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1.
Theory of integer equivariant estimation with application to GNSS   总被引：4，自引：4，他引：0  
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.  相似文献   

2.
This paper provides numerical examples for the prediction of height anomalies by the solution of Molodensky's boundary value problem. Computations are done within two areas in the Canadian Rockies. The data used are on a grid with various grid spacings from 100 m to 5 arc-minutes. Numerical results indicate that the Bouguer or the topographicisostatic gravity anomalies should be used in gravity interpolation. It is feasible to predict height anomalies in mountainous areas with an accuracy of 10 cm (1) if sufficiently dense data grids are used. After removing the systematic bias, the differences between the geoid undulations converted from height anomalies and those derived from GPS/levelling on 50 benchmarks is 12 cm (1) when the grid spacing is 1km, and 50 cm (1) when the grid spacing is 5. It is not necessary, in most cases, to require a grid spacing finer than 1 km, because the height anomaly changes only by 3 cm (1) when the grid spacing is increased from 100 m to 1000 m. Numerical results also indicate that, only the first two terms of the Molodensky series have to be evaluated in all but the extreme cases, since the contributions of the higher order terms are negligible compared to the objective accuracy.  相似文献   

3.
Since the earth is closer to a revolving ellipsoid than a sphere, it is very important to study directly the original model of the Stokes' BVP on the reference ellipsoid, where denotes the reference ellipsoid, is the Somigliana normal gravity, andh is the outer normal direction of. This paper deals with: 1) simplification of the above BVP under preserving accuracy to , 2) derivation of computational formula of the elliptical harmonic series, 3) solving the BVP by the elliptical harmonic series, and 4) providing a principle for finding the elliptical harmonic model of the earth's gravity field from the spherical harmonic coefficients ofg. All results given in the paper have the same accuracy as the original BVP, that is, the accuracy of the BVP is theoretically preserved in each derivation step.  相似文献   

4.
Summary The authors explored the possibility of separating gravitation from inertia in the frame of general relativity. The Riemann tensor is intimately related with gravitational fields and has nothing to do with inertial effects. One can judge the existence or nonexistence of a gravitational field according as the Riemann tensor does not vanish or vanishes. In the free fall case, by using a gradiometer on a satellite, gravitational effects can be separated from inertia completely. Furthermore, the authors put forward a general method of determining the relativistic gravity field by using gradiometers mounted on satellites. At the same time the following two statements are proved: in the case of using gradiometers on a satellite, with some kind of approximation the Riemann tensorR can be found; in the case of free motion, if the measured Riemannian componentsR (i0j0) are equal to zero, the Riemann tensorR equals zero.  相似文献   

5.
Marine gravity surveying line system adjustment   总被引：6，自引：0，他引：6  
The general theories and methods of marine surveying line system adjustment were introduced in (1979) and Tang (1991) . According to the characteristics of marine gravity measurement, this paper presents a new method of combined adjustment which takes into account both direct and indirect influence of position errors. The method is particularly suitable to be used in the post- processing of marine gravity observation data. With some practical applications, it is proved to be effective in improving the quality of marine gravity data.  相似文献   

6.
Today the combination of Stokes formula and an Earth gravity model (EGM) for geoid determination is a standard procedure. However, the method of modifying Stokes formula varies from author to author, and numerous methods of modification exist. Most methods modify Stokes kernel, but the most widely applied method, the remove compute restore technique, removes the EGM from the gravity anomaly to attain a residual gravity anomaly under Stokes integral, and at least one known method modifies both Stokes kernel and the gravity anomaly. A general model for modifying Stokes formula is presented; it includes most of the well-known techniques of modification as special cases. By assuming that the error spectra of the gravity anomalies and the EGM are known, the optimum model of modification is derived based on the least-squares principle. This solution minimizes the expected mean square error (MSE) of all possible solutions of the general geoid model. A practical formula for estimating the MSE is also presented. The power of the optimum method is demonstrated in two special cases. AcknowledgementsThis paper was partly written whilst the author was a visiting scientist at The University of New South Wales, Sydney, Australia. He is indebted to Professor W. Kearsley and his colleagues, and their hospitality is acknowledged.  相似文献   

