Software tools for accessing the GPS Seamless Archive

The Scripps Orbit and Permanent Array Center (SOPAC) has completed development for the UNAVCO community of first-generation GPS Seamless Archive (GSAC) software. The GSAC is a virtual archive composed of an assembly of agencies and investigators exchanging information about their respective GPS-related data holdings in a well defined, cohesive manner. The superset of this published information is collected and ingested into centralized databases administered currently by two data brokers (Retailers), who make the data available to the public in a seamless manner. There are three user interfaces available: the interactive GSAC Wizard, a command-line Unix-style executable called gsac-client, and a front door HTTP service called the GSAC Retailer Service Interface. Each user interface provides access to the data collections of 6 different GPS archives (GSAC Wholesalers) in North America. Together these archives have published more than 2 million GPS data files pertaining to over 10,000 different geodetic monuments. These datasets are composed in large part of data collected by US scientists and their collaborators over the period 1986 to the present in Western North America and other tectonically active regions around the globe, as well as the holdings of two IGS global data centers. In this article, we describe how the three GSAC user interfaces provide the community a powerful set of tools for seamlessly mining information and collecting data files from a distributed network of GPS archives.The GPS Toolbox is a column dedicated to highlighting algorithms and source code utilized by GPS Engineers and scientists. If you have an interesting program or software package you would like to share with our readers, please pass it along; e-mail it to us at gps-toolbox@ngs.noaa.gov. To comment on any of the source code discussed here, or to download source code, visit our website at . This column is edited by Stephen Hilla, National Geodetic Survey, NOAA, Silver Spring, Maryland, and Mike Craymer, Geodetic Survey Division, Natural Resources Canada, Ottawa, Ontario, Canada.     

High-resolution regional geoid computation without applying Stokes’s formula: a case study of the Iranian geoid

A new theory for high-resolution regional geoid computation without applying Stokess formula is presented. Operationally, it uses various types of gravity functionals, namely data of type gravity potential (gravimetric leveling), vertical derivatives of the gravity potential (modulus of gravity intensity from gravimetric surveys), horizontal derivatives of the gravity potential (vertical deflections from astrogeodetic observations) or higher-order derivatives such as gravity gradients. Its algorithmic version can be described as follows: (1) Remove the effect of a very high degree/order potential reference field at the point of measurement (POM), in particular GPS positioned, either on the Earths surface or in its external space. (2) Remove the centrifugal potential and its higher-order derivatives at the POM. (3) Remove the gravitational field of topographic masses (terrain effect) in a zone of influence of radius r. A proper choice of such a radius of influence is 2r=4×10⁴ km/n, where n is the highest degree of the harmonic expansion. (cf. Nyquist frequency). This third remove step aims at generating a harmonic gravitational field outside a reference ellipsoid, which is an equipotential surface of a reference potential field. (4) The residual gravitational functionals are downward continued to the reference ellipsoid by means of the inverse solution of the ellipsoidal Dirichlet boundary-value problem based upon the ellipsoidal Abel–Poisson kernel. As a discretized integral equation of the first kind, downward continuation is Phillips–Tikhonov regularized by an optimal choice of the regularization factor. (5) Restore the effect of a very high degree/order potential reference field at the corresponding point to the POM on the reference ellipsoid. (6) Restore the centrifugal potential and its higher-order derivatives at the ellipsoidal corresponding point to the POM. (7) Restore the gravitational field of topographic masses ( terrain effect) at the ellipsoidal corresponding point to the POM. (8) Convert the gravitational potential on the reference ellipsoid to geoidal undulations by means of the ellipsoidal Bruns formula. A large-scale application of the new concept of geoid computation is made for the Iran geoid. According to the numerical investigations based on the applied methodology, a new geoid solution for Iran with an accuracy of a few centimeters is achieved.Acknowledgments. The project of high-resolution geoid computation of Iran has been support by National Cartographic Center (NCC) of Iran. The University of Tehran, via grant number 621/3/602, supported the computation of a global geoid solution for Iran. Their support is gratefully acknowledged. A. Ardalan would like to thank Mr. Y. Hatam, and Mr. K. Ghazavi from NCC and Mr. M. Sharifi, Mr. A. Safari, and Mr. M. Motagh from the University of Tehran for their support in data gathering and computations. The authors would like to thank the comments and corrections made by the four reviewers and the editor of the paper, Professor Will Featherstone. Their comments helped us to correct the mistakes and improve the paper.     

