Rapid orbit determination of LEO satellites using IGS clock and ephemeris products

Different types of GPS clock and orbit data provided by the International GPS Service (IGS) have been used to assess the accuracy of rapid orbit determination for satellites in low Earth orbit (LEO) using spaceborne GPS measurements. To avoid the need for reference measurements from ground-based reference receivers, the analysis is based on an undifferenced processing of GPS code and carrier-phase measurements. Special attention is therefore given to the quality of GPS clock data that directly affects the resulting orbit determination accuracy. Interpolation of clock data from the available 15 min grid points is identified as a limiting factor in the use of IGS ultra-rapid ephemerides. Despite this restriction, a 10-cm orbit determination accuracy can be obtained with these products data as demonstrated for the GRACE-B spacecraft during selected data arcs between 2002 and 2004. This performance may be compared with a 5-cm orbit determination accuracy achievable with IGS rapid and final products using 5 min clock samples. For improved accuracy, high-rate (30 s) clock solutions are recommended that are presently only available from individual IGS centers. Likewise, a reduced latency and more frequent updates of IGS ultra-rapid ephemerides are desirable to meet the requirements of upcoming satellite missions for near real-time and precise orbit determination.     

Research on a method of real-time combination of precise GPS clock corrections

GPS Solutions - The acquisition of real-time satellite orbit and clock corrections is necessary for real-time PPP. There are nine International GNSS Service (IGS) analysis centers (ACs) that...     

An a priori solar radiation pressure model for the QZSS Michibiki satellite

It has been noted that the satellite laser ranging (SLR) residuals of the Quasi-Zenith Satellite System (QZSS) Michibiki satellite orbits show very marked dependence on the elevation angle of the Sun above the orbital plane (i.e., the \(\beta \) angle). It is well recognized that the systematic error is caused by mismodeling of the solar radiation pressure (SRP). Although the error can be reduced by the updated ECOM SRP model, the orbit error is still very large when the satellite switches to orbit-normal (ON) orientation. In this study, an a priori SRP model was established for the QZSS Michibiki satellite to enhance the ECOM model. This model is expressed in ECOM’s D, Y, and B axes (DYB) using seven parameters for the yaw-steering (YS) mode, and additional three parameters are used to compensate the remaining modeling deficiencies, particularly the perturbations in the Y axis, based on a redefined DYB for the ON mode. With the proposed a priori model, QZSS Michibiki’s precise orbits over 21 months were determined. SLR validation indicated that the systematic \(\beta \)-angle-dependent error was reduced when the satellite was in the YS mode, and better than an 8-cm root mean square (RMS) was achieved. More importantly, the orbit quality was also improved significantly when the satellite was in the ON mode. Relative to ECOM and adjustable box-wing model, the proposed SRP model showed the best performance in the ON mode, and the RMS of the SLR residuals was better than 15 cm, which was a two times improvement over the ECOM without a priori model used, but was still two times worse than the YS mode.     

Impact of Earth radiation pressure on GPS position estimates

GPS satellite orbits available from the International GNSS Service (IGS) show a consistent radial bias of up to several cm and a particular pattern in the Satellite Laser Ranging (SLR) residuals, which are suggested to be related to radiation pressure mismodeling. In addition, orbit-related frequencies were identified in geodetic time series such as apparent geocenter motion and station displacements derived from GPS tracking data. A potential solution to these discrepancies is the inclusion of Earth radiation pressure (visible and infrared) modeling in the orbit determination process. This is currently not yet considered by all analysis centers contributing to the IGS final orbits. The acceleration, accounting for Earth radiation and satellite models, is introduced in this paper in the computation of a global GPS network (around 200 IGS sites) adopting the analysis strategies from the Center for Orbit Determination in Europe (CODE). Two solutions covering 9 years (2000–2008) with and without Earth radiation pressure were computed and form the basis for this study. In previous studies, it has been shown that Earth radiation pressure has a non-negligible effect on the GPS orbits, mainly in the radial component. In this paper, the effect on the along-track and cross-track components is studied in more detail. Also in this paper, it is shown that Earth radiation pressure leads to a change in the estimates of GPS ground station positions, which is systematic over large regions of the Earth. This observed “deformation” of the Earth is towards North–South and with large scale patterns that repeat six times per GPS draconitic year (350 days), reaching a magnitude of up to 1 mm. The impact of Earth radiation pressure on the geocenter and length of day estimates was also investigated, but the effect is found to be less significant as compared to the orbits and position estimates.     

