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1.
Summary Within potential theory of Poisson-Laplace equation the boundary value problem of physical geodesy is classified asfree andnonlinear. For solving this typical nonlinear boundary value problem four different types of nonlinear integral equations corresponding
to singular density distributions within single and double layer are presented. The characteristic problem of free boundaries,
theproblem of free surface integrals, is exactly solved bymetric continuation. Even in thelinear approximation of fundamental relations of physical geodesy the basic integral equations becomenonlinear because of the special features of free surface integrals. 相似文献
2.
《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
3.
Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm 总被引：4，自引：0，他引：4
Erik W. Grafarend 《GPS Solutions》2000,4(2):31-44
In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange
observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued
parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review
the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference
operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated
by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined
by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities)
and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to
the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove
that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued
unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated
by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')−1[L'◯] ∈ ℤ
m
where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ
m
, the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc. 相似文献
4.
O. Remmer 《Journal of Geodesy》1969,43(2):99-122
A method for filtering of geodetic observationwhich leaves the final result normally distributed, is presented. Furthermore, it is shown that if you sacrifice100.a% of all the observations you may be (1−β).100% sure that a gross error of the size Δ is rejected.
Another and, may be intuitively, more appealing method is presented; the two methods are compared and it is shown why Method
1 should be preferred to Method 2 for geodetic purposes.
Finally the two methods are demonstrated in some numerical examples. 相似文献
5.
In the field of biomass estimation, terrain radiometric calibration of airborne polarimetric SAR data for forested areas is an urgent problem. Illuminated area correction of σ -naught could not completely remove terrain features. Inspired by Small and Shimada, this paper tested gamma-naught on one mountainous forested area using airborne Uninhabited Aerial Vehicle Synthetic Aperture Radar data and found it could remove most terrain features. However, a systematic increasing trend from far range to near range is found in airborne SAR cases. This paper made an attempt to use the relationship between distance to SAR sensor and γ-naught to calibrate γ -naught. Two quantitative evaluation methods are proposed. Experimental results demonstrate that variation of γ -naught can be constrained to a limited extent from near range to far range. Since this method is based on ground range images, it avoids complicated orthorectification. 相似文献
6.
Determination of complexity factor and its relationship with accuracy of representation for DEM terrain 总被引：1，自引：0，他引：1
Based on the estimating rule of the normal vector angles between two adjacent terrain units, we use the concept of terrain
complexity factor to quantify the terrain complexity of DEM, and then the formula of terrain complexity factor in Raster DEM
and TIN DEM is deduced theoretically. In order to make clear how the terrain complexity factor E
CF
and the average elevation h affect the accuracy of DEM terrain representation RMSE
Et
, the formula of Gauss synthetical surface is applied to simulate several real terrain surfaces, each of which has different
terrain complexity. Through the statistical analysis of linear regression in simulation data, the linear equation between
accuracy of DEM terrain representation RMSE
Et
, terrain complexity factor E
CF
and the average elevation h is achieved. A new method is provided to estimate the accuracy of DEM terrain representation RMSE
Et
with a certain terrain complexity and it gives convincing theoretical evidence for DEM production and the corresponding error
research in the future. 相似文献
7.
8.
《测量评论》2013,45(83):224-230
AbstractMr. A. J. Morley has contributed a series of articles in the Review (E.S.R., iv, 23, 16; iv, 25, 136 and vi, 40, 76) on the adjustment of trigonometrical levels and the evaluation of the coefficient of terrestrial refraction with a view to ascertaining how other Colonies and Dominions deal with these problems. This object is very commendable as several problems concerning both the observational and theoretical sides arise in height determinations, regarding which there is not much guidance in the usual treatises on the subject. 相似文献
9.
《测量评论》2013,45(49):134-135
AbstractIn the Empire Survey Review, no. 4, 1932, Mr. Clendinning has described a method of interpolating from traverse tables to seconds. Below is another method, due to Prof. Nekrassov, for use with traverse tables published by him. The method is described in The Geodezist, Moscow, 1936, no. I, pp. 47–52. 相似文献
10.
《测量评论》2013,45(85):319-325
AbstractIn a recent issue of this Review, an example is given of the conformal transformation of a network of triangulation using Newton's interpolation formula with divided differences. While the application of the method appears to be new, attention should be drawn to the fact that Kruger employed Lagrange's interpolation formula in a discussion and extension of the Schols method in a paper which was published in the Zeitschrift für Vermessungswesen in 1896. A reference to this paper was given at the end of the paper, “Adjustment of the Secondary Triangulation of South Africa”, published in a previous issue of the E.S.R. (iv, 30, 480). 相似文献
11.
AbstractThe proof of the attraction of a uniformly thin vertical block in the last issue (No. 24, p. 87) does not appear as satisfactory as the textbook would suggest. It is proposed to attempt here a more direct explanation, independent of substitutional expedients. 相似文献
12.
13.
《测量评论》2013,45(84):274-277
AbstractMr. Rainsford's paper in E.S.R. No. 78 establishes as thoroughly as one can wish by computational example that there is little to choose in relative accuracy between direction adjustment and angle adjustment, and that the deciding factor is really ease and speed of computation. 相似文献
14.
15.
《测量评论》2013,45(78):366-368
AbstractThe method of reducing circummeridian altitudes or zenith distances to the meridian, using the factors m and n as tabulated by Chauvenet, is well known. The following method, which does not use these factars, has been faund both more convenient and more accurate in practice. The formula can be easily obtained by expanding m and n in powers of t, but far the sake af campleteness the derivatian is here given from the beginning. 相似文献
16.
《测量评论》2013,45(1):31-33
AbstractThe figure which follows shows the geometrical solution of Simple Resection by Cassini in 1669, two years before the Collins solution. It is clearly the geometrical illustration of the Delambre (1786) solution; for db = b cosec β, dc = c cosec γ and the angle QAR is known, being BAC + β + γ ? 180°. Hence the Delambre solution-that in most common use to-day—reduces to a triangle in which two sides and the contained angle are given, as has been mentioned elsewhere. 相似文献
17.
《测量评论》2013,45(54):311-314
AbstractThere has always been a marked difference of opinion on the relative merits of the methods of bearings and of angles as applied to triangulation, though it is probable that the majority of writers prefer the method of bearings for first-order work. The subject was mentioned in a recent issue of this Review (vii, 47, 19). 相似文献
18.
AbstractThat admirable annual, The Surveyor (Ceylon), was generously forwarded to us some months ago. In this issue, vol. 2, no. 4, p. 93, there is given the solution of a question on resection in an examination paper. Since the solution appears rather laboured and the problem is interesting in itself and by no means valueless, it seems not out of place to attempt a simpler and more obvious answer. 相似文献
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20.
《测量评论》2013,45(62):311-314
AbstractIn E.S.R., viii, 56, 70, Brigadier K. M. Papworth has given expressions for the angular corrections, known as (t – t) corrections, in the Lambert NO.2 Projection, derived from empirical considerations based on actual detailed calculations. Apparently some difficulty has been experienced in offering a proof. In view of the widespread use of the Lambert Projection in World War II, it is hoped that the following proof will be found to be of more than academic interest. 相似文献