A comparison of a Hi/Lo GPS constellation with a populated conventional GPS constellation in support of RTK: A covariance analysis

This study makes an initial comparison of three GPS-like constellations. Starting with a simplified constellation of 25 GPS satellites as a reference, GPS(25), we determine what kinematic positioning improvements would result from a constellation comprising a Hi component of 16 GPS satellites (at roughly 16.8 earth radii) coupled with a Lo component of 49 GPS satellites (at roughly 2.1 earth radii). We also include a GPS constellation of 49 GPS satellites, GPS(49), which comprises orbits like the GPS(25) constellation. The GPS(49) and the Hi(16)/Lo(49) constellations have semi-major axes selected so that they have exactly the same average number of satellites above 7.5 degrees elevation (averaged over 24 hours). What motivated this study was a need to measure the benefits, to precision differential kinematic positioning methods (i.e., RTK), which result from the higher Doppler shifts (hence speedier integrated Doppler) generated by the Lo component. Quicker initial convergence was anticipated, of course.     

The value of ocean reflections of GPS signals to enhance satellite altimetry: data distribution and error analysis

The time and space distribution of general reflection altimetry from two satellites (senders and receivers) via the the oceans surface is examined with specific reference to GPS senders and two current receiving satellites. While a considerable enhancement of conventional altimeter coverage is possible in all configurations if the reflection signals can be used, repeating passes of these (with GPS senders) having reasonably small cycle times (days to tens of days) occur only if the receiving orbit is nearly polar. Results of an analysis of the fundamental geometry show that over a large range of reflection angles the error of recovered sea heights depends almost entirely on the errors in the delay signal and the radial error of the receiving satellite (using current estimates of GPS orbit accuracies). The most critical element is the precision of the delay measurement. Both it and the accuracy of the receiving orbit should be below the decimeter level for the technique to achieve its full potential.     

On Helmert’s methods of condensation

Helmerts first and second method of condensation are reviewed and generalized in two respects: First, the point at which the effects of topographical and condensation masses are calculated may be situated on or outside the topographical surface; second, the depth of the condensation layer below the geoid is arbitrary. While the first extension permits the application of the generalized model to the evaluation of airborne and satellite data, the second one gives an additional degree of freedom which can be used to provide a smooth gravity field after reducing the observation data. The respective formulae are derived for the generalized condensation model in both planar and spherical approximation. A comparison of the planar and the spherical model shows some structural differences, which are primarily visible in the out-of-integral terms. Considering the respective formulae for the combined topographic–condensation reduction on the background of the density structure of the Earths lithosphere, the consequences for the residual gravity field are investigated; it is shown that the residual field after applying Helmerts second model of reduction is very rough, making this procedure unfavourable for downward continuation. Further considerations refer to the question of which sets of formulae should be used in geoid and quasigeoid determination. It is concluded that for high-precision applications the generalized spherical model, involving a depth of the condensation layer of between 20 and 30 km, should be superior to Helmerts second model of condensation, although it requires the direct calculation of the indirect effect, which is larger than in the case of Helmerts second method of condensation.     

The permanent tide in GPS positioning

The treatment of the permanent tidal deformation of the Earth in GPS computation has been an almost unmentioned topic in the GPS literature. However, the ever increasing accuracy and the need to combine the GPS based coordinates with other methods requires a consistent way to handle the tides. Our survey shows that both the ITRF-xx coordinates and the GPS based coordinates are nowadays reduced to a non-tidal crust, conventionally defined using physically meaningless parameters. We propose to use instead the zero-crust concept which corresponds to concepts already accepted in the resolution of IAG in 1983 for gravimetric works.     

