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     

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     

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.     

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     

Laser-based validation of GLONASS orbits by short-arc technique

 The International GLONASS Experiment (IGEX-98) was carried out between 19 October 1998 and 19 April 1999. Among several objectives was the precise orbit determination of GPS and GLONASS satellites and its validation by laser ranging observations. Local laser-based orbit corrections (radial, tangential and normal components in a rotating orbital local reference frame) are computed using a geometrical short-arc technique. The order of magnitude of these corrections is at the level of few decimeters, depending on the considered components. The orbit corrections are analyzed as a function of several parameters (date, orbital plane, geographical area). The mean corrections are at the level of several centimeters. However, when averaging over the entire campaign and for all the satellites, no mean radial, tangential and normal orbit corrections are found. The origin of the observed corrections is considered (errors due to the geocentric gravitational constant, the non-gravitational forces, the thermal equilibrium of on-board equipment, the reference systems, the location and the signature of the retroreflector array, and the precision of the satellite laser ranges). Some features are also due to errors in the radio-tracking GLONASS orbits. Further investigations will be needed to better understand the origin of various biases. Received: 17 February 2000 / Accepted: 31 January 2001     

ITRS, PZ-90 and WGS 84: current realizations and the related transformation parameters

 The first results of the International GLONASS Experiment 1998 (IGEX-98) campaign have provided significant material to illustrate the mutual benefits of the GLONASS system and the realization of the International Terrestrial Reference System (ITRS). A specific aspect, namely the relationship between the World Geodetic System 1984 (WGS 84) and the PZ-90 system using ITRS as a primary standard, is investigated. A review of current works is carried out. A transformation strategy is proposed for the three systems based on recent results from IGEX-98 and an independent set of transformation parameters derived by the Jet Propulsion Laboratory from ITRF97 and PZ-90 coordinates for 16 global stations. Received: 9 June 2000 / Accepted: 12 June 2001     

Stochastic assessment of GPS carrier phase measurements for precise static relative positioning

 Global positioning system (GPS) carrier phase measurements are used in all precise static relative positioning applications. The GPS carrier phase measurements are generally processed using the least-squares method, for which both functional and stochastic models need to be carefully defined. Whilst the functional model for precise GPS positioning is well documented in the literature, realistic stochastic modelling for the GPS carrier phase measurements is still both a controversial topic and a difficult task to accomplish in practice. The common practice of assuming that the raw GPS measurements are statistically independent in space and time, and have the same accuracy, is certainly not realistic. Any mis-specification in the stochastic model will inevitably lead to unreliable positioning results. A stochastic assessment procedure has been developed to take into account the heteroscedastic, space- and time-correlated error structure of the GPS measurements. Test results indicate that the reliability of the estimated positioning results is improved by applying the developed stochastic assessment procedure. In addition, the quality of ambiguity resolution can be more realistically evaluated. Received: 13 February 2001 / Accepted: 3 September 2001     

Combination procedure for length-of-day time series according to the noise frequency behavior

 Length-of-day (LOD) estimates from seven Global Positioning System (GPS) and three satellite laser ranging (SLR) analysis centers were combined into an even-spaced time series for a 27-month period (1996–1998). This time series was compared to the multi-technique Earth-orientation-parameter (EOP) combined solution (C04) derived at the Central Bureau of the International Earth Rotation Service (IERS/CB). Due to inhomogeneities in the different series derived from the various techniques (time, length, quality, and spatial resolution), the concept of a combined solution is justified. The noise behavior in LOD for different techniques varies with frequency; the data series were divided into frequency windows after removing both biases and trends. Different weight factors were assigned in each window, discriminating by technique, and produced one-technique combined solutions. Finally, these one-technique combined solutions were combined to obtain the final multi-technique solution. The LOD combined time series obtained by the present method based on the frequency windows combined series (FWCS) is very close to the IERS C04 solution. It could be useful to generate a new LOD reference time series to be used in the study of high-frequency variations of Earth rotation. Received: 28 March 2000 / Accepted: 15 February 2001     

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     

Analysis of the first year of Earth rotation parameters with a sub-daily resolution gained at the CODE processing center of the IGS

 The solutions of the CODE Analysis Center submitted to the IGS, the International Global Position System (GPS) Service for Geodynamics, are based on three days of observation of about 80–100 stations of the IGS network. The Earth rotation parameters (ERPs) are assumed to vary linearly over the three days with respect to an a priori model. Continuity at the day boundaries as well as the continuity of the first derivatives are enforced by constraints. Since early April 1995 CODE has calculated a new ERP series with an increased time resolution of 2 hours. Again continuity is enforced at the 2-hours-interval boundaries. The analysis method is described, particularly how to deal with retrograde diurnal terms in the ERP series which may not be estimated with satellite geodetic methods. The results obtained from the first year of data covered by the time series (time interval from 4 April 1995 to 30 June 1996) are also discussed. The series is relatively homogeneous in the sense of the used orbit model and the a priori model for the ERPs. The largest source of excitation at daily and sub-daily periods is likely to be the effect of the ocean tides. There is good agreement between the present results and Topex/Poseidon ocean tide models, as well as with models based on Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data. Non-oceanic periodic variations are also observed in the series. Their origin is most probably a consequence of the GPS solution strategy; other possible sources are the atmospheric tides. Received: 13 July 1999 / Accepted: 21 March 2000     

