Exact and heuristic formulae to compute the geodetic height from the ellipse equation

The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy.The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates.This research analyzes this influence and how it can contribute to their solutions.The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation.In addition,a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed,which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %.The calculation is stable,and the cost is low.

A new method for deriving broad-band polar motion geodetic excitations

While the geodetic excitationχ(t)of polar motion p(t)is essential to improve our understanding of global mass redistributions and relative motions with respect to the terrestrial frame,the widely adopted method to deriveχ(t)from p(t)has biases in both amplitude and phase responses.This study has developed a new simple but more accurate method based on the combination of the frequency-and time-domain Liouville's equation(FTLE).The FTLE method has been validated not only with 6-h sampled synthetic excitation series but also with daily and 6-h sampled polar motion measurements as well asχ(t)produced by the interactive webpage tool of the International Earth Rotation and Reference Systems Service(IERS).Numerical comparisons demonstrate thatχ(t)derived from the FTLE method has superior performances in both the time and frequency domains with respect to that obtained from the widely adopted method or the IERS webpage tool,provided that the input p(t)series has a length around or more than 25 years,which presents no practical limitations since the necessary polar motion data are readily available.The FTLE code is provided in the form of Mat Lab function.

Geodetic图的几个定理

若图 G中任一对不同顶点都有唯一的一条最短路 ,则称图 G是 geodetic图 .在此条件下构造了几类 geodetic图和讨论了具有 Hamilton圈的 geodetic图 .

Geodetic Number and Geo-Chromatic Number of 2-Cartesian Product of Some Graphs

A set S ⊆ V (G) is called a geodetic set if every vertex of G lies on a shortest u-v path for some u, v ∈ S, the minimum cardinality among all geodetic sets is called geodetic number and is denoted by . A set C ⊆ V (G) is called a chromatic set if C contains all vertices of different colors in G, the minimum cardinality among all chromatic sets is called the chromatic number and is denoted by . A geo-chromatic set Sc ⊆ V (G) is both a geodetic set and a chromatic set. The geo-chromatic number of G is the minimum cardinality among all geo-chromatic sets of G. In this paper, we determine the geodetic number and the geo-chromatic number of 2-cartesian product of some standard graphs like complete graphs, cycles and paths.

Estimation of Geodetic Parameters with VLBI Data of Last 5 Years

The meaning to research the potential of VLBI for geodetic applications is summarized. And the observation models and their related parameters of geodetic interest are investigated. Then, the principle and method of using the random model in VLBI data processing are investigated. With the world wide VLBI data from 2000-2004, the conditions to compute the parameters of geodetic interest are introduced, and so are the computing methods and processes. And the computed resuits of the parameters of geodetic interest are analyzed.

Geodetic Height Determination in 2005 Qomolangma Survey

Determining the geodetic height of Mount Qomolangma was one of the very important missions in the 2005 Qomolangma height survey. There were three GPS networks in the survey: regional GPS crustal deformation network, geodetic GPS control network, and GPS measurement on the mountain summit. Data collection and processing were introduced. The final data processing strategy and reasonable geodetic height were fairly determined based on careful data analysis.

Expression of strain and rotation tensor in geodetic coordinates

In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordinates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellipsoid are also discussed.

Continued Fraction Cartesian to Geodetic Coordinate Transformation

A singularity-free perturbation solution is presented for inverting the Cartesian to Geodetic transformation.Conventional approaches for inverting the transformation use the natural ellipsoidal coordinates,this work explores the use of the satellite ground-track vector as the differential correction variable.The geodetic latitude is recovered by well-known elementary means.A high-accuracy highperformance 3D vector-valued continued fraction iteration is constructed.Rapid convergence is achieved because the starting guess for the ground-track vector provides a maximum error of 30 m for the satellite height above the Earth’s surface,throughout the LEO-GEO range of applications.As a result,a single iteration of the continued fraction iteration yields a maximum error for the satellite height of 10??11 km.and maximum error for the geodetic anomaly of 10??9 rad.The coordinate transformation is completed by non-iteratively recovering the satellite height and the geodetic anomaly.No Taylor expansions are introduced and no Jacobian sensitivity calculations are required.For all practical applications the new algorithm provides a closed-form solution.The accuracy and algorithmic performance of the proposed approach is compared with other state of the art algorithms.

