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     

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     

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     

Residual errors in altimetry data detected by combinations of single- and dual-satellite crossovers

 The single- and dual-satellite crossover (SSC and DSC) residuals between and among Geosat, TOPEX/Poseidon (T/P), and ERS 1 or 2 have been used for various purposes, applied in geodesy for gravity field accuracy assessments and determination as well as in oceanography. The theory is presented and various examples are given of certain combinations of SSC and DSC that test for residual altimetry data errors, mostly of non-gravitational origin, of the order of a few centimeters. There are four types of basic DSCs and 12 independent combinations of them in pairs which have been found useful in the present work. These are defined in terms of the `mean' and `variable' components of a satellite's geopotential orbit error from Rosborough's 1st-order analytical theory. The remaining small errors, after all altimeter data corrections are applied and the relative offset of coordinate frames between altimetry missions removed, are statistically evaluated by means of the Student distribution. The remaining signal of `non-gravitational' origin can in some cases be attributed to the main ocean currents which were not accounted for among the media or sea-surface corrections. In future, they may be resolved by a long-term global circulation model. Experience with two current models, neither of which are found either to cover the most critical missions (Geosat & TOPEX/Poseidon) or to have the accuracy and resolution necessary to account for the strongest anomalies found across them, is described. In other cases, the residual signal is due to errors in tides, altimeter delay corrections or El Ni?o. (Various examples of these are also presented.) Tests of the combinations of the JGM 3-based DSC residuals show that overall the long-term data now available are well suited for a gravity field inversion refining JGM 3 for low- and resonant-order geopotential harmonics whose signatures are clearly seen in the basic DSC and SSC sets. Received: 15 January 1999 / Accepted: 9 September 1999     

Analytical solar radiation pressure modelling for GLONASS using a pixel array

 A new method for calculating analytical solar radiation pressure models for GNSS spacecraft has been developed. The method simulates the flux of light from the Sun using a pixel array. The method can cope with a high level of complexity in the spacecraft structure and models effects due to reflected light. Models have been calculated and tested for the Russhar global navigation satellite system GLONASS IIv spacecraft. Results are presented using numerical integration of the force model and long-arc satellite laser ranging (SLR) analysis. The integrated trajectory differs from a precise orbit calculated using a network of global tracking stations by circa 2 m root mean square over a 160 000-km arc. The observed − computed residuals for the 400-day SLR arc are circa 28 mm. Received: 23 December 1999 / Accepted: 28 August 2000     

The impact of accelerometry on CHAMP orbit determination

 The contribution of the STAR accelerometer to the CHAMP orbit precision is evaluated and quantified by means of the following results: orbital fit to the satellite laser ranging (SLR) observations, GPS reduced-dynamic vs SLR dynamic orbit comparisons, and comparison of the measured to the modeled non-gravitational accelerations (atmospheric drag in particular). In each of the four test periods in 2001, five CHAMP arcs of 2 days' length were analyzed. The mean RMS-of-fit of the SLR observations of the orbits computed with STAR data or the non-gravitational force model were 11 and 24 cm, respectively. If the accelerometer calibration parameters are not known at least at the few percent level, the SLR orbit fit deteriorates. This was tested by applying a 10% error to the along-track scale factor of the accelerometer, which increased the SLR RMS-of-fit on average to 17 cm. Reference orbits were computed employing the reduced-dynamic technique with GPS tracking data. This technique yields the most accurate orbit positions thanks to the estimation of a large number of empirical accelerations, which compensate for dynamic modeling errors. Comparison of the SLR orbits, computed with STAR data or the non-gravitational force model, to the GPS-based orbits showed that the SLR orbits employing accelerometer observations are twice as accurate. Finally, comparison of measured to modeled accelerations showed that the level of geomagnetic activity is highly correlated with the atmospheric drag model error, and that the largest errors occur around the geomagnetic poles. Received: 7 May 2002 / Accepted: 18 November 2002 Correspondence to: S. Bruinsma Acknowledgments. The TIGCM results were obtained from the CEDAR database. This study was supported by the Centre National d'Etudes Spatiales (CNES). The referees are thanked for their helpful remarks and suggestions.     

The impact of errors in predicted GPS orbits on zenith troposphere delay estimation

The impact of precise GPS ephemeris errors on estimated zenith tropospheric delays (ZTD) is studied for applications in meteorology. First, the status of IGS ultra-rapid orbit prediction is presented and specific problems are outlined. Second, a simplified analytical solution of the impact of ephemeris errors on estimated ZTDs is presented. Two widely used methods are studied—the precise point positioning technique (PPP) and the double-difference network approach. A simulation experiment is additionally conducted for the network approach to assess the capability of ephemeris error compensation by the ambiguities. An example of marginal requirements for ephemeris accuracy is presented, assuming the compensation by ZTD only and admitting the error of 1 cm in ZTD. The requirement for the maximum orbit error 1 cm for radial and 8 cm for tangential position components using PPP approach, versus 217 cm (radial) and 19 cm (tangential) using network solution. Furthermore, an assessment of possible compensations of ephemeris errors by other estimated parameters was considered. In radial orbit position, an error of a few meters can be still absorbed by satellite clocks (96%) and phase ambiguities (96%) even for the PPP technique. A tangential orbit position error up to 16 cm for PPP and 38 cm for network solutions should not bias ZTD by more than 1 cm, but any bigger error could, in general. The error impact on ZTD in such cases depends on the compensation ability of ambiguities and clocks (PPP).     

