CONDITION FOR THE CONSTRUCTION OF A CONFORMAL PROJECTION

Abstract

In 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.     

The free nonlinear boundary value problem of physical geodesy

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.     

THE CONFORMAL TRANSFORMATION OF A NETWORK OF TRIANGULATION

Abstract

In 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).     

DEVIATION OF THE VERTICAL. DISCUSSION

Abstract

The following is a report of the discussion on the paper by Mr. A. R. Robbins on “Deviation of the Vertical” which was read at a meeting of the Land Surveying Division of the Royal Institution of Chartered Surveyors held on Tuesday, 12th December, 1950, and which was published in the January issue of this Review (xi, 79, 28–36).     

TRIANGULATION: BEARINGS VERSUS ANGLES

Abstract

There 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).     

EARLY MEASUREMENTS OF ARC IN ‘IRAQ

Abstract

In a tale, delightfully told in vol. ii, no. 8, pp. 121–2 of this Review, Mr. Kitching revealed how he was called upon to assist in determining the length of an Arab mile. In the notes following the story a reference was made to measurements of arc carried out in the ninth century A.D. The following notes add some more details to those already given. The full table of the Arab units of length is given below; in the reference above, one step was left out.     

Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm

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.     

SARAWAK LANDS AND SURVEY DEPARTMENT

Abstract

Financial.—The revenue collection for the year was 479,591.75, consisting of Lands and Survey Revenue 356,087.52 and Mining Revenue 123,504.23.     

A statistical filter for geodetic observations

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.     

SARAWAK LANDS AND SURVEY DEPARTMENT ANNUAL REPORT FOR 1936

Abstract

General.—The Surplus of Revenue over Expenditure was again a record, as the following figures show: 1933, 4,538;1934, 185,387; 1935, 196,669; 1936, 225,148.     

THE NEW GEODETIC TAVISTOCK THEODOLITE

Abstract

Work on the original Geodetic Tavistock Theodolite was commenced in the autumn of 1931, and after suitable tests this instrument was sent out to East Africa and used on the East African Arc. Bt Major M. Hotine, R.E., writing in the E.S.R. of April 1935 (no. 16, vol. iii), stated: “The Tavistock instrument, although a first model, gave uniformly satisfactory service throughout and was used for over half the main angular observations.”     

TWO PROBLEMS OF RESECTION

Abstract

That 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.     

Terrain radiometric calibration of airborne UAVSAR for forested area

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.     

THE SEVEN-LENS AIR-SURVEY CAMERA

Abstract

By kind permission of the Editor of the Royal Engineers Journal, this paper has been adapted from the article by the Author in the issue of June 1937 (Vol. li, pp. 217–223). We are also indebted to the Editor for placing generously at our disposal the blocks used to illustrate the paper.     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In two previous articles (E.S.R., vol. iv, nos. 23 and 25) it was shown that, at the time of maximum diurnal temperature in the tropics, a definite relationship exists in the lower layers of the atmosphere between the magnitude of the coefficient of terrestrial refraction at a point and the height of that point above plain level, provided the weather is fine and clear. In fact the coefficient K increases with the height h, within certain limits which are probably defined by the condensation layer.     

CONVENTIONS AND GENERALIZED FORMULAE FOR THE ASTRONOMICAL TRIANGLE

Abstract

In the October 1953 issue of this Review (E.S.R. xii, 90, 174), Mr. J. G. Freislich has written of the difficulties of a southern hemisphere computer attempting to use astronomical formulae from a textbook prepared for use in the northern hemisphere. He proposes a solution in which different conventions are adopted in the two hemispheres, leading to different formulae for the two cases, a solution which the present writer does not favour.     

SARAWAK LANDS AND SURVEY DEPARTMENT, 1940

Abstract

Financial.-The revenue collection for the year was 440,790.30, consisting of Land revenue 336,422.97 and Mining revenue 104,360.33. The expenditure for the year was 206,476.02, of which only 192.05 was Special. This does not include salaries, amounting to 14,313, of Officers seconded for Food Control. Expenditure was again below normal because of the secondment of staff to other duties.     

Determination of complexity factor and its relationship with accuracy of representation for DEM terrain

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.     

ATTRACTION OF THE “COMPENSATION”: A NOTE

Abstract

The 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.