Prospective study of high geodetic resolution to future VGOS reference point determination

The fast slewing rate and wide band of the VLBI2010 Global Observing System(VGOS) telescopes are beneficial to procure more observations and to obtain VLBI reference points(RPs) of high precisions.Meanwhile, with the development of synchronous tracking of fixed targets on telescopes during the observing, the RPs also can be determined in near real time based on a frame defined by other techniques. These opportunities provide us a possibility to explore the high geodetic resolution of VGOS telescopes. We design a thermal variation in RP as true values, and schedule a synchronous session of VGOS and target point(TP) series observing. Then VGOS delays and TP series are simulated and solved via piecewise functions. The results show that the accuracy of vertical component of the RP could be determined at an accuracy of 0.5 ± 0.3 mm in an hour using TP series, whereas the vertical components of RP solved by using VGOS delay measurements have a greater uncertainty due to the random error in the simulated atmosphere and bad radio source sky coverage in a shorter time interval. Some details in the data processing and accuracy evaluation are also introduced.

Comparison of methods to transition geodetic latitude

With the wide application of GPS technology, the application of the system of space rectangular coordinates is more and more extensive. Transformation of space rectangular coordinates into geodetic coordinates becomes a very popular problem. In order to evaluate various kinds of algorithms existing for solving the problem, three evaluation criteria of the algorithm were put forward at first, that is, precision, calculation speed and algorithm regional suitability. After given some basic formula, three kinds of representative algorithms, classics iteration algorithm, ellipsoidal parameter transformation algorithm and rational polynomials approximation algorithm were introduced. Through a test program made by MATLAB, these three kinds of algorithms were compared. Some helpful conclusions were drawn.

Three-dimensional geodetic deformation surveying for Naner area in Daqing oilfield

Geodetic deformation severely affects the development of the oilfield and probably causes casing damage or abandonment of injection wells and producers. Therefore, it is meaningful to survey and study three-dimensional geodetic deformation in the process of the oilfield development. In order to study this issue, 11-year long term surveying of three-dimensional geodetic deformation has been carried out while developing Naner area in Daqing oilfield. Basic rules of 3-D geodetic deformation have been obtained through surveying. Results show that production and injection under high pressure may cause the changes of surface elevation, and geodetic deformation correlates with simultaneous formation pressure. Precautions and relative technological measurements have been put forward in the waterflood development in Naner region and provide theoretical guidelines for the production and casing preservation of the oilfield. Finally, surveying results are interpreted by porous elastic theory. Mathematical model to calculate 3-D geodetic deformation is put forward in the course of the oilfield development.

Statistical tests of recent plate tectonic units by using geodetic data

The statistical testing models of the plate tectonic units and the hypothesis of their rigidity is presented by using the dense geodetic data, and to a certain extent the established statistic value can be regarded as a quantitative index to compare the rigidity degrees of different blocks. The several conclusions about the global megaplates and the regional tectonics of China are tested and verified by actual calculations, which testifies the effectiveness of this method in testing the rigidity degree and delineating their boundaries.

STABILITY OF SOLUTION FOR DYNAMIC GEODETIC NETWORK ADJUSTMENT

This paper discusses theoretically the stability of solutions for dynamic geodetic network adjustment,Kalman filtering and sequence adjustment,and two examples are given.The solution for dynamic geodetic network adjustment is stable if the dynamic geodetic network is a classical network.There is not rank deficit in datum,or else the solution is not stable,which will depend on the initial value.

Development of new geodetic coordinate datum management system

Current situations of geodetic coordinate datum development procedures and management methods in China were presented. The precisions of astronomic geodetic network and space geodetic network were introduced. Geodetic datum requirements under the current and future new surveying technologies and their applications were discussed. The necessity for upgrading national astronomic geodetic network and development of a new open coordinate geodetic datum management method was investigated.

EDGE SUBDIVISIONS OF A GIVEN GEODETIC BLOCK PRESERVING ITS PROPERTY TO BEGEODETIC

In this paper authors have obtained a new necessary and sufficient condition for a graph G to be a geodetic graph. Let g : E --> Z(+) be a function from the set of edges of a graph G to the set of nonnegative integers and let g(G) denote the graph obtained from G by replacing each edge e is an element of E by a suspended are (path) P-g(e+2) of length g(e) + 1. and by using this condition, established a criterion for a function g to be a function which can generate a new geodetic block g(G) from a given geodetic block G.

