Demonstration of sub-meter GPS orbit determination and 1.5 parts in 108 three-dimensional baseline accuracy

Differential tracking of theGPS satellites in high-earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the fullGPS constellation. To demonstrate this capability, we have determined baselines of up to2000 km in North America by estimating high-accuracyGPS orbits and ground receiver positions simultaneously. The2000 km baselines agree with very long baseline interferometry(VLBI) solutions at the level of1.5 parts in10 ⁸ and showrms daily repeatability of0.3–2 parts in10 ⁸. The orbits determined for the most thoroughly trackedGPS satellites are accurate to better than1 m. GPS orbit accuracy was assessed from orbit predictions, comparisons with independent data sets, and the accuracy of the continental baselines determined along with the orbits. The bestGPS orbit strategies included data arcs of at least one week, process noise models for tropospheric fluctuations, estimation ofGPS solar pressure coefficients, and combined processing ofGPS carrier phase and pseudorange data. For data arcs of two weeks, constrained process noise models forGPS dynamic parameters significantly improved the solutions.     

Local geoid determination and comparison with GPS results

Ellipsoidal heights have been determined for a test network in Lower Saxony withGPS. TheGPS results, with a relative precision of a few centimeters, have been used to compute quasigeoid heights by substracting leveling heights. This data set is compared to mainly gravimetrically determined quasigeoid heights using least squares collocation techniques. The discrepancies between the two data sets amount to about ±2cm, the maximum interstation distance is about50 km. This agreement shows, thatGPS can be used in combination with gravity information to obtain normal heights withcm-precision.     

Improvement of the GPS time comparisons by simultaneous relative positioning of the receiver antennas

The Global Positioning System,GPS, is widely used for time comparisons between distant laboratories. Over distances of the order of 1000km or less, the system has the capability of 1 to 2ns accuracy. However this requires a relative positioning with errors lower than 30cm. We show that this positioning can be derived from theGPS time comparisons themselves. An example for European laboratories is given.     

Stochastic estimation of tropospheric path delays in global positioning system geodetic measurements

Water vapor radiometric (WVR) and surface meteorological (SM) measurements taken during three Global Positioning System (GPS) geodetic experiments are used to calculate process noise levels for random walk and first-order Gauss-Markov temporal models of tropospheric path delays. Entire wet and combined wet and dry zenith delays at each network site then are estimated simultaneously with the geodetic parameters without prior calibration. The path delays and corresponding baseline estimates are compared to those obtained with calibrated data and stochastic residual delays. In this manner, the marginal utility of a priori tropospheric calibration is assessed given the ability to estimate the path delays directly using only theGPS data. Estimation of total zenith path delays with appropriate random walk or Gauss-Markov models yields baseline repeatabilities of a few parts in 10⁸. This level of geodetic precision, and accuracy as suggested by analyses on collocated baselines estimated independently by very long baseline interferometry, is comparable to or better than that obtained after path delay calibration usingWVR and/orSM measurements. Results suggest thatGPS data alone have sufficient strength to resolve centimeter-level zenith path delay fluctuations over periods of a few minutes.     

Global positioning system carrier phase: Description and use

After removing the modulation from the Global Positioning System (GPS) signal (L ₁ orL ₂) a pure carrier signal remains. Suppose this carrier is continuously and precisely tracked by aGPS receiver. Furthermore, suppose the phase of the carrier is periodically measured and recorded (nearly simultaneously at two or more locations) with respect to receiver oscillators having the same nominal frequency as theGPS carrier. This paper first considers alternative modeling and processing approaches to these observational data for static operations. Then an approach to dynamic relative positioning using triple differences is presented. This approach should lend itself to performing centimeter accuracy relative surveys in seconds rather than hours. An approach to fixing cycle slips, automatically, is included.     

A contribution to the kinematics of plate tectonics

Modern geodetic positioning techniques likeVLBI, SLR, andGPS can be used for plate tectonic studies. A very simple model considers a number of rigid plates rotating individually with a constant rotation rate. An equally simple mathematical model, extended to deformable plates, is presented, based on vector calculus, which relates both absolute and relative point positioning observations to the plate rotation and deformation parameters (rotation rate, direction of rotation vector, deformation rate and direction of deformation center) in a consistent and elementary way. The determination of these plate parameters from various geodetic positioning observations is outlined.     

Applications of an orbiting gravity gradiometer

Considering present attempts to develop a gradiometer with an accuracy between 10⁻³ E and 10⁻⁴ E, two applications for such a device have been studied: (a) mapping the gravitational field of the Earth, and (b) estimating the geocentric distance of a satellite carrying the instrument. Given a certain power spectrum for the signal and 10⁻⁴ E (rms) of white measurement noise, the results of an error analysis indicate that a six-month mission in polar orbit at a height of 200 km, with samples taken every three seconds, should provide data for estimating the spherical harmonic potential coefficients up to degree and order 300 with less than 50% error, and improve the coefficients through degree 30 by up to four orders of magnitude compared to existing models. A simulation study based on numerical orbit integrations suggests that a simple adjustment of the initial conditions based on gradiometer data could produce orbits where the geocentric distance is accurate to 10 cm or better, provided the orbits are 2000 km high and some improvement in the gravity field up to degree 30 is first achieved. In this sense, the gravity-mapping capability of the gradiometer complements its use in orbit refinement. This idea can be of use in determining orbits for satellite altimetry. Furthermore, by tracking the gradiometer-carrying spacecraft when it passes nearly above a terrestrial station, the geocentric distance of this station can also be estimated to about one decimeter accuracy. This principle could be used in combination with VLBI and other modern methods to set up a world-wide 3-D network of high accuracy.     

