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1.
《测量评论》2013,45(9)
AbstractThe following method will be found better and quicker than the usual logarithmic process in computing the co-ordinates of intersected points in minor triangulation and traverse work. Let A and B be two stations whose co-ordinates (x 1 y 1), (x 2 y 2) are known. Let P be an intersected point whose co-ordinates (x, y) we wish to determine. Let α and β be the observed angles at A and B respectively. 相似文献
2.
On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms 总被引：2，自引：1，他引：1
The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E
Y
= (X−E
X
) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E
Y
and E
X
. Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation
matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix
X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem
by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative
algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition.
For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert
cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing
the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment
of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift
to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares
and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion
matrix of the estimated parameters. 相似文献
3.
4.
AbstractFor the sake of the junior reader we may repeat an old and simple investigation. Let us suppose that the paper on which a map is printed undergoes a regular expansion p in one direction, say the X direction, and another regular expansion q in the Y direction, perpendicular to the former; it is required to know the effect of these expansions on the area of any parcel on the map. Note that, so far as the mathematics are affected, X and Y are not necessarily parallel to the margins of the sheet; we shall take them here as axes of any rectangular coordinate system. The symbols p and q are regarded as ratios, so that 100p and 100p represent the percentage expansions; if the paper contracts instead of expanding, no more is necessary than to change the sign. 相似文献
5.
《测量评论》2013,45(46):474-487
AbstractWe are indebted to Professor R. V. Southwell for the approximate method of computation known as the systematic relaxation of constraints. In an article to the Empire Survey Review, 1938, Mr A. N. Black showed how Southwell's ideas could be applied to the adjustment of the co-ordinates of a point. 相似文献
6.
《测量评论》2013,45(56):53-68
AbstractThis extremely simple and elegant method of computing geographical co-ordinates, given the initial azimuth and length of line from the standpoint, was published by Col. A. R. Clarke in 1880. There is no other known method giving the same degree of accuracy with the use of only three tabulated spheroidal factors. Clarke himself regarded this as an approximate formula (vide his remark in section 5, p. 109, “Geodesy”); but as this article demonstrates, it is capable of a high degree of precision in all occupied lati tudes when certain corrections are applied to the various terms. These corrections are comparatively easy to compute, require no further spheroidal factors, and some of them may be tabulated directly once and for all. 相似文献
7.
《测量评论》2013,45(95):22-30
AbstractThe procedure for aerotriangulation on the Wild A5 and similar plotting instruments is well known. The first overlap is set up in absolute orientation on well spaced plan and height control and successive overlaps are set up relatively, each to the previous overlap, by eliminating want of correspondence and preserving the height agreement of points falling in the common portion of successive overlaps. When each overlap is correctly set, the co-ordinates of selected points are measured on the instrument (machine co-ordinates). These co-ordinates differ from true ground co-ordinates only in origin, azimuth and scale, provided the settings and measurements are precisely done on error-free models, precisely connected together. However, such ideal conditions are never obtained, and the errors in azimp.th, scale and height datum increase with the number of overlaps added along a strip. 相似文献
8.
Applications of graph theory to gross error detection for GPS geodetic control networks 总被引：1，自引：0，他引：1
Samwel Simon Katambi 《地球空间信息科学学报》2002,5(4):26-31
1 ＧｒａｐｈｔｈｅｏｒｙａｎｄｄｅｆｉｎｉｔｉｏｎｓＡｇｒａｐｈＧｃｏｎｓｉｓｔｓｏｆｐｏｉｎｔｓ (ＮＯＤＥＳ)ａｎｄｌｉｎｅｓ (ＥＤＧＥＳ)ｃｏｎｎｅｃｔｉｎｇｔｈｅｓｅｐｏｉｎｔｓ .Ｔｈｅｐｏｉｎｔｓａｒｅｃａｌｌｅｄｎｏｄｅｓａｎｄｌｉｎｅｓａｒｅｅｄｇｅｓ .Ａｄｉｒｅｃｔｅｄｇｒａｐｈｉｓａｇｒａｐｈｉｎｗｈｉｃｈｔｈｅｅｄｇｅｓｃｏｎ ｎｅｃｔｉｎｇｔｈｅｎｏｄｅｓａｒｅｓｐｅｃｉｆｉｅｄ .Ａｔｒｅｅｉｓａｃｏｎｎｅｃｔｅｄｇｒａｐｈｗｉｔｈｏｕｔａｎｙｌｏｏｐ .Ａｌｏｏｐｉｓａｃｌｏｓ… 相似文献
9.
