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1.
Vector-based algorithms for the computation of azimuth, elevation and the ellipsoidal normal unit vector from 3D Cartesian coordinates are presented. As a by-product, the formulae for the ellipsoidal normal vector can also be used to iteratively transform rectangular Cartesian coordinates (X, Y, Z) into geodetic coordinates (φ, λ, h) for a height range from −5600 km to 108 km. Comparisons with existing methods indicate that the new transformation can compete with them.  相似文献   

2.
Fast transform from geocentric to geodetic coordinates   总被引：3，自引：0，他引：3  
 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10−15, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision. Received: 13 November 1998 / Accepted: 27 August 1999  相似文献   

3.
 Two iterative vector methods for computing geodetic coordinates (φ, h) from rectangular coordinates (x, y, z) are presented. The methods are conceptually simple, work without modification at any latitude and are easy to program. Geodetic latitude and height can be calculated to acceptable precision in one iteration over the height range from −106 to +109 m. Received: 13 December 2000 / Accepted: 13 July 2001  相似文献   

4.
The Cartesian-to-Geodetic coordinate transformation is re-cast as a minimization algorithm for the height of the Satellite above the reference Earth surface. Optimal necessary conditions are obtained that fix the satellite ground track vector components in the Earth surface. The introduction of an artificial perturbation variable yields a rapidly converging second order power series solution. The initial starting guess for the solution provides 3–4 digits of precision. Convergence of the perturbation series expansion is accelerated by replacing the series solution with a Padé approximation. For satellites with heights < 30,000 km the second-order expansions yields ~mm satellite geodetic height errors and ~10−12 rad errors for the geodetic latitude. No quartic or cubic solutions are required: the algorithm is both non-iterative and non-singular. Only two square root and two arc-tan calculations are required for the entire transformation. The proposed algorithm has been measured to be ~41% faster than the celebrated Bowring method. Several numerical examples are provided to demonstrate the effectiveness of the new algorithm.  相似文献   

5.
The vector-based algorithm to transform Cartesian (X, Y, Z ) into geodetic coordinates (, λ, h) presented by Feltens (J Geod, 2007, doi:) has been extended for triaxial ellipsoids. The extended algorithm is again based on simple formulae and has successfully been tested for the Earth and other celestial bodies and for a wide range of positive and negative ellipsoidal heights.  相似文献   

6.
World Geodetic Datum 2000   总被引：7，自引：1，他引：6  
 Based on the current best estimates of fundamental geodetic parameters {W 0,GM,J 2,Ω} the form parameters of a Somigliana-Pizzetti level ellipsoid, namely the semi-major axis a and semi-minor axis b (or equivalently the linear eccentricity ) are computed and proposed as a new World Geodetic Datum 2000. There are six parameters namely the four fundamental geodetic parameters {W 0,GM,J 2,Ω} and the two form parameters {a,b} or {a,ɛ}, which determine the ellipsoidal reference gravity field of Somigliana-Pizzetti type constraint to two nonlinear condition equations. Their iterative solution leads to best estimates a=(6 378 136.572±0.053)m, b=(6 356 751.920 ± 0.052)m, ɛ=(521 853.580±0.013)m for the tide-free geoide of reference and a=(6 378 136.602±0.053)m, b=(6 356 751.860±0.052)m, ɛ=(521 854.674 ± 0.015)m for the zero-frequency tide geoid of reference. The best estimates of the form parameters of a Somigliana-Pizzetti level ellipsoid, {a,b}, differ significantly by −0.39 m, −0.454 m, respectively, from the data of the Geodetic Reference System 1980. Received: 1 February 1999 / Accepted: 31 August 1999  相似文献   

7.
A new local existence and uniqueness theorem is obtained for the scalar geodetic boundary-value problem in spherical coordinates. The regularities H α and H 1+α are assumed for the boundary data g (gravity) and v (gravitational potential) respectively. Received: 27 July 1998 / Accepted: 19 April 1999  相似文献   

8.
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.  相似文献   

9.
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 K0.7 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 K0.5. 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.  相似文献   

10.
An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {,,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10–8 m2/s2 for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10–4m2/s2. Since 1.5× 10–4 m2/s2 is equivalent to 1.5×10–5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.Acknowledgments. This research has been financially supported by the University of Tehran based on grant number 621/4/859. This support is gratefully acknowledged. The authors are also grateful for the comments and corrections made to the initial version of the paper by Dr. S. Petrovic from GFZ Potsdam and the other two anonymous reviewers. Their comments helped to improve the structure of the paper significantly.  相似文献   

11.
目前的一些地心坐标向大地坐标的转换模型在计算速度,稳定性或精度方面存在一定的局限性。本文探讨了非线性方程组数值迭代的求解方法及其在MATLAB 7.0中的编程实现,并将结果与基于一元三次方程求解的严密方法做了比较分析,结果证明该方法是可以在实际中参考应用的。  相似文献   

