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 HYDROGRAPHIC YEAR 1930

Abstract

For some years past the work of the Hydrographic Service of H.M. Navy afloat has been carried out by eight of H.M. Surveying Vessels. These ships, of which four are employed abroad and four in home waters, work at sea for about eight months in the year and are refitted during the remaining four months, usually during the winter or bad-weather season. Whilst the ships are being refitted for further service the officers are employed in drawing the fair charts of the season's work and in preparing Sailing Directions and other work in connection with the Survey.     

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.     

SILTING AND ISLAND GROWTH IN THE ZAMBEZI NEAR LIVINGSTONE

Abstract

The Northern Rhodesia Survey Department recently carried out a series of measurements of certain cross-sections of the Zambezi in the vicinity of Livingstone. The stretch of river over which the above were made is that known as the Regatta Course and extends between the top of Loando or Long Island downstream to the mouth of the Maramba River. This stretch is about three and a half miles southwest of Livingstone and two to four miles upstream from the Victoria Falls.     

A TEST OF AUTO-COLLIMATION

Abstract

In the July 1940 issue of the Empire Survey Review Mr A. V. Lawes contributes a valuable article, “The Application of the Gauss Method of Collimation to the Adjustment of Survey Instruments”. One section of the article describes four methods of adjusting collimators at solar focus, in other words of assuring that the emitted rays are parallel or that the target appears at an infinite distance. Mr Lawes rightly claims that auto-collimation is the most accurate of the four methods, and he warns readers that “the reflector used in this method must be as perfect optically as the objective”. However, he fails to give any method of testing the result obtained by following his directions, and experience suggests that auto-collimation may give a result considerably in error even though the reflector may with some justification be presumed to be good.     

THOUGHTS ON THE RUWANDIZ ROAD

Abstract

THE article on Road-Surveying in the East by Mr. J. N. List in the Empire Survey Review, No.6, 263–74, is well worthy of perusal. From the beginning, with his apt quotation from Kipling, to the end where he compares the text-book ideal of road location with the indifferent compromise amidst difficulties that the British engineer in the East is lucky to be able to achieve, I felt in accord with his observations. Having spent four years on a similar kind of work, I consider that this article well deserves the appreciation of its author's profession.     

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 MATHEMATICAL APPROACH TO PROBLEMS IN PHOTOGRAMMETRY

Abstract

Many have tried their hands at one time or another at developing practical methods in respect to the solutions of the four fundamental problems viz., (1) space resection, (2) orientation of photograph in space and relative to one another, (3) space intersection, and (4) photogrammetric extension of surveys without ground control. The trouble so far has been that each worker had his own particular problem to solve and hence a completely general and comprehensive approach to the problems is lacking. In this paper these four fundamental problems are considered as essentially one of a system of linear transformations, from one set of coordinates to another, bearing in mind the existence of the significant correspondence between pairs of image points and points in space.     

FORSAT: a 3D forest monitoring system for cover mapping and volumetric 3D change detection

ABSTRACT

A 3D forest monitoring system, called FORSAT (a satellite very high resolution image processing platform for forest assessment), was developed for the extraction of 3D geometric forest information from very high resolution (VHR) satellite imagery and the automatic 3D change detection. FORSAT is composed of two complementary tasks: (1) the geometric and radiometric processing of satellite optical imagery and digital surface model (DSM) reconstruction by using a precise and robust image matching approach specially designed for VHR satellite imagery, (2) 3D surface comparison for change detection. It allows the users to import DSMs, align them using an advanced 3D surface matching approach and calculate the 3D differences and volume changes (together with precision values) between epochs. FORSAT is a single source and flexible forest information solution, allowing expert and non-expert remote sensing users to monitor forests in three and four (time) dimensions. The geometric resolution and thematic content of VHR optical imagery are sufficient for many forest information needs such as deforestation, clear-cut and fire severity mapping. The capacity and benefits of FORSAT, as a forest information system contributing to the sustainable forest management, have been tested and validated in case studies located in Austria, Switzerland and Spain.     

THE ENGINEER SURVEYOR

Abstract

Survey Training for the Civil Engineer at the University has been discussed in four articles in the Review. (R. N. Ray, M.A., xii, 89, 104–110; H. Biesheuvel, B.Sc., xii, 90, 159–165; A. Stephenson, O.B.E., M.A., F.R.I.C.S., xii, 91, 217–222; K. R. Peattie, B.Sc., Ph.D., A.R.T.C., A.M.I.C.E., xii, 94, 376–379.) Cost of equipment for a large class and limitation of time in an already heavily loaded curriculum prevent the student acquiring enough training to undertake the survey work required on alarge engineering scheme. The schemes of training described in the four articles are greatly to be admired and it is hard to see how any improvement can be made.     

The geopotential to (14, 14) from a combination of satellite and gravimetric data

A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γ_E=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γ_E withf=1/298.25, KM=3.9860122·10 ²² cm ³ /sec ² , the consistent equatorial radius was found to be6378143 m.     

Fehlertheoretische Maxwell-Boltzmann-Verteilung

Summary The probability to find an error vector in multiples of the Helmert-Maxwell-Boltzmann point error σ² δ_ij(δ_ij 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.      

MARGINAL SCALES OF LATITUDE AND LONGITUDE ON TRANSVERSE MERCATOR MAPS

Abstract

The problem of computing marginal scales of latitude and longitude on a rectangular map on the Transverse Mercator projection, where the sheet boundaries are projection co-ordinate lines, may be solved in various ways. A simple method is to compute the latitudes and longitudes of the four corners of the sheet, and then, assuming a constant scale, to interpolate the parallels and meridians between these corner values. Although it is probably sufficiently accurate for practical purposes, this method is not precise. It is not difficult to adapt the fundamental formulce of the projection to give a direct solution of the problem.     

Coloured Roads on Ordnance Survey First Edition 1 : 2500 Plans and One-Inch Maps 1897–1935, and the Rights Of Way Disclaimer

Abstract

In 1892 a government committee of inquiry into the Ordnance Survey suggested that the Survey should make a distinction between public and private second class roads at the one-inch scale. This study is confined to England and Wales and looks at the nineteenth-century practice of colouring roads on the large-scale plans, and compares the representation of coloured rural roads on early Ordnance Survey one-inch maps with near contemporary highway records of the county of Huntingdonshire, sixteen rural district councils in six counties and an estate in Suffolk. The results show that all but four of the coloured roads on the one-inch maps in these areas are recorded as publicly maintainable highways.     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

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.     

First Steps Towards a Model of Tactile Graphicacy

Abstract

This paper describes our initial