AbstractIf the geographical co-ordinates, Φ0, L 0, and the azimuth A 0 at a station O of a triangulation undergo corrections, ?Φ0, ?L 0 and ?A 0, the geographical co-ordinates, Φ, L, and the azimuth A have to be re-computed for all the vertices throughout the whole triangulation. This is a tedious operation. It may be vastly simplified, however, by the employment of differential formulae. The derivation of these formulae would consume considerable space, so that the results alone are given here. 相似文献
10.
This paper generalizes the Stokes formula from the spherical boundary surface to the ellipsoidal boundary surface. The resulting
solution (ellipsoidal geoidal height), consisting of two parts, i.e. the spherical geoidal height N
0 evaluated from Stokes's formula and the ellipsoidal correction N
1, makes the relative geoidal height error decrease from O(e
2) to O(e
4), which can be neglected for most practical purposes. The ellipsoidal correction N
1 is expressed as a sum of an integral about the spherical geoidal height N
0 and a simple analytical function of N
0 and the first three geopotential coefficients. The kernel function in the integral has the same degree of singularity at
the origin as the original Stokes function. A brief comparison among this and other solutions shows that this solution is
more effective than the solutions of Molodensky et al. and Moritz and, when the evaluation of the ellipsoidal correction N
1 is done in an area where the spherical geoidal height N
0 has already been evaluated, it is also more effective than the solution of Martinec and Grafarend.
Received: 27 January 1999 / Accepted: 4 October 1999 相似文献
11.
《测量评论》2013,45(20):354-358
Abstract 6. Further Expansions.—Equations (4.3) and (5.5) enable a computer to transform coordinates from the Cassini projection to the Gauss projection without recourse to geographical coordinates. If applied to one or two points, no doubt these equations would be quite satisfactory; but if applied to 100,000 points their use would be laborious and it would be difficult to adapt them to machine computing. 相似文献
12.
《测量评论》2013,45(58):142-152
AbstractIn January 1940, in a paper entitled “The Transverse Mercator Projection: A Critical Examination” (E.S.R., v, 35, 285), the late Captain G. T. McCaw obtained expressions for the co-ordinates of a point on the Transverse Mercator projection of the spheroid which appeared to cast suspicion on the results originally derived by Gauss. McCaw considered, in fact, that his expressions gave the true measures of the co-ordinates, and that the Gauss method contained some invalidity. He requested readers to report any flaw that might be discovered in his work, but apparently no such flaw had been detected at the time of his death. It can be shown, however, that the invalidities are in McCaw's methods, and there seems no reason for doubting the results derived by the Gauss method. 相似文献
13.
Y. Kozai 《Journal of Geodesy》1968,42(3):355-357
From periodic variations of the orbital inclinations of three artificial satellites 1959Alpha 1, 1960Iota 2, and 1962Beta Mu 1 Love’s number of the earth and time lag of the bodily tide due to the friction are determined, respectively,0.29±0.03 and(10±5) minutes in time.
While the previous paper on the determination of Love’s number of the earth (Kozai, 1967) was in press, a minor error was
discovered in the Differential Orbit Improvement program(DOI) of the Smithsonian Astrophysical Observatory(SAO). Since the analysis was based on time-variations of the orbital inclinations which were derived by theDOI from precisely reduced Baker-Nunn observations, it is likely that the results in the previous paper was affected by the error
in theDOI. Therefore, the analysis is iterated by using the revisedDOI. Three satellites, 1959Alpha 1 (Vanguard 2), 1960Iota 2 (rocket ofEcho 1), and 1962Beta Mu 1 (Anna) (see Table 1) are adopted for determining Love’s number in the present paper. The satellite, 1959Eta, which was used in the previous paper, is not adopted here, since the inclination of this satellite shows irregular variations
unexplained. Instead of 1959Eta 1962Beta Mu 1 is adopted as orbital elements from precisely reduced Baker-Nunn observations have become available for a long interval of
time for this satellite. 相似文献
14.
E. Grafarend 《Journal of Geodesy》1970,44(1):41-49
Summary The probability to find an error vector in multiples of the Helmert-Maxwell-Boltzmann point error σ2 δij(δij Kronecker symbol) is calculated. It is found that the probability is for σ39%, for2 σ86% and for3 σ99% in two dimensions, for σ20%, for2 σ74% and for3 σ97% in three dimensions. The fundamental Maxwell-Boltzmann-distribution is tabulated0,02 (0,02) 4,50.
相似文献
15.