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.     

The ERS-2 altimetric bias and gravity field enhancement using dual crossovers between ERS and TOPEX/Poseidon

 Dual satellite crossovers (DXO) between the two European Remote Sensing satellites ERS-1 and ERS-2 and TOPEX/Poseidon are used to (1) refine the Earth's gravity field and (2) extend the study of the ERS-2 altimetric range stability to cover the first four years of its operation. The enhanced gravity field model, AGM-98, is validated by several methodologies and will be shown to provide, in particular, low geographically correlated orbital error for ERS-2. For the ERS-2 altimetric range study, TOPEX/Poseidon is first calibrated through comparison against in situ tide gauge data. A time series of the ERS-2 altimeter bias has been recovered along with other geophysical correction terms using tables for bias jumps in the range measurements at the single point target response (SPTR) events. On utilising the original version of the SPTR tables the overall bias drift is seen to be 2.6±1.0 mm/yr with an RMS of fit of 12.2 mm but with discontinuities at the centimetre level at the SPTR events. On utilising the recently released revised tables, SPTR2000, the drift is better defined at 2.4±0.6 mm/yr with the RMS of fit reduced to 3.7 mm. Investigations identify the sea-state bias as a source of error with corrections affecting the overall drift by close to 1.2 mm/yr. Received: 25 May 2000 / Accepted: 24 January 2001     

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     

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.     

Analytical solution of perturbed circular motion: application to satellite geodesy

 Starting from the analytical theory of perturbed␣circular motions presented in Celestial Mechanics (Bois 1994) and from specific extended formulations of the perturbations in a uniformly rotating plane of constant inclination, this paper presents an extended formulation of the solution. The actual gain made through this extension is the establishment of a first-order predictive theory written in spherical coordinates and thus free of singularities, whose perturbations are directly expressed in the local orbital frame generally used in satellite geodesy. This new formulation improves the generality, the precision and the field of applications of the theory. It is particularly devoted to the analysis of satellite position perturbations for satellites in low eccentricity orbits usually used for many Earth observation applications. An application to the TOPEX/Poseidon (T/P) orbit is performed. In particular, contour maps are provided which show the geographical location of orbit differences coming from geopotential coefficient differences of two recent gravity field models. Comparison of predicted radial and along-track orbit differences with respect to numerical results provided by the French group (CNES, in Toulouse) in charge of the T/P orbit are convincing. Received 22 January 1996; Accepted 19 September 1996     

Prediction of surface horizontal displacements, and gravity and tilt changes caused by filling the Three Gorges Reservoir

 Horizontal displacements, and gravity and tilt changes induced by filling the Three Gorges Reservoir are modeled using elastic loading Green functions. When the water surface reaches its highest level, the effects become maximum on the reservoir banks. The longitudinal and latitudinal components of the horizontal displacements reach −8.2 and 7.7 mm respectively, gravity is increased by up to 3.4 mGal, and the prime vertical and meridian components of the tilt changes are −7.8 and −17.5 arcseconds respectively. Accordingly, the filling of the reservoir will influence values observed from global positioning system (GPS), gravimetry and tilt measurements in the area. The results given can be used to provide important corrections for extracting earthquake-related signals from observed data. Received: 19 January 2001 / Accepted: 3 September 2001     

Tectonic plate motion and co-seismic steps surveyed by DORIS field beacons: the New Hebrides experiment

 The New Hebrides experiment consisted of setting up a pair of DORIS beacons in remote tropical islands in the southwestern Pacific, between 1993 and 1997. Because of orbitography requirements on TOPEX/Poséidon, the beacons were only transmitting to SPOT satellites. Root-mean-square (RMS) scatters at the centimeter level on the latitude and vertical components were achieved, but 2-cm RMS scatters affected the longitude component. Nevertheless, results of relative velocity (123 mm/year N250°) are very consistent with those obtained using the global positioning system (GPS) (126 mm/yr N246°). The co-seismic step (12 mm N60°) related to the Walpole event (M _W = 7.7) is consistent with that derived from GPS (10 mm N30°) or from the centroid moment tensor (CMT) of the quake (12 mm N000°). Received: 19 November 1999 / Accepted: 17 May 2000     