Anomalous harmonics in the spectra of GPS position estimates

Prior studies of the power spectra of GPS position time series have found pervasive seasonal signals against a power-law background of flicker noise plus white noise. Dong et al. (2002) estimated that less than half the observed GPS seasonal power can be explained by redistributions of geophysical fluid mass loads. Much of the residual variation is probably caused by unidentified GPS technique errors and analysis artifacts. Among possible mechanisms, Penna and Stewart (2003) have shown how unmodeled analysis errors at tidal frequencies (near 12- and 24-hour periods) can be aliased to longer periods very efficiently. Signals near fortnightly, semiannual, and annual periods are expected to be most seriously affected. We have examined spectra for the 167 sites of the International GNSS (Global Navigation Satellite Systems) Service (IGS) network having more than 200 weekly measurements during 1996.0–2006.0. The non-linear residuals of the weekly IGS solutions that were included in ITRF2005, the latest version of the International Terrestrial Reference Frame (ITRF), have been used. To improve the detection of common-mode signals, the normalized spectra of all sites have been stacked, then boxcar smoothed for each local north (N), east (E), and height (H) component. The stacked, smoothed spectra are very similar for all three components. Peaks are evident at harmonics of about 1 cycle per year (cpy) up to at least 6 cpy, but the peaks are not all at strictly 1.0 cpy intervals. Based on the 6th harmonic of the N spectrum, which is among the sharpest and largest, and assuming a linear overtone model, then a common fundamental of 1.040 ± 0.008 cpy can explain all peaks well, together with the expected annual and semiannual signals. A flicker noise power-law continuum describes the background spectrum down to periods of a few months, after which the residuals become whiter. Similar sub-seasonal tones are not apparent in the residuals of available satellite laser ranging (SLR) and very long baseline interferometry (VLBI) sites, which are both an order of magnitude less numerous and dominated by white noise. There is weak evidence for a few isolated peaks near 1 cpy harmonics in the spectra of geophysical loadings, but these are much noisier than for GPS positions. Alternative explanations related to the GPS technique are suggested by the close coincidence of the period of the 1.040 cpy frequency, about 351.2 days, to the “GPS year”; i.e., the interval required for the constellation to repeat its inertial orientation with respect to the sun. This could indicate that the harmonics are a type of systematic error related to the satellite orbits. Mechanisms could involve orbit modeling defects or aliasing of site-dependent positioning biases modulated by the varying satellite geometry.     

Zero-difference GPS ambiguity resolution at CNES–CLS IGS Analysis Center

CNES (Centre National d’Etudes Spatiales) and CLS (Collecte Localisation Satellites) became an International GNSS Service (IGS) Analysis Center (AC) the 20th of May 2010. Since 2009, we are using the integer ambiguity fixing at the zero-difference level strategy in our software package (GINS/Dynamo) as an alternative to classical differential approaches. This method played a key role among all the improvements in the GPS processing we made during this period. This paper provides to the users the theoretical background, the strategies and the models used to compute the products (GPS orbits and clocks, weekly station coordinate estimates and Earth orientation parameters) that are submitted weekly to the IGS. The practical realization of the two-step, ambiguity-fixing scheme (wide-lane and narrow-lane) is described in detail. The ambiguity fixing improved our orbit overlaps from 6 to 3?cm WRMS in the tangential and normal directions. Since 2008, our products have been also regularly compared to the IGS final solutions by the IGS Analysis Center Coordinator. The joint effects of ambiguity fixing and dynamical model changes (satellite solar radiation pressure and albedo force) improved the consistency with IGS orbits from 35 to 18?mm 3D-WRMS. Our innovative strategy also gives additional powerful properties to the GPS satellite phase clock solutions. Single receiver (zero-difference) ambiguity resolution becomes possible. An overview of the applications is given.     

精密卫星钟差加密方法及其对星载GPS低轨卫星定轨精度影响

系统分析、比较了几种精密卫星钟差加密方法，研究了利用全球分布的IGS永久跟踪站的GPS观测数据估计高采样率卫星钟差参数的原理与方法，并将各种卫星钟差加密方法得到的结果与IGS数据分析中心估计的卫星钟差结果相比较。最后将不同加密方法得出的精密卫星钟差结果用于基于星载GPS双频非差观测值的CHAMP低轨卫星的定轨，并将不同方法得到的定轨精度进行比较。结果表明，利用地面跟踪站的GPS观测数据，可高精度、高密度地估计GPS卫星钟差，估计精度可达0．1～0．5ns。经地面GPS跟踪站数据估计的GPS卫星钟差，应用于基于PPP方法的低轨卫星定轨，其定轨精度在10cm以内。     