Monitoring selective availability dither frequencies and their effect on GPS data

Summary The signals transmitted by Block II satellites of the Global Positioning System (GPS) can be degraded to limit the highest accuracy of the system (10 m or better point positioning) to authorized users. This mode of degraded operation is called Selective Availability (S/A). S/A involves the degradation in the quality of broadcast orbits and satellite clock dithering. We monitored the dithered satellite oscillator and investigated the effect of this clock dithering on high accuracy relative positioning. The effect was studied over short 3-meter and zero-baselines with two GPS receivers. The equivalent S/A effects for baselines ranging from 0 to >10,000 km can be examined with short test baselines if the receiver clocks are deliberately mis-synchronized by a known and varying amount. Our results show that the maximum effect of satellite clock dithering on GPS double difference phase residuals grows as a function of the clock synchronization error according to: S/A _effect =0.04 cm/msec, and it increases as a function of baseline length like: S/A _effect =0.014 cm/100 km. These are equations for maximum observed values of post-fit residuals due to S/A. The effect on GPS baselines is likely to be smaller than the 0.14 mm for a baseline separation of 100 km. We therefore conclude, for our limited data set, and for the level of S/A during our tests, that S/A clock dithering has negligible effect on all terrestrial GPS baselines if double difference processing techniques are employed and if the GPS receivers remain synchronized to better than 10 msec. S/A may constitute a problem, however, if accurate point processing is required, or if GPS receivers are not synchronized. We suggest and test two different methods to monitor satellite frequency offsets due to S/A. S/A modulates GPS carrier frequencies in the range of-2 Hz to +2 Hz over time periods of several minutes. The methods used in this paper to measure the satellite clock dither could be applied by the civilian GPS community to continuously monitor S/A clock dithering. The monitored frequencies may aid high accuracy point positioning applications in a postprocessing mode (Malys and Ortiz 1989), and differential GPS with poorly synchronized receivers (Feigl et al. 1991).     

Atmospheric tides and rotation of the Earth

The six-hourly values of the atmospheric angular momentum (AAM) functions computed by the U.S. National Meteorological Center (NMC) were used to estimate the effects of the atmospheric tides on the Earth's rotation. Variations of the equatorial components ₁ and ₂ of the AAM have periods close to gravitational tidesP ₁ andK ₁.The amplitudes of the detected variations in ₁ and ₂ functions have been found to be much larger than the theoretical ones, the reason of this amplification remains unexplained. According to theoretical formulations, these waves can be expressed only as retrograde motions. Because of frame effects, there is a correspondance between diurnal retrograde polar motion and precession-nutations and the atmospheric effect on polar motion cannot be detected from observations.The second part of this paper deals the effects of atmospheric tides in Earth rotation. High-frequency UT1 variations have been derived from VLBI and GPS techniques during the SEARCH'92 campaign (Study ofEarth-AtmosphereRapidCHanges) (Dickey et al. 1994). They have been compared to values derived by Ray et al. (1994) from global ocean tide model. The results obtained in the present paper show the existence of variations of thermal origin with an amplitude of about 1µs in Universal Time UT1. The agreement between observed and theoretical values is better when the determined thermal atmospheric tides are taken into account.Oceanic tidal signal explains a large part (60% of the signal variance) of the diurnal and sub-diurnal variations. Our results show that only a small part of the residuals (5%) accounts for the atmospheric tidal effects. The residual signal remains unexplained; it might be due to mismodelization of oceanic or atmospheric tides or effect of other geophysical phenomena.     

Clinometric records with two long water levels in Lohja,Finland, during the total solar eclipse in 1990

Two water tube clinometers are installed in a deep mine in Lohja, Finland. One, lying in an E-W direction, is 177 m long and the other, lying in a N-S direction, is 62 m long. These instruments are used for tidal records and research. Because the station was on the zone of totality of the 1990 solar eclipse, the instruments offered a suitable tool for investigating whether there was any shielding effect on the direction of the vertical. During the eclipse, the resolution of the instruments was increased to 0.00001 and 0.00004, respectively. p ]Recordings and data evaluation are discussed, and the results obtained show that no gravitational shielding was found at the level of the above accuracy.     