Application of Digital Image Correlation and Geodetic Displacement Measuring Methods to Monitor Water Dam Behavior under Dynamic Load

This paper presents experiment results of the measurement conducted at the Roznew Dam power plant. For a course of starting and operating of turbo-plants, downstream face of the dam was monitored in relation to its eventual displacements on direction parallel to the construction axis. For the purpose of the experiment, geodetic measurement techniques and 2D DIC （digital image correlation） method （utilizing photographs of the object recorded with digital camera） were compared with regard to credibility, efficiency and accuracy. The vertical and horizontal displacements were monitored by tachometers measurements. The deformations in x-axis and y-axis on the wall surface was monitored by 2D DIC. It has been noticed that 2D DIC method is a surface method, continuous--not discreet. It allows for continuous observations of surface deformations, which is not possible in case of tachemetric measurements. Despite many advantages, the 2D DIC method lacks unambiguous evaluation of precision and relevance of designated displacements, which is rather significant for possibilities of utilization in technical control of large engineered objects. It should be also marked that the tachometric method is more reliable but is more laborious. Research of this type might comprise additional element for the assessment of the influence of dynamic loads, such as activating turbine water flow, onto the overall condition of the surveyed structure.

Development of Virtual Reference Station in Kinematic Schemes of Geodetic GPS Network Using the Method of Maximum Informative Zone

The factual data on error of positioning in VRS GPS networks have been analyzed, where the mobile receiver is provided with VRS. The method of highly informative zone is suggested for removal of initial vagueness in selection of reference stations for purposes of development of VRS on the basis of minimum GPS network, composed of three reference stations. The recommendations on use of suggested method are given.

The Characteristics of Recent Geodetic Deformation and Seismicity in North-South Seismic Zone and East of the Qinghai-Xizang Block

In this paper,the corresponding relation of the evolutionary characteristics of geodetic deformation fields with seismic activity for more than 20 years in the North-South seismic zone and East of Qinghai-Xizang Mess has been investigated.Not only is geodetic deformation in non-homogeneity for the space-time distribution but also deformation fields are in macroscopic similarity for the identical time interval.The inherited tectonic movement is a total tendency of recent crustal movement,and the motion mode is in undulations.There are stages of accumulation and release-adjusting of strain energy in crustal movement processes,which may be the dynamic mechanism of relatively quiet and active seismicity.The analysis of the crustal movement tendency since 1991 is of some significance for judging the stress state and the large seismic situation in the area.

CHINA: MAIN GEODETIC ACTIONS 1996-2000

This article reviews the progress made in geodetic work in China since the 1980s.In order to meet the needs of China’s economic and defense construction,and scientific and social development in the early 21th century,some main geodetic actions which should be completed before 2000 are proposed as follows.(1) Monitoring vertical crustal movements and conducting studies on its mechanism.Releveling of the second phase of the national first order leveling network.Computation of the vertical crustal movement.(2) Improvement of national space geodetic network.The main task is to lay down a national B-order GPS network and complete its data processing.(3) Refining of Chinese local gravity field on land and sea.The determination of Chinese local quasi geoid with higher than one meter accuracy.Application of

Determination of global geodetic parameters using satellite laser ranging to Galileo,GLONASS,and BeiDou satellites

The new Global Navigation Satellite System(GNSS)satellites,including GLONASS,Galileo,and BeiDou system,are equipped with Laser Retroreflector Arrays(LRA)to support Satellite Laser Ranging(SLR)tracking,which contributes to the estimation of global geodetic parameters.In this study,we estimate the global geodetic parameters using the SLR observations to GNSS satellites and also investigate the effects of different data processing strategies on the estimated Earth Rotation Parameters(ERP),geocenter motion,and terrestrial scale.The results indicate that setting range bias parameters for each satellite-station pair can effectively account for the satellite-specific biases induced by LRAs,leading to smaller Root Mean Square Errors(RMSE)of the post-fit SLR residuals.Furthermore,estimating the range biases for each satellite-station pair improves the accuracy of the estimated station coordinates and ERP.We also examine the impact of different arc lengths on the estimates of ERP,geocenter motion,and terrestrial scale.The results show that extending arc length can significantly reduce the formal error of ERP.The 7-day strategy produces the smallest RMSEs of 473 microarcseconds and 495 microarcseconds for the estimated X-and Y-component of pole coordinates,and 52 microseconds for length-of-day,respectively.However,the estimated geocenter motion is less affected by the arc length,even the shortest 1-day arc strategy can capture the seasonal variations of geocenter motion in Z component.For scale estimation,extending the arc length notably improves the accuracy of the estimated station coordinates and scale,but this advantage becomes less noticeable in longer arcs.The 7-day solution also obtains the closet scale results compared to ITRF2014,with the RMSE of 2.10×10^(–9).