGS观测站及南加州区域站观测数据,对改正方法及策略进行了实验对比与分析。结果表明:对接收机天线相位中心和卫星天线相位中心采用模型改正,而卫星天线相位中心偏移不改正,所得到的基线解算结果较好[2];地面接收机天线方位角的变化对U方向的基线解算结果有较大影响,在高精度GPS测量中,必须进行天线方位角的变化改正。     

GNSS技术在GEO、IGSO航天器中的导航精度与适用性分析

现阶段高轨道航天器导航主要依靠地基测控系统,为了研究全球卫星导航系统(GNSS)技术用于高轨道航天器导航的可行性,对GNSS技术在地球静止轨道(GEO)卫星、倾斜地球同步轨道(IGSO)卫星航天器中的导航精度及适用性展开了分析研究. 采用2021年11月9日的两行轨道数据(TLE)仿真GNSS星座,以不同星下点的GEO卫星和不同倾角的IGSO卫星作为目标星展开导航仿真试验. 实验结果表明:为了满足GNSS解算所需的卫星数量,须通过接收旁瓣信号来增加可见卫星数目. 对GEO目标星而言,当接收机灵敏度高于?169 dB时,导航精度可达30 m;利用GPS对7个不同的GEO或IGSO轨道目标星进行导航实验表明,GPS对目标星导航的位置误差约为35 m;北斗三号(BDS-3)、GPS、GLONASS、Galileo的导航位置误差均值分别为28.03 m、21.16 m、37.15 m、25.09 m,具有良好的内符合精度,其中GPS精度最高,GLONASS精度最低,但大部分时段也在45 m内.      

An investigation of GNSS atomic clock behavior at short time intervals

A technique for obtaining clock measurements from individual GNSS satellites at short time intervals is presented. The methodology developed in this study allows for accurate satellite clock stability analysis without an ultra-stable clock at the ground receiver. Variations in the carrier phase caused by the satellite clock are isolated using a combination of common GNSS carrier-phase processing techniques. Furthermore, the white phase variations caused by the thermal noise of the collection and processing equipment are statistically modeled and removed, allowing for analysis of clock performance at subsecond intervals. Allan deviation analyses of signals collected from GPS and GLONASS satellites reveal distinct intervals of clock noise for timescales less than 100 s. The clock data collected from GPS Block IIA, IIR, IIR-M, and GLONASS satellites reveal similar stability performance at time periods greater than 20 s. The GLONASS clock stability in the 0.6–10 s range, however, is significantly worse than GPS. Applications that rely on ultra-stable clock behavior from the GLONASS satellites at these timescales may therefore require high-rate corrections to estimate and remove oscillator-based errors in the carrier phase.     

GNSS卫星精密定轨综述:现状、挑战与机遇

GNSS卫星精密轨道是高精度GNSS应用的基础与前提,GNSS卫星精密定轨技术也一直都是卫星导航领域的研究重点与热点。本文首先介绍了GNSS星座与跟踪数据概况,梳理了精密定轨函数模型、动力学模型及随机模型构建过程中的关键问题,归纳了低轨星载观测和星间链路观测等多源数据增强GNSS精密定轨的研究进展;然后,从应用的角度总结了当前GNSS精密轨道产品的基本状态,并进行了精度评估;最后,讨论了GNSS精密定轨在大网快速解算、多层次观测数据融合、太阳光压模型精化及高精度实时定轨等方面所面临的挑战,并展望了低轨星座、光钟、激光链路等新技术给GNSS精密定轨带来的机遇。     

M_DCB: Matlab code for estimating GNSS satellite and receiver differential code biases

Global navigation satellite systems (GNSS) have been widely used to monitor variations in the earth’s ionosphere by estimating total electron content (TEC) using dual-frequency observations. Differential code biases (DCBs) are one of the important error sources in estimating precise TEC from GNSS data. The International GNSS Service (IGS) Analysis Centers have routinely provided DCB estimates for GNSS satellites and IGS ground receivers, but the DCBs for regional and local network receivers are not provided. Furthermore, the DCB values of GNSS satellites or receivers are assumed to be constant over 1?day or 1?month, which is not always the case. We describe Matlab code to estimate GNSS satellite and receiver DCBs for time intervals from hours to days; the software is called M_DCB. The DCBs of GNSS satellites and ground receivers are tested and evaluated using data from the IGS GNSS network. The estimates from M_DCB show good agreement with the IGS Analysis Centers with a mean difference of less than 0.7?ns and an RMS of less than 0.4?ns, even for a single station DCB estimate.     

GPS,Galileo, QZSS and IRNSS differential ISBs: estimation and application

Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISBs) corresponding to signals of different constellations but transmitted at identical frequencies can be calibrated, such that only one common pivot satellite is sufficient for inter-system ambiguity resolution at that particular frequency. Recently, many new GNSS satellites have been launched. At the beginning of 2016, there were 12 Galileo IOV/FOC satellites and 12 GPS Block IIF satellites in orbit, while the Indian Regional Navigation Satellite System (IRNSS) had five satellites launched of which four are operational. More launches are scheduled for the coming years. As a continuation of the earlier studies, we analyze the magnitude and stability of the DISBs corresponding to these new satellites. For IRNSS this article presents for the first time DISBs with respect to the L5/E5a signals of GPS, Galileo and QZSS for a mixed-receiver baseline. It is furthermore demonstrated that single-frequency (L5/E5a) ambiguity resolution is tremendously improved when the multi-GNSS observations are all differenced with respect to a common pivot satellite, compared to classical differencing for which a pivot satellite is selected for each constellation.     

GNSS satellite transmit power and its impact on orbit determination

Antenna thrust is a small acceleration acting on Global Navigation Satellite System satellites caused by the transmission of radio navigation signals. Knowledge about the transmit power and the mass of the satellites is required for the computation of this effect. The actual transmit power can be obtained from measurements with a high-gain antenna and knowledge about the properties of the transmit and receive antennas as well as losses along the propagation path. Transmit power measurements for different types of GPS, GLONASS, Galileo, and BeiDou-2 satellites were taken with a 30-m dish antenna of the German Aerospace Center (DLR) located at its ground station in Weilheim. For GPS, total L-band transmit power levels of 50–240 W were obtained, 20–135 W for GLONASS, 95–265 W for Galileo, and 130–185 W for BeiDou-2. The transmit power differs usually only slightly for individual spacecraft within one satellite block. An exception are the GLONASS-M satellites where six subgroups with different transmit power levels could be identified. Considering the antenna thrust in precise orbit determination of GNSS satellites decreases the orbital radius by 1–27 mm depending on the transmit power, the satellite mass, and the orbital period.