Absolute orientation is a basic technical work in digital image geologic logging of underground coal mine. Traditional control-point-based absolute orientation method requires setting object space control points of the known three-dimensional coordinates, which may lead to low efficiency. Therefore, this paper proposed a point-free close-range photogrammetry absolute orientation algorithm, which utilized direction line segments including plumb line segments and line segments with known directions and lengths to identify the dimensional orientation of a stereoscopic model. Experiment results show that the precision of the orientation results is favorable. σ X and σ Y are as high as 0.5 mm, and σ Z is 0.3 mm. Finally, this paper introduced the application of the proposed algorithm in rapid geological logging of coal mine roadway, which was fast and reliable, convenient and feasible. 相似文献
16.
《测量评论》2013,45(60):221-227
AbstractIn a previous article in this Review, the writer endeavoured to show that chains of minor triangulation could be adjusted by plane rectangular co-ordinates ignoring the spherical form of the earth with little loss of accuracy, provided that the two ends were held fixed in position. It was demonstrated that the plane co-ordinates produced by the rigorous adjustment between the fixed starting and closing sides, differ by only a comparatively small amount from the projection co-ordinates produced by a rigorous adjustment on the Transverse Mercator projection. The saving in time when computing by plane co-ordinates as opposed to rigorous computation on the projection by any method will be apparent to any computer with experience of both methods. 相似文献
17.
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
18.
Since the beginning of the International Global Navigation Satellite System (GLONASS) Experiment, IGEX, in October 1998,
the Center for Orbit Determination in Europe (CODE) has acted as an analysis center providing precise GLONASS orbits on a
regular basis. In CODE's IGEX routine analysis the Global Positioning System (GPS) orbits and Earth rotation parameters are
introduced as known quantities into the GLONASS processing. A new approach is studied, where data from the IGEX network are
combined with GPS observations from the International GPS Service (IGS) network and all parameters (GPS and GLONASS orbits,
Earth rotation parameters, and site coordinates) are estimated in one processing step. The influence of different solar radiation
pressure parameterizations on the GLONASS orbits is studied using different parameter subsets of the extended CODE orbit model.
Parameterization with three constant terms in the three orthogonal directions, D, Y, and X (D = direction satellite–Sun, Y = direction of the satellite's solar panel axis), and two periodic terms in the X-direction, proves to be adequate for GLONASS satellites. As a result of the processing it is found that the solar radiation
pressure effect for the GLONASS satellites is significantly different in the Y-direction from that for the GPS satellites, and an extensive analysis is carried out to investigate the effect in detail.
SLR observations from the ILRS network are used as an independent check on the quality of the GLONASS orbital solutions. Both
processing aspects, combining the two networks and changing the orbit parameterization, significantly improve the quality
of the determined GLONASS orbits compared to the orbits stemming from CODE's IGEX routine processing.
Received: 10 May 2000 / Accepted: 9 October 2000 相似文献
19.
《测量评论》2013,45(47):30-35
AbstractIn the Empire Survey Review for October 1938 (iv, 30, 480) a simple demonstration of the condition to be satisfied for conformal representation was given. This condition may be expressed by the equation w = f(z), where w and z are complex variables representing corresponding points in the w-plane and z-plane respectively, and f(z) is an analytic function of z. 相似文献
20.
Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution 总被引：4，自引：0，他引：4
Harmonic coefficients of the 2nd degree are separated into the invariant quantitative (the 2nd-degree variance) and the qualitative
(the standardized harmonic coefficients) characteristics of the behavior of the potential V
2(t). On this basis the evolution of the Earth's dynamical figure is described as a solution of the time-dependent eigenvalues–eigenvectors
problem in the canonical form. Such a canonical quadratic form is defined only by temporal variations of the harmonic coefficients
and always remains finite, even within an infinite time interval. An additional condition for the correction or the determination
of temporal variations of the 2nd degree is obtained. Temporal variations of the fully normalized sectorial harmonic coefficients
are estimated in addition to ˙Cˉ
20, ˙Cˉ
21, and ˙Sˉ
21 of the EGM96 gravity model. In addition, a non-linear hyperbolic model for Cˉ
2m
(t), Sˉ
2m
(t) is constructed. The trigonometric form of the hyperbolic model leads to the consideration of the potential V
2(ψ) instead of V
2(t) within the closed interval −π/2≤ψ≤+π/2. Thus, it is possible to evaluate the global trend of V
2(t), the Earth's principal axes and the differences of the moments of inertia within the whole infinite time interval.
Received: 25 September 1998 / Accepted: 28 June 2000 相似文献