7.
The regularized solution of the external sphericalStokes boundary value problem as being used for computations of geoid undulations and deflections of the vertical is based upon theGreen functions S 1(0, 0, , ) ofBox 0.1 (R = R 0) andV 1(0, 0, , ) ofBox 0.2 (R = R 0) which depend on theevaluation point {0, 0} S R0 2 and thesampling point {, } S R0 2 ofgravity anomalies (, ) with respect to a normal gravitational field of typegm/R (free air anomaly). If the evaluation point is taken as the meta-north pole of theStokes reference sphere S R0 2 , theStokes function, and theVening-Meinesz function, respectively, takes the formS() ofBox 0.1, andV 2() ofBox 0.2, respectively, as soon as we introduce {meta-longitude (azimuth), meta-colatitude (spherical distance)}, namely {A, } ofBox 0.5. In order to deriveStokes functions andVening-Meinesz functions as well as their integrals, theStokes andVening-Meinesz functionals, in aconvolutive form we map the sampling point {, } onto the tangent plane T0S R0 2 at {0, 0} by means ofoblique map projections of type(i) equidistant (Riemann polar/normal coordinates),(ii) conformal and(iii) equiareal.Box 2.1.–2.4. andBox 3.1.– 3.4. are collections of the rigorously transformedconvolutive Stokes functions andStokes integrals andconvolutive Vening-Meinesz functions andVening-Meinesz integrals. The graphs of the correspondingStokes functions S 2(),S 3(r),,S 6(r) as well as the correspondingStokes-Helmert functions H 2(),H 3(r),,H 6(r) are given byFigure 4.1–4.5. In contrast, the graphs ofFigure 4.6–4.10 illustrate the correspondingVening-Meinesz functions V 2(),V 3(r),,V 6(r) as well as the correspondingVening-Meinesz-Helmert functions Q 2(),Q 3(r),,Q 6(r). The difference between theStokes functions / Vening-Meinesz functions andtheir first term (only used in the Flat Fourier Transforms of type FAST and FASZ), namelyS 2() – (sin /2)–1,S 3(r) – (sinr/2R 0)–1,,S 6(r) – 2R 0/r andV 2() + (cos /2)/2(sin2 /2),V 3(r) + (cosr/2R 0)/2(sin2 r/2R 0),, illustrate the systematic errors in theflat Stokes function 2/ or flatVening-Meinesz function –2/2. The newly derivedStokes functions S 3(r),,S 6(r) ofBox 2.1–2.3, ofStokes integrals ofBox 2.4, as well asVening-Meinesz functionsV 3(r),,V 6(r) ofBox 3.1–3.3, ofVening-Meinesz integrals ofBox 3.4 — all of convolutive type — pave the way for the rigorousFast Fourier Transform and the rigorousWavelet Transform of theStokes integral / theVening-Meinesz integral of type equidistant, conformal and equiareal.  相似文献   

8.
Summary The least-squares collocation method has been used for the computation of a geoid solution in central Spain, combining a geopotential model complete to degree and order 360, gravity anomalies and topographic information. The area has been divided in two 1°× 1° blocks and predictions have been done in each block with gravity data spacing about 5 × 5 within each block, extended 1/2°. Topographic effects have been calculated from 6 × 9 heights using an RTM reduction with a reference terrain model of 30 × 30 mean heights.  相似文献   

9.
W. Sun 《Journal of Geodesy》2003,77(7-8):381-387
An asymptotic theory is presented for calculating co-seismic potential and geoid changes, as an approximation of the dislocation theory for a spherical Earth. This theory is given by a closed-form mathematical expression, so that it is mathematically simple and can be applied easily. Moreover, since the asymptotic theory includes sphericity and vertical structure effects, it is physically more reasonable than the flat-Earth theory. A comparison between results calculated by three dislocation theories (the flat-Earth theory, the theory for a spherical Earth and its asymptotic solution) shows that the true co-seismic geoid changes are approximated better by the asymptotic results than by those of a flat Earth. Numerical results indicate that the sphericity effect is obvious large, especially for a tensile source on a vertical fault plane. AcknowledgementsThe author is grateful to Dr S. Okubo for his helpful suggestions and discussions. Comments by anonymous reviewers are also greatly acknowledged. This research was financially supported by JSPS research grants (C13640420) and Basic design and feasibility studies for the future missions for monitoring Earths environment.  相似文献   

10.
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.  相似文献   

11.
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.  相似文献   

12.
In a modern application of Stokes formula for geoid determination, regional terrestrial gravity is combined with long-wavelength gravity information supplied by an Earth gravity model. Usually, several corrections must be added to gravity to be consistent with Stokes formula. In contrast, here all such corrections are applied directly to the approximate geoid height determined from the surface gravity anomalies. In this way, a more efficient workload is obtained. As an example, in applications of the direct and first and second indirect topographic effects significant long-wavelength contributions must be considered, all of which are time consuming to compute. By adding all three effects to produce a combined geoid effect, these long-wavelength features largely cancel. The computational scheme, including two least squares modifications of Stokes formula, is outlined, and the specific advantages of this technique, compared to traditional gravity reduction prior to Stokes integration, are summarised in the conclusions and final remarks. AcknowledgementsThis paper was written whilst the author was a visiting scientist at Curtin University of Technology, Perth, Australia. The hospitality and fruitful discussions with Professor W. Featherstone and his colleagues are gratefully acknowledged.  相似文献   