How to handle topography in practical geoid determination: three examples

 Three different methods of handling topography in geoid determination were investigated. The first two methods employ the residual terrain model (RTM) remove–restore technique, yielding the quasigeoid, whereas the third method uses the classical Helmert condensation method, yielding the geoid. All three methods were used with the geopotential model Earth Gravity Model (1996) (EGM96) as a reference, and the results were compared to precise global positioning system (GPS) levelling networks in Scandinavia. An investigation of the Helmert method, focusing on the different types of indirect effects and their effects on the geoid, was also carried out. The three different methods used produce almost identical results at the 5-cm level, when compared to the GPS levelling networks. However, small systematic differences existed. Received: 18 March 1999 / Accepted: 21 March 2000     

From GPS and GLONASS via EGNOS to Galileo – Positioning and Navigation in the Third Millennium

Positioning and navigation – as are presently possible with the American Global Positioning System (GPS) and the Russian GLONASS system – is briefly reviewed. Deficiencies, which have led to augmentations like the European Geostationary Navigation Overlay System (EGNOS), are outlined. Europe's decision to get involved in the definition and possible set-up of a Global Navigation Satellite System (GNSS) of the second generation (GNSS-2), called Galileo, is discussed in detail as well as the GPS modernization program that might take place during the sample phase. Finally, some brief thoughts on the benefit of GNSS-2 for geodesy and surveying are given. ? 2000 John Wiley & Sons, Inc.     

GPS-based precise orbit determination of the very low Earth-orbiting gravity mission GOCE

 A prerequisite for the success of future gravity missions like the European Gravity field and steady-state Ocean Circulation Explorer (GOCE) is a precise orbit determination (POD). A detailed simulation study has been carried out to assess the achievable orbit accuracy based on satellite-to-satellite tracking (SST) by the US global positioning system (GPS) and in conjunction the implications for gravity field determination. An orbit accuracy at the few centimeter level seems possible, sufficient to support the GOCE gravity mission and in particular its gravity gradiometer. Received: 21 January 2000 / Accepted: 4 July 2000     

Accurate absolute GPS positioning through satellite clock error estimation

 An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore, the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them. Received: 16 May 2000 / Accepted: 23 October 2000     

Integer estimation in the presence of biases

 Carrier phase ambiguity resolution is the key to fast and high-precision GNSS (Global Navigation Satellite System) kinematic positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. Very high success rates are therefore required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower the success rate and thus increase the chance of unsuccessful ambiguity resolution. The performance of integer ambiguity estimation in the presence of such biases is studied. Particular attention is given to integer rounding, integer bootstrapping and integer least squares. Lower and upper bounds, as well as an exact and easy-to-compute formula for the bias-affected success rate, are presented. These results will enable the evaluation of the bias robustness of ambiguity resolution. Received: 28 September 2000 / Accepted: 29 March 2001     

On determination of heights by using terrestrial clocks and GPS signals

 Considering a GPS satellite and two terrestrial stations, two types of equations are derived relating the heights of the two stations to the measured data (frequency ratio or clock rate differences) and the coordinates and velocity components of all three participating objects. The potential possibilities of using such relations for the determination of heights (in terms of geopotential numbers or orthometric heights) are discussed. Received: 6 December 2000 / Accepted: 9 July 2001     

Integrity Monitoring of IGEX-98 Data,Part I: Availability

The International GLONASS Experiment 1998 (IGEX-98) was the first international tracking campaign of the Russian counterpart to the Global Positioning System (GPS), GLONASS. Started in October 1998, the campaign was originally scheduled to last for three months. However, the launch of additional GLONASS satellites and a widespread enthusiasm among the participants led to an indefinite continuation of the campaign on a “best effort” basis. At the Delft University of Technology, the data of six IGEX-98 stations have been analyzed in detail with integrity monitoring software, developed at the Department of Mathematical Geodesy and Positioning of the University. The software aims to detect outliers and slips in code and phase observations in real time. In addition, the software also allows the validation of the information contained in the broadcast navigation messages. The results of the IGEX-98 data analyses will be presented in a three-part series. In the second part, GLONASS outlier and slips statistics will be discussed, while in the third part the anomaly detection results of the GLONASS and GPS messages will be shown. In this first part of the series, however, the most basic of all statistics will be considered: a simple day-to-day count of the number of GLONASS and GPS observations. Although simple, this statistic yields a surprising amount of information both on the availability of the GLONASS satellites and on the peculiarities of some of the receiver makes participating in the IGEX-98 campaign. ? 2000 John Wiley & Sons, Inc.     