12.
By using Halley’s third-order formula to find the root of a non-linear equation, we develop a new iterative procedure to solve an irrational form of the “latitude equation”, the equation to determine the geodetic latitude for given Cartesian coordinates. With a limit to one iteration, starting from zero height, and minimizing the number of divisions by means of the rational form representation of Halley’s formula, we obtain a new non-iterative method to transform Cartesian coordinates to geodetic ones. The new method is sufficiently precise in the sense that the maximum error of the latitude and the relative height is less than 6 micro-arcseconds for the range of height, −10 km ≤ h ≤ 30,000 km. The new method is around 50% faster than our previous method, roughly twice as fast as the well-known Bowring’s method, and much faster than the recently developed methods of Borkowski, Laskowski, Lin and Wang, Jones, Pollard, and Vermeille.  相似文献   

13.
Direct transformation from geocentric coordinates to geodetic coordinates   总被引：5，自引：0，他引：5  
 The transformation from geocentric coordinates to geodetic coordinates is usually carried out by iteration. A closed-form algebraic method is proposed, valid at any point on the globe and in space, including the poles, regardless of the value of the ellipsoid's eccentricity. Received: 14 August 2000 / Accepted: 26 June 2002  相似文献   

14.
We consider the problem of designing a geodetic survey when using more than twoGPS receivers.R.A. Snay previously published a solution to the problem for the case of 3 and 4 receivers. We present a solution for the case of 5, 6, 7 and 8 receivers. Finally we show an application of the method proposed.  相似文献   

15.
Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W 0(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order 360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms of the spheroidal “free-air” potential reduction in order to produce the spheroidal W 0(1993.4) value. As a mean of those 25 W 0(1993.4) data as well as a root mean square error estimation we computed W 0(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W 0 data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made. Received: 7 November 1996 / Accepted: 27 March 1997  相似文献   

16.
The development of lasers, new electro-optic light modulation methods, and improved electronic techniques have made possible significant improvements in the range and accuracy of optical distance measurements, thus providing not only improved geodetic tools but also useful techniques for the study of other geophysical, meteorological, and astronomical problems. One of the main limitations, at present, to the accuracy of geodetic measurements is the uncertainty in the average propagation velocity of the radiation due to inhomogeneity of the atmosphere. Accuracies of a few parts in ten million or even better now appear feasible, however, through the use of the dispersion method, in which simultaneous measurements of optical path length at two widely separated wavelengths are used to determine the average refractive index over the path and hence the true geodetic distance. The design of a new instrument based on this method, which utilizes wavelengths of6328 ? and3681 ? and3 GHz polarization modulation of the light, is summarized. Preliminary measurements over a5.3 km path with this instrument have demonstrated a sensitivity of3×10 −9 in detecting changes in optical path length for either wavelength using1-second averaging, and a standard deviation of3×10 −7 in corrected length. The principal remaining sources of error are summarized, as is progress in other laboratories using the dispersion method or other approaches to the problem of refractivity correction.  相似文献   

17.
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.  相似文献   

18.
Computing geodetic coordinates from geocentric coordinates   总被引：1，自引：1，他引：0  
A closed-form algebraic method to transform geocentric coordinates to geodetic coordinates has previously been proposed. The validity domain of latitude and height formulae in the vicinity of the Earths core is specified. A new expression of longitude is proposed, excluding indetermination and sensitivity to round-off error around the ±180 degrees longitude discontinuity.  相似文献   

19.
We have determined approximate average rates of deformation in the Qinghai-Tibet plateau and its margins from the GPS data for last 10 years and the moment tensors from earthquakes between 1900 and 1999.We also determined the strain rate (seismic strain rate) associated with the seismic deformation using 254 Mw≥5.0 earthquakes,and estimated the shortening and extension rates for every block in the area as well.We also estimated the strain rate (geodetic strain rate)by 80 GPS sites' velocity vectors and analyzed characteristic of kinematics by two kinds of strain rates and discussed earthquake potential in the area.As a result,the deformation rates from seismic moment tensors and from GPS velocities are basically agreed with each other.It is feasible to analyze seismic risk by comparing geodetic strain rate with seismic strain rate based on the opinion that strain energy will be released through earthquake.It is concluded that there is no strong earthquake potential (＞M7) in the Qinghai-Tibet plateau and its margins,but there is earthquake potential (＞M5) in middle Tibet in a few years.  相似文献   

20.
A geodetic boundary value problem (GBVP) approach has been formulated which can be used for solving the problem of height datum unification. The developed technique is applied to a test area in Southwest Finland with approximate size of 1.5° × 3° and the bias of the corresponding local height datum (local geoid) with respect to the geoid is computed. For this purpose the bias-free potential difference and gravity difference observations of the test area are used and the offset (bias) of the height datum, i.e., Finnish Height Datum 2000 (N2000) fixed to Normaal Amsterdams Peil (NAP) as origin point, with respect to the geoid is computed. The results of this computation show that potential of the origin point of N2000, i.e., NAP, is (62636857.68 ± 0.5) (m2/s2) and as such is (0.191 ± 0.003) (m) under the geoid defined by W 0 = 62636855.8 (m2/s2). As the validity test of our methodology, the test area is divided into two parts and the corresponding potential difference and gravity difference observations are introduced into our GBVP separately and the bias of height datums of the two parts are computed with respect to the geoid. Obtaining approximately the same bias values for the height datums of the two parts being part of one height datum with one origin point proves the validity of our approach. Besides, the latter test shows the capability of our methodology for patch-wise application.  相似文献   

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