Theory of integer equivariant estimation with application to GNSS

Carrier phase ambiguity resolution is the key to high-precision global navigation satellite system (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. The so-called fixed baseline estimator is known to be superior to its float counterpart in the sense that its probability of being close to the unknown but true baseline is larger than that of the float baseline, provided that the ambiguity success rate is sufficiently close to its maximum value of one. Although this is a strong result, the necessary condition on the success rate does not make it hold for all measurement scenarios. It is discussed whether or not it is possible to take advantage of the integer nature of the ambiguities so as to come up with a baseline estimator that is always superior to both its float and its fixed counterparts. It is shown that this is indeed possible, be it that the result comes at the price of having to use a weaker performance criterion. The main result of this work is a Gauss–Markov-like theorem which introduces a new minimum variance unbiased estimator that is always superior to the well-known best linear unbiased (BLU) estimator of the Gauss–Markov theorem. This result is made possible by introducing a new class of estimators. This class of integer equivariant estimators obeys the integer remove–restore principle and is shown to be larger than the class of integer estimators as well as larger than the class of linear unbiased estimators. The minimum variance unbiased estimator within this larger class is referred to as the best integer equivariant (BIE) estimator. The theory presented applies to any model of observation equations having both integer and real-valued parameters, as well as for any probability density function the data might have. AcknowledgementsThis contribution was finalized during the authors stay, as a Tan Chin Tuan Professor, at the Nanyang Technological Universitys GPS Centre (GPSC) in Singapore. The hospitality of the GPSCs director Prof Law Choi Look and his colleagues is greatly appreciated.     

Setting-up local “mapping geoids” with the aid of GPS/LEV traverses. Application to the geoids of Sardinia and Calabria

The problem of fitting a pre-existing geoid on local GPS/LEV points is first taken into account, a possible way for its solution is proposed, based on techniques similar to the aerophotogrammetric absolute orientation.This approach is then used to compute themapping geoids of Sardinia and Calabria i.e. geoids with decimetric accuracy, needed for the heigthing of large scale maps. The pre-existing geoids EAGGI by Brennecke et al. (1983), and EGG2 by Denker et al (1993) are utilized, fitted on points of GPS/LEV traverses.The complete input-output data, the contour maps of both geoids, and a substantial checking on some Calabrian GPS/TRIG points of the entreprise IGM.95 are finally reported.     

A proposed GPS method with multi-antennae and single receiver

A method based on multi-antennae linked to a common GPS receiver is proposed. The goal of the technique is to improve height determination for baselines a few kilometres in length. The advantage of this technique resides in the elimination of relative clock parameters in the between-antenna single difference observations. Because single difference observations are free of clock errors more geometrical strength remains to determine the baseline components. This statement is valid as long as intercable biases can be carefully calibrated. For millimetre height determination, the intercable calibration must be done at the same level of accuracy. Under this assumption it is shown that in general the height standard deviation improves by a factor of about three compared to standard GPS data processing. With the proposed method, the effect of relative tropospheric zenith delay errors becomes a bit smaller (in absolute value), compared to standard data processing. To absorb this error, a relative tropospheric zenith delay parameter may be estimated. Even with this additional parameter in the solution the height standard deviation remains two times smaller than the results of standard processing techniques (without tropospheric zenith delay parameter), and at least five times smaller than in the results obtained from standard processing including one tropospheric zenith delay parameter.     

The Rolling Pig or How does a surveyor creep through a pipeline?

The inspection of a pipeline from the inside becomes more and more widespread. An inspection tool, called Geometry Pig, carries a variety of sensors, among which a strapdown inertial system provides essential geometric information on the pipeline. In this paper the inspection pig is described as a surveying tool, which delivers information on centre line, shape and features of the pipe. After some background information it is explained, why the inertial system is the optimal instrument to deliver some structural parameters of the pipeline. The interaction between data evaluation and measurement procedure is discussed in view of the very few possibilities to vary the procedure. One of them is a forced rotation about the forward axis. Analogies are shown to traditional surveying procedures. Finally some results of actual surveys are presented. A positioning accuracy of 1:2500 is achieved with respect to tie points.     

