EXPANSION OF PAPER AS AFFECTING BEARING

Abstract

The problem of the influence of the paper itself on bearings taken off maps or plans has been recently discussed by G. T. M. in this Review (iii, 22, 479). The following alternative method of solving the problem may be of interest; the same figure and symbols are used as in the article mentioned.     

CHECKING TRAVERSE COMPUTATIONS

Abstract

Traverse Computations must be Checked.—A traverse is a chain of points connected by angular and linear measurements. The check on observations is provided by the agreement, obtained in computations, between the terminals of the traverse (terminal bearings and terminal co-ordinates) taken as fixed. This check is not sufficient, however, to serve as a check on the computations. As a matter of principle, computations should be free of errors; there are no limits of tolerance in computational work except for discrepancies arising from inaccuracy of last figures. Secondly, errors in computation may occur that are not revealed by the traverse misclosures, not to speak of compensational errors, the field for which is very favourable in traverse work.     

A MODIFICATION OF BOWDITCH'S RULE,TO PRESERVE THE BEARING OF THE DATUM LINE IN A CLOSED TRAVERSE

Abstract

The article derives formulae for adjusting the lengths and bearings of a traverse so as to obtain an exact closure, whilst obeying the Least Squares condition and an added condition that the original bearing of one of the traverse lines is to remain unaltered.     

SEMIGRAPHIC FIXATION ON A CURVED SURFACE

Abstract

The commonly known methods for semigraphic fixation of trigonometrical stations depend on rectangular coordinates and bearings computed therefrom, but the extension of such methods to cases in which the distances are so great that second-order terms in coordinate differences become appreciable is never undertaken on account of the heavy computations involved. The following method, which is not found in the ordinary text-books, may be of interest to some surveyors not only because it can be applied to fixations using triangles of any size, but also because it can be employed to fix points in a triangulation that has been adjusted but not coordinated, since it is quite independent of coordinates and bearings.     

THE USE OF THE MAGNETIC NEEDLE ON SURVEYS IN TRINIDAD

Abstract

In Trinidad the magnetic needle is used on all secondary surveys. The term “compass surveys” was given, unfortunately, to these secondary surveys in order to distinguish them from surveys carried out in open country in the ordinary manner with the theodolite oriented by means of solar observations or by bearings obtained direct from the trigonometrical framework.     

CALIBRATION OF PRISMATIC COMPASSES

Abstract

Apart from “stickiness” of the suspension and looseness of the sights, prismatic compasses are subject to three internal sources of error:- <list list-type="roman-lower"> <list-item>

Collimation error. This may be caused by <list list-type="alpha-lower"> <list-item>

magnetic axis not being parallel to the zero line of the graduated circle;</list-item> <list-item>

line of sight not passing through the axis of rotation.</list-item> </list> It is unnecessary to aftempt to distinguish between the above faults, which introduce constant errors into the compass readings.</list-item> <list-item>

Eccentricity error. This is caused by the axis of rotation failing to pass through the centre of the graduated circle. This introduces an error into the compass readings of E sin θ cosec I°/R where E is the eccentricity, R the radius of the graduated circle and θ the angle between the line of sight and the line joining the centre of the circle to the axis of rotation. Eccentricity error is completely eliminated by observing both forward and back bearings, but this is not always practicable.</list-item> <list-item>

Irregular division of the graduated circle. This error is negligible in any modern compass.</list-item> </list>     

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.     

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.     

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.     

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.     

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.     

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 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).     

TABULAR AZIMUTH

Abstract

In a known latitude Φ the azimuth A of a heavenly body, of known declination δ, is determinable if its altitude h is measured by a theodolite or other instrument. The azimuth of course is that for the instant of observation.     

CORRECTION TO BEARING FOR HEIGHT OF SIGNAL

Abstract

When a beacon B _h stands on a mountain of height h, the bearing of B _h as seen from another station A is in general affected by its elevation. The correction never exceeds one second of arc, but in primary triangulation it is not always negligible.     

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.     

TRIGONOMETRICAL HEIGHTS AND THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

Mr. 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.     

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.     

INTERPOLATING FROM TRAVERSE TABLES TO SECONDS

Abstract

In 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.     

A DRAFTING MACHINE FOR CIRCULAR ARCS OF ANY RADIUS

Abstract

1. Theory.—In Figs. 1. a and 1. b the letters R represent in each case four equal links of any length forming a freely jointed rhombus. L, L are two equal links of any length. (n ± 1), n are respectively a fixed and a rotating link whose lengths are in the ratio (n ± 1)/n.