A New Solar Radiation Pressure Model for GPS Satellites

The largest error in currently used GPS orbit models is due to the effect of solar radiation pressure. Over the last few years many improvements were made in modeling the orbits of GPS satellites within the International GPS Service (IGS). Howeer, most improvements were achieved by increasing the number of estimated orbit and/or solar radiation pressure parameters. This increase in the number of estimated satellite parameters weakens the solutions of all estimated parameters (not only orbit parameters). Because of correlations the additional orbit parameters may introduce biases in other estimated quantities, for example the length of day. We present a recently developed solar radiation pressure model for the GPS satellites. This model is based on experiences and results gained at the Center for Orbit Determination in Europe (CODE) in the context of its IGS activities since June 1992. The performance of the new model is almost an order of magnitude better than that of the existing ROCK models. It also allows a reduction of the number of orbit parameters that have to be estimated. ? 1999 John Wiley & Sons, Inc.     

Evaluation of GPS orbit prediction strategies for the IGS Ultra-rapid products

The International GNSS Service (IGS) provides Ultra-rapid GPS & GLONASS orbits every 6 h. Each product is composed of 24 h of observed orbits with predicted orbits for the next 24 h. We have studied how the orbit prediction performance varies as a function of the arc length of the fitted observed orbits and the parameterization strategy used to estimate the empirical solar radiation pressure (SRP) effects. To focus on the dynamical aspects of the problem, nearly ideal conditions have been adopted by using IGS Rapid orbits and known earth rotation parameters (ERPs) as observations. Performance was gauged by comparison with Rapid orbits as truth by examining WRMS and median orbit differences over the first 6-h and the full 24-h prediction intervals, as well as the stability of the Helmert frame alignment parameters. Two versions of the extended SRP orbit model developed by the Centre for Orbit Determination in Europe (CODE) were tested. Adjusting all nine SRPs (offsets plus once-per-revolution sines and cosines in each satellite-centered frame direction) for each satellite shows smaller mean sub-daily, scale, and origin translation differences. On the other hand, eliminating the four once-per-revolution SRP parameters in the sun-ward and the solar panel axis directions yields orbit predictions that are much more rotationally stable. We found that observed arc lengths of 40–45 h produce the most stable and accurate predictions during 2010. A combined strategy of rotationally aligning the 9 SRP results to the 5 SRP frame should give optimal predictions with about 13 mm mean WRMS residuals over the first 6 h and 50 mm over 24 h. Actual Ultra-rapid performance will be degraded due to the unavoidable rotational errors from ERP predictions.     

利用SLR检核GPS35卫星精密轨道

论述了利用SLR检核IGS提供的GPS卫星精密轨道的方法。采用2005年9月1日到30日的SLR观测数据对IGS提供的GPS35卫星精密轨道进行了检核实验,实验结果表明,SLR观测站存在一定的系统偏差,IGS提供的精密轨道没有明显的系统偏差,其精度优于2 cm。     

A simplified yaw-attitude model for eclipsing GPS satellites

A simplified yaw-attitude modeling, consistent with Bar-Sever (1996), has been implemented and tested in the NRCan PPP software. For Block IIR GPS satellite it is possible to model yaw-attitude control during eclipsing periods by using the constant hardware yaw rate of 0.20°/s. The Block IIR satellites maintain the nominal yaw attitude even during a shadow crossing (Y. E. Bar-Sever, private communication, 2007), except for the noon and shadow midnight turn maneuvers, both of which can be modeled and last up to 15 min. Thus, for Block IIR satellites it is possible to maintain continuous satellite clock estimation even during eclipsing periods. For the Block II/IIA satellites, it is possible to model satisfactorily the noon turns and also shadow crossing, thanks to the permanent positive yaw bias of 0.5°, implemented in November 1995. However, in order to model the Block II/IIA shadow crossings, satellite specific yaw rates should be used, either solved for or averaged yaw-rate solutions. These yaw rates as estimated by the Jet Propulsion Laboratory (JPL) can differ significantly from the nominal hardware values. The Block II/IIA post-shadow recovery periods, which last about 30 min, should be considered uncertain and cannot be properly modeled. Data from post-shadow recovery periods should, therefore, not be used in precise global GPS analyses (Bar-Sever 1996). For high-precision applications, it is essential that users implement a yaw-attitude model, which is consistent with the generation of the satellite clocks. Initial testing and analyses, based on the IGS and AC Final orbits and clocks have revealed that during eclipsing periods, significant inconsistencies in yaw-attitude modeling still exist amongst the IGS Analyses Centers, which contribute to the errors of the IGS Final clock combinations.     