A new hybrid geoid model for Japan, GSIGEO2000

 The latest gravimetric geoid model for Japan, JGEOID2000, was successfully combined with the nationwide net of GPS at benchmarks, yielding a new hybrid geoid model for Japan, GSIGEO2000. The least-squares collocation (LSC) method was applied as an interpolation for fitting JGEOID2000 to the GPS/leveling geoid undulations. The GPS/leveling geoid undulation data were reanalyzed in advance, in terms of three-dimensional positions from GPS and orthometric heights from leveling. The new hybrid geoid model is, therefore, compatible with the new Japanese geodetic reference frame. GSIGEO2000 was evaluated internally and independently and the precision was estimated at 4 cm throughout nearly the whole region. Received: 15 October 2001 / Accepted: 27 March 2002 Acknowledgments. Messrs. Toshio Kunimi and Tadashi Saito at the Third Geodetic Division of the Geographical Survey Institute (GSI) mainly carried out the computations of most of the updated leveled heights. With regard to the reanalysis of GPS data, the discussions with Messrs. Yuki Hatanaka and Shoichi Matsumura of GSI were of great help in building the analysis strategy. Messrs. Kazuyuki Tanaka and Hiromi Shigematsu collaborated in the preparatory stages of GPS data computation. The authors' thanks are extended to these colleagues. Some plots were made by GMT software (Wessel and Smith 1991). Correspondence to: Y. Kuroishi     

Time transfer using GPS carrier phase: error propagation and results

 A joint time-transfer project between the Astronomical Institute of the University of Berne (AIUB) and the Swiss Federal Office of Metrology and Accreditation (METAS) was initiated to investigate the power of the time transfer using GPS carrier phase observations. Studies carried out in the context of this project are presented. The error propagation for the time-transfer solution using GPS carrier phase observations was investigated. To this purpose a simulation study was performed. Special interest was focussed on errors in the vertical component of the station position, antenna phase-center variations and orbit errors. A constant error in the vertical component introduces a drift in the time-transfer results for long baselines in east–west directions. The simulation study was completed by investigating the profit for time transfer when introducing the integer carrier phase ambiguities from a double-difference solution. This may reduce the drift in the time-transfer results caused by constant vertical error sources. The results from the present time-transfer solution are shown in comparison to results obtained with independent time-transfer techniques. The interpretation of the comparison benefits from the investigations of the error propagation study. Two types of solutions are produced on a regular basis at AIUB: one based on the rapid orbits from CODE, the other on the CODE final orbits. The rapid solution is available the day after the observations and has nearly the same quality as the final solution, which has a latency of about one week. The differences between these two solutions are below the nanosecond level. The differences from independent time-transfer techniques such as TWSTFT (two-way satellite time and frequency transfer) are a few nanoseconds for both products. Received: 15 November 2001 / Accepted: 6 September 2002 Correspondence to:R. Dach     

Sensitivity of GPS and GLONASS orbits with respect to resonant geopotential parameters

The Center for Orbit Determination in Europe (CODE) has been involved in the processing of combined GPS/GLONASS data during the International GLONASS Experiment (IGEX). The resulting precise orbits were analyzed using the program SORBDT. Introducing one satellites positions as pseudo-observations, the program is capable of fitting orbital arcs through these positions using an orbit improvement procedure based on the numerical integration of the satellites orbit and its partial derivative with respect to the orbit parameters. For this study, the program was enhanced to estimate selected parameters of the Earths gravity field. The orbital periods of the GPS satellites are —in contrast to those of the GLONASS satellites – 2:1 commensurable (P _Sid:P _GPS) with the rotation period of the Earth. Therefore, resonance effects of the satellite motion with terms of the geopotential occur and they influence the estimation of these parameters. A sensitivity study of the GPS and GLONASS orbits with respect to the geopotential coefficients reveals that the correlations between different geopotential coefficients and the correlations of geopotential coefficients with other orbit parameters, in particular with solar radiation pressure parameters, are the crucial issues in this context. The estimation of the resonant geopotential terms is, in the case of GPS, hindered by correlations with the simultaneously estimated radiation pressure parameters. In the GLONASS case, arc lengths of several days allow the decorrelation of the two parameter types. The formal errors of the estimates based on the GLONASS orbits are a factor of 5 to 10 smaller for all resonant terms. AcknowledgmentsThe authors would like to thank all the organizations involved in the IGS and the IGEX campaign, in particular those operating an IGS or IGEX observation site and providing the indispensable data for precise orbit determination.