An approach to GLONASS ambiguity resolution

 When processing global navigation satellite system (GLONASS) carrier phases, the standard double-differencing (DD) procedure cannot cancel receiver clock terms in the DD phase measurement equations due to the multiple frequencies of the carrier phases. Consequently, a receiver clock parameter has to be set up in the measurement equations in addition to baseline components and DD ambiguities. The resulting normal matrix unfortunately becomes singular. Methods to deal with this problem have been proposed in the literature. However, these methods rely on the use of pseudo-ranges. As pseudo-ranges are contaminated by multi-path and hardware delays, biases in these pseudo-ranges are significant, which may result in unreliable ambiguity resolution. A new approach is addressed that is not sensitive to the biases in the pseudo-ranges. The proposed approach includes such steps as converting the carrier phases to their distances to cancel the receiver clock errors, and searching for the most likely single-differenced (SD) ambiguity. Based on the results from the theoretical investigation, a practical procedure for GLONASS ambiguity resolution is presented. The initial experimental results demonstrate that the proposed approach is useable in cases of GLONASS and combined global positioning system (GPS) and GLONASS positioning. Received: 19 August 1998 / Accepted: 12 November 1999     

Gravitational perturbation theory for intersatellite tracking

 An analytical gravitational perturbation theory for the intersatellite tracking range and range-rate measurement between two satellites is developed. The satellite-to-satellite tracking (SST) range data measure the difference between the position perturbations of two satellites along the direction of the intersatellite range. The SST range-rate data measure the difference between the velocity perturbations along the direction of the intersatellite range, and the difference of the position perturbation along the direction perpendicular to the intersatellite range (cross-range). The SST range and range rate depend on different orbital excitations for mapping the gravity field. For the Gravity Recovery and Climate Experiment (GRACE), approximately 97% of the geopotential coefficient pairs produce perturbations with a root-mean-square larger than 1 m on the range and 0.1 m/sec on the range rate based on the EGM96 gravity field truncated at degree and order 140. Results in this study showed that ocean tides produce significant perturbations in the range and range-rate measurements. An ocean tide field with a higher degree and order (>70) is required to model the ocean tide perturbations on the intersatellite range and range-rate measurement. Received: 17 May 2000 / Accepted: 3 September 2001     

On fine orbit selection for particular geodetic and oceanographic missions involving passage through resonances

 The identification of mean semi-major axes (suitably defined) for satellite orbits to satisfy a variety of requirements for geodesy, geophysics and oceanography, in terms of repeat orbits (with orbital resonances), is investigated. Various options for the definition of semi-major axis, from the viewpoint of satellite dynamics, are described. Simple simulations of the expected resonant changes in inclination are presented, and tools for the analysis of orbit resonances to extract certain lumped harmonic coefficients of the geopotential (e.g. from the very precise CHAMP orbit) are resurrected. Finally, a preliminary example of the 46th-order resonance analysis possible for CHAMP, based on the mean orbital elements produced by GFZ (GeoForschungs Zentrum) for ephemeris prediction, is presented. Received: 10 July 2001 / Accepted: 17 July 2002 Correspondence to: J. Klokočník at Ondřejov Observatory Acknowledgements. We thank Prof. Dr. Ch. Reigber, Dr. P. Schwintzer, Dr. T. Gruber and Dr. R. K?nig from GFZ Potsdam for various consultations and discussions, and for the CHAMP two-line mean elements. This investigation was performed under the aegis of CEDR (Center for Earth's Dynamics Research, Prague-Ondřejov); it has been supported by project LN00A005 (provided by the Ministry of Education of the Czech Republic) and by grant A 3004 of the Grant Agency of the Academy of Sciences of the Czech Republic.     

Short-arc analysis of intersatellite tracking data in a gravity mapping mission

 A technique for the analysis of low–low intersatellite range-rate data in a gravity mapping mission is explored. The technique is based on standard tracking data analysis for orbit determination but uses a spherical coordinate representation of the 12 epoch state parameters describing the baseline between the two satellites. This representation of the state parameters is exploited to allow the intersatellite range-rate analysis to benefit from information provided by other tracking data types without large simultaneous multiple-data-type solutions. The technique appears especially valuable for estimating gravity from short arcs (e.g. less than 15 minutes) of data. Gravity recovery simulations which use short arcs are compared with those using arcs a day in length. For a high-inclination orbit, the short-arc analysis recovers low-order gravity coefficients remarkably well, although higher-order terms, especially sectorial terms, are less accurate. Simulations suggest that either long or short arcs of the Gravity Recovery and Climate Experiment (GRACE) data are likely to improve parts of the geopotential spectrum by orders of magnitude. Received: 26 June 2001 / Accepted: 21 January 2002     

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。     

Data gaps in finite-dimensional boundary value problems for satellite gradiometry

 In the framework of a boundary value problem (BVP), when areas on the boundary are void of data the solution of the problem becomes undetermined and clearly more difficult. Physically, this could be the situation in which a gradiometer on a satellite on a perfectly circular orbit covers a sphere with measured second radial derivatives: if the satellite orbit is not polar, there are caps at satellite altitude which are not covered by data. A solution is presented based on an iterative algorithm, under the hypothesis of using a finite-dimensional model as is usually done in the time-wise approach. The convergence of the iterative solution is proved and a numerical example is shown to confirm the theoretical result. Received: 14 August 2000 / Accepted: 12 April 2001