A unified scheme for processing GPS dual-band phase observations

A unified computational scheme is presented for sequential least-squares processing ofGPS dual-band carrier-beat-phase observations in network-mode positioning with orbit relaxation, and in orbit determination applications. This scheme is applicable to any spatial and temporal distribution of stations and satellites during a particularGPS experiment. Full covariance matrices can be specified for carrier-beat-phases and for weighted constraints on the ionosphere in order to improve phase ambiguity resolution. Physically meaningful choices for these covariance matrices are developed.     

GPS双频精密单点定位软件及其精度分析

简要介绍了GPS双频精密单点定位数学模型及自主研制的精密单点定位软件。采用不同运动状态的实测数据进行静态、静态模拟动态和机载动态解算实验并从外符合的角度进行精度评估。实验结果表明:单天静态解精度达到cm级;动态解算精度达到cm-dm级。     

Use of phase data for accurate differential GPS kinematic positioning

DifferentialGPS land kinematic positioning tests conducted at velocities of20 to100 km/h over a baseline of1,000 km using a combination of pseudo-range and phase measurements are described. An algorithm designed for high reliability and accuracy of1 to2 m in real time field operational mode was utilized. The relatively long baseline used for the tests provided valuable information on the effects of broadcast ephemeris errors on the differential results. The tests were conducted with two Texas InstrumentsTI4100 receivers using both theP andC/A codes to assess the effect of both code measurement noise, and ionospheric irregularities on differential positioning over such a baseline. The use of cesium clocks to constrain time was also tested. Accuracies (in terms of repeatabilities) of the order of1 to3 ppm, i.e.,1 to3 m, were obtained.     

A demonstration of 1–2 parts in 107 accuracy using GPS

By interferometric analysis ofGPS phase observations made at Owens Valley, Mojave, and Mammoth Lakes, California, we determined the coordinate components of the71–245–313 km triangle of baselines connecting these sites. A separate determination was made on each of four days, April 1–4, 1985. The satellite ephemerides used in these determinations had been derived from observations on other baselines. Therms scatters of the four daily determinations of baseline vector components about their respective means ranged from a minimum of6 mm for the north component of the71-km baseline to a maximum of34 mm for the vertical component of the245-km baseline. To test accuracy, we compared the mean of ourGPS determinations of the245-km baseline between Owens Valley and Mojave with independent determinations by others using very-long-baseline interferometry(VLBI) and satellite laser ranging(SLR). TheGPS-VLBI difference was within 2 parts in10 ⁷ for every vector component. TheGPS-SLR difference was within6 parts in10 ⁸ in the horizontal coordinates, but83 mm in height.     

Further considerations on combining earth rotation observations from different space geodetic systems

Additional results are presented concerning a study that consider improvements over present Earth Rotation Parameter (ERP) determination methods by directly combining observations from various space geodetic systems in one adjustment. Earlier results are extended, showing that in addition to slight improvements in accuracy substantial (a factor of three or more) improvements in precision and significant reductions in correlations between various parameters can be obtained (by combining Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) to Lageos, and Very Long Baseline Interferometry (VLBI) data in one adjustment) as compared to results from individual systems. Smaller improvements are also seen over the weighted means of the individual system results. Although data transmission would not be significantly reduced, negligible additional computer time would be required if (standardized) normal equations were available from individual solutions. Suggestions for future work and implications for the new International Earth Rotation Service (IERS) are also presented.     

First direct geodetic link between Europe,Africa and South America with a multi station VLBI array

The first geodetic experiment tying Europe, Africa and South-America was realized in July 1985 by Very Long Baseline Interferometry with a network of 5 radiotelescopes. TheVLBI technique and data analysis are presented, with special emphasis on the ionosphere modeling because of its importance in this particular experiment. Comparisons of the results with other geodetic information confirm the achievement of decimetric accuracy.     