13.
Mean 5 × 5 heights and depths from ETOPO5U (Earth Topography at 5 spacing Updated) Digital Terrain Model (DTM) were compared with corresponding quantities of a local DTM in the test area [38° 40°, 21° 24°]. From this comparison a shift of ETOPO5U with respect to the local DTM in the longitudinal direction equal to 5 min was found after applying an efficient fast Fourier transform (FFT) technique. Furthermore, sparse mean height differences larger than 1,000 m were observed between ETOPO5U and the local DTM due rather to errors of ETOPO5U. The effect of these errors on gravity and height anomalies was computed in a subregion of the area under consideration.  相似文献   

14.
Integrated adjustment of CHAMP, GRACE, and GPS data   总被引：16，自引：3，他引：13  
Various types of observations, such as space-borne Global positioning system (GPS) code and phase data, accelerometer data, K-band range and range-rate data, and ground-based satellite laser ranging data of the CHAllenging Minisatellite Payload (CHAMP) and GRAvity Climate Experiment (GRACE) satellite missions, are used together with ground-based GPS code and phase data in a rigorous adjustment to eventually solve for the ephemerides of the CHAMP, GRACE, and GPS satellites, geocenter variations, and low-degree gravity field parameters. It turns out that this integrated adjustment considerably improves the accuracy of the ephemerides for the high and low satellites, geocenter variations, and gravity field parameters, compared to the case when the adjustment is carried out stepwise or in individual satellite solutions.Acknowledgments. This study has been supported by the German Ministry of Education and Research through the Geotechnologies Programme grants 03F0333A/CHAMP and 03F0326A/GRACE.  相似文献   

15.
Geoid determination in Turkey (TG-91)   总被引：1，自引：0，他引：1  
It is considered that precise geoid determination is one of the main current geodetic problems in Turkey since GPS defined coordinates require geoidal heights in practice. In order to determine the geoid by least squares collocation (LSC) the area covering Turkey was divided into 114 blocks of size 1° × 1°. LSC approximation to the geoid based upon the tailored geopotential model GPM2-T1 is constructed within each block. The model GPM2-T1 complete to degree and order 200 has been developed by tailoring of the model GPM2 to mean free-air anomalies and mean heights of one degree blocks in Turkey. Terrain effect reduced point gravity data spaced 5 × 5 within each block which the sides extended 0°.5 were used in LSC. Residual terrain model (RTM) depends on point heights at 15×20 griding and 5×5 and 15×15 mean heights has been carried out in terrain effect reduction. Indirect effect of RTM on geoid is also taken into account. The geoid, called Turkish Geoid 1991 (TG-91), referenced to GRS-80 ellipsoid has been computed at 3 × 3 griding nodes within each block. The quality of the TG-91 is also evaluated by comparing computed and GPS derived geoidal height differences, and 2.1 – 2.6 ppm accuracy for average baseline lenght of 45 km is obtained.  相似文献   

16.
On Helmert’s methods of condensation   总被引：2，自引：0，他引：2  
B. Heck 《Journal of Geodesy》2003,77(3-4):155-170
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.  相似文献   

17.
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.  相似文献   

18.
Global gravity field models have been determined based on kinematic orbits covering an observation period of one year beginning from March 2002. Three different models have been derived up to a maximum degree of n=90 of a spherical harmonic expansion of the gravitational potential. One version, ITG-CHAMP01E, has been regularized beginning from degree n=40 upwards, based on the potential coefficients of the gravity field model EGM96. A second model, ITG-CHAMP01K, has been determined based on Kaulas rule of thumb, also beginning from degree n=40. A third version, ITG-CHAMP01S, has been determined without any regularization. The physical model of the gravity field recovery technique is based on Newtons equation of motion, formulated as a boundary value problem in the form of a Fredholm-type integral equation. The observation equations are formulated in the space domain by dividing the one-year orbit into short sections of approximately 30-minute arcs. For every short arc, a variance factor has been determined by an iterative computation procedure. The three gravity field models have been validated based on various criteria, and demonstrate the quality of not only the gravity field recovery technique but also the kinematically determined orbits.  相似文献   

19.
The role of the map in a Web-GIS environment   总被引：2，自引：1，他引：1  
The World Wide Web has changed the perspective on the role that maps can play. Their traditional function remains, e.g. to represent an abstraction of a selected part of reality to offer insight into geospatial patterns and relations. Additionally the map can be an important part of a search engine, especially in the context of geospatial data infrastructure. Maps can also function as an interface to other geographic and non-geographic information on the Web. The question What are the implications of this expanding role of maps for a WebGIS environment? is addressed in this paper.  相似文献   

20.
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.  相似文献   

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