Interannual variability of low-degree gravitational change, 1980–2002

Time variations in the Earths gravity field at periods longer than 1 year, for degree-two spherical harmonics, C₂₁, S₂₁, and C₂₀, are estimated from accurately measured Earth rotational variations. These are compared with predictions of atmospheric, oceanic, and hydrologic models, and with independent satellite laser ranging (SLR) results. There is remarkably good agreement between Earth rotation and model predictions of C₂₁ and S₂₁ over a 22-year period. After decadal signals are removed, Earth-rotation-derived interannual C₂₀ variations are dominated by a strong oscillation of period about 5.6 years, probably due to uncertainties in wind and ocean current estimates. The model-predicted C₂₀ agrees reasonably well with SLR observations during the 22-year period, with the exception of the recent anomaly since 1997/1998.     

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.     

The common short periodic oscillations in the Earth's rate of rotation,atmospheric angular momentum and solar activity

In order to find short periodic oscillations in the Earth's rate of rotation, atmospheric angular momentum, solar activity the Maximum Entropy Spectral Analysis — MESA (Burg, 1967) has been applied. The MESA with moving autoregressive order has been introduced in order to detect more accurately periods of very weak short periodic variations. Oscillations with periods of about 75, 50, 27 and 18 days have been found in length of day — LOD, from which tidal oscillations were removed up to 35 days — LODR computed by the Center for Space Research — CSR from Lageos Laser Ranging data, in the axial component of atmospheric angular momentum — ₃ determined by the U.S. National Meteorological Center — NMC and in the geomagnetic activity represented by the geomagnetic index —A _p (Lincoln, 1967). These oscillations computed by Ormsby band pass filter (Ormsby, 1961) are in a very good phase agreement in the case of oscillations with periods of 50 and 18 days in these 3 series. The MESA of the cross covariance estimations between LODR- ₃, ₃-A _p,A _p-LODR, LODR-FLUX, ₃-FLUX, andA _p-FLUX has confirmed the existence of common oscillations with periods of 70, 50, 27 and 18 days. This indicates a possible relationship between solar activity and the short periodic exchange of angular momentum between the atmosphere and the solid Earth.     

Evaluation of the accuracy of the EIGEN-1S and -2 CHAMP-derived gravity field models by satellite crossover altimetry

Since the advent of CHAMP, the first in a series of low-altitude satellites being almost continuously and precisely tracked by GPS, a new generation of long-wavelength gravitational geopotential models can be derived. The accuracy evaluation of these models depends to a large extent on the comparison with external data of comparable quality. Here, two CHAMP-derived models, EIGEN-1S and EIGEN-2, are tested with independent long-term-averaged single satellite crossover (SSC) sea heights from three altimetric satellites (ERS-1, ERS-2 and Geosat). The analyses show that long-term averages of crossover residuals still are powerful data to test CHAMP gravity field models. The new models are tested in the spatial domain with the aid of ERS-1/-2 and Geosat SSCs, and in the spectral domain with latitude-lumped coefficient (LLC) corrections derived from the SSCs. The LLC corrections allow a representation of the satellite-orbit-specific error spectra per order of the models spherical harmonic coefficients. These observed LLC corrections are compared to the LLC projections from the models variance–covariance matrix. The excessively large LLC errors at order 2 found in the case of EIGEN-2 with the ERS data are discussed. The degree-dependent scaling factors for the variance-covariance matrices of EIGEN-1S and –2, applied to obtain more realistic error estimates of the solved-for coefficients, are compatible with the results found here.     

Productivity convergence and spatial dependence among Spanish regions

This paper estimates the evolution of labor productivity disparities among 48 Spanish regions over 1980–1996 according to the concepts of - and -convergence. The results of -convergence emphasize the importance of including the impact of neighboring locations productivity and a disaggregate analysis at a sectoral level. In order to measure the narrowing of inequalities, we examine -convergence and reveal that convergence occurs in aggregate labor productivity but not in productivities per sector. The reason comes from a transfer of resources from agriculture towards more productive sectors that has been more pronounced in the poor regions than in the rich ones.The author would like to thank Julie Le Gallo, an anonymous referee, and the participants of the 50th North American Meetings of the RSAI and of the 43rd Annual Meeting of the WRSA for their valuable comments. This paper won the first place the 2004 Tiebout Prize competition, which was awarded at the WRSA meeting, Hawaii, USA, February 26–28.