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     

Application of GPS for transportation related engineering surveys

Summary The Texas State Department of Highways and Public Transportation(SDHPT) has been usingGPS for over two years to establish primary geodetic reference points for engineering projects and mapping control. In accordance with a Five YearGPS Implementation Plant developed in 1982, fourGPS, unmanned, automatic Regional Reference Point(RRP) stations will be installed by September 1, 1986. Five additional stations are planned as justified. EachRRP will consist of a dual frequencyGPS receiver that will ultimately track the satellites continuously. Operation of the receiver, telecommunications and other station keeping chores will be handled by a microcomputer. TheRRP station network will be controlled through another centrally located microcomputer which is also interfaced with a larger mainframe system. EachRRP is designed to service an area bounded by a200 KM radius and will act as the “other” receiver for roving field units operating in aGPS differential measurement mode. In order to meet the installation schedule, early decisions are being made concerning satellite tracking rates, operational scenarios, and telecommunications to facilitate development of the basic hardware and software systems. A period of continual enhancement to hardware, software andRRP operational procedures is expected asGPS technology expands.     

The North American datum of 1983: Project methodology and execution

A new adjustment of the geodetic control networks in North America has been completed, resulting in a new continental datum—the North American Datum of 1983 (NAD 83). The establishment ofNAD 83 was the result of an international project involving the National Geodetic Survey of the United States, the Geodetic Survey of Canada, and the Danish Geodetic Institute (responsible for surveying in Greenland). The geodetic data in Mexico and Central America were collected by the Inter American Geodetic Survey and validated by the Defense Mapping Agency Hydrographic/Topographic Center. The fundamental task ofNAD 83 was a simultaneous least squares adjustment involving 266,436 stations in the United States, Canada, Mexico, and Central America. The networks in Greenland, Hawaii, and the Caribbean islands were connected to the datum through Doppler satellite and Very Long Baseline Interferometry (VLBI) observations. The computations were performed with respect to the ellipsoid of the Geodetic Reference System of 1980. The ellipsoid is positioned in such a way as to be geocentric, and its axes are oriented by the Bureau International de l'Heure Terrestrial System of 1984. The mathematical model for theNAD readjustment was the height-controlled three-dimensional system. The least squares adjustment involved 1,785,772 observations and 928,735 unknowns. The formation and solution of the normal equations were carried out according to the Helmert block method. [Authors' note:This article is a condensation of the final report of the NAD 83 project. The full report (Schwarz,1989) contains a more complete discussion of all the topics.]     

Ambiguity resolution in precise point positioning with hourly data

Precise point positioning (PPP) has become a powerful tool for the scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station in PPP has been considered difficult, due to the receiver- and satellite-dependent uncalibrated hardware delays (UHD). However, recent studies show that if these UHD can be determined accurately in advance within a network of stations, then ambiguity resolution at a single station becomes possible. In this study, the method proposed by Ge et al. J Geod 82(7):389–399, 2007 is adopted with a refinement in which only one single-difference narrow-lane UHD between a pair of satellites is determined within each full pass over a regional network. This study uses the EUREF (European Reference Frame) Permanent Network (EPN) to determine the UHD from Day 245 to 251 in 2007. Then 12 International GNSS Service stations inside the EPN and 15 outside the EPN are used to conduct ambiguity resolution in hourly PPP. It is found that the mean positioning accuracy in all hourly solutions for the stations inside the EPN is improved from (3.8, 1.5, 2.8) centimeters to (0.5, 0.5, 1.4) centimeters for the East, North and Up components, respectively. For the stations outside the EPN, some of which are over 2,000 km away from the nearest EPN stations, the mean positioning accuracy in the East, North and Up directions still achieves (0.6, 0.6, 2.0) centimeters, respectively, when the EPN-based UHD are applied to these stations. These results demonstrate that ambiguity resolution at a single station can significantly improve the positioning accuracy in hourly PPP. Particularly, UHD can be even applied to a station which is up to thousands of kilometers from the UHD-determination network, potentially showing a great advantage over current network-based GPS augmentation systems. Therefore, it is feasible and beneficial for the operators of GPS regional networks and providers of PPP-based online services to provide these UHD estimates as an additional product.     

Transformation of coordinates between two horizontal geodetic datums

The following topics are discussed in this paper: the geocentric coordinate system and its different realizations used in geodetic practice; the definition of a horizontal geodetic datum (reference ellipsoid) and its positioning and orientation with respect to the geocentric coordinate system; positions on a horizontal datum and errors inherent in the process of positioning; and distortions of geodetic networks referred to a horizontal datum. The problem of determining transformation parameters between a horizontal datum and the geocentric coordinate system from known positions is then analysed. It is often found necessary to transform positions from one horizontal datum to another. These transformations are normally accomplished through the geocentric coordinate system and they include the transformation parameters of the two datums as well as the representation of the respective network distortions. Problems encountered in putting these transformations together are pointed out.     

Conventional terrestrial system by VLBI a kinematic approach

The paper examines the potential ofVLBI time delay observables for the establishment and maintenance of a Conventional Terrestrial System (CTS). TheCTS is defined in2-D by the standard epoch positions and velocities of a network of control points located on a spherical reference surface. VLBI time delay observables are sensitive to the rotational motion of theCTS control points with respect to a Conventional Inertial System (CIS) which is represented by a network of radio sources. The motion of a control point with respect to theCIS is partitioned into global and regional components. The global components represent the rotational motion of the sphere with respect to theCIS, while the regional components represent the motion of theCTS points with respect to the sphere.     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.