一种基于IGS超快星历的区域性实时精密单点定位方法

实时GPS精密单点定位需要实时的卫星轨道和钟差产品,为此提出一种利用区域GPS连续运行参考站和IGS发布的IGU超快轨道进行实时精密单点定位的方法.该方法首先利用连续运行参考站观测数据与IGU超快轨道预报部分进行实时GPS卫星钟差的估计,然后利用估计得到的实时GPS卫星钟差产品和IGU超快轨道预报部分,进行用户GPS接...     

太阳活动对GPS卫星广播星历的影响

采用了切比雪夫拟合多项式内插IGS精密星历,计算了GPS卫星广播星历轨道误差,比较了其在太阳活动谷值和峰值时的误差,讨论了其与太阳活动状况的关系。     

New IGS Station and Satellite Clock Combination

Following the principles set forth in the Position Paper #3 at the 1998 Darmstadt Analysis Center (AC) Workshop on the new International GPS Service (IGS) International Terrestrial Reference Frame (ITRF) realization and discussions at the 1999 La Jolla AC workshop, a new clock combination program was developed. The program allows for the input of both SP3 and the new clock (RINEX) format (ftp://igsch.jpl.nasa.gov//igscb/data/format/rinex_clock.txt). The main motivation for this new development is the realization of the goals of the IGS/BIPM timing project. Besides this there is a genuine interest in station clocks and a need for a higher sampling rate of the IGS clocks (currently limited to 15 min due to the SP3 format). The inclusion of station clocks should also allow for a better alignment of the individual AC solutions and should enable the realization of a stable GPS time-scale. For each input AC clock solution the new clock combination solves and corrects for reference clock errors/instabilities as well as satellite/station biases, geocenter and station/satellite orbit errors. External station clock calibrations and/or constraints, such as those resulting from the IGS/BIPM timing pilot project, can be introduced via a subset of the fiducial timing station set, to facilitate a precise and consistent IGS UTC realization for both station and satellite combined clock solutions. Furthermore, the new clock combination process enforces strict strict conformity and consistency with the current and future IGS standards. The new clock combination maintains orbit/clock consistency at millimeter level, which is comparable to the best AC orbit/clock solutions. This is demonstrated by static GIPSY precise point positioning tests using GPS week 0995 data for stations in both Northern and Southern Hemispheres and similar tests with the Bernese software using more recent data from GPS week 1081. ? 2001 John Wiley & Sons, Inc.     

GPS精密卫星钟差估计与分析

探讨了GPS精密卫星钟差的估计方法,并分析了伪距与相位观测值对估计精度的影响。基于PAN-DA软件,采用全球均匀分布的40个IGS跟踪站的实测数据,对GPS精密钟差进行估计与分析。试验结果表明,目前采用PANDA软件估计的GPS精密卫星钟差与IGS事后精密卫星钟差比较,互差优于0.2 ns,与国际IGS各分析中心估计的卫星钟差精度相当。     

Precise Point Positioning Using IGS Orbit and Clock Products

The contribution details a post-processing approach that used undifferentiated dual-frequency pseudorange and carrier phase observations along with IGS procise orbit products, for stand-alone precise geodetic point positioning (static or kinematic) with cm precision. This is possible if one takes advantage of the satellite clock estimates available with the satellite coordinates in the IGS precise orbit products and models systematic effects that cause cm variations in the satelite to user range. This paper will describe the approach, summarize the adjustment procedure, and specify the earth- and space-based models that must be implementetd to achieve cm-level positioning in static mode. Furthermore, station tropospheric zenth path delays with cm precision and GPS receiver clock estimates procise to 0.1 ns are also obtained. ? 2001 John Wiley & Sons, Inc.     

Is the long-term variation of the estimated GPS differential code biases associated with ionospheric variability?

The global positioning system (GPS) differential code biases (DCB) provided by the International GNSS Service (IGS) show solar-cycle-like variation during 2002–2013. This study is to examine whether this variation of the GPS DCBs is associated with ionospheric variability. The GPS observations from low earth orbit (LEO) satellites including CHAMP, GRACE and Jason-1 are used to address this issue. The GPS DCBs estimated from the LEO-based observations at different orbit altitudes show a similar tendency as the IGS DCBs. However, this solar-cycle-like dependency is eliminated when the DCBs of 13 continuously operating GPS satellites are constrained to zero-mean. Our results thus revealed that ionospheric variation is not responsible for the long-term variation of the GPS DCBs. Instead, it is attributed to the GPS satellite replacement with different satellite types and the zero-mean condition imposed on all satellite DCBs.     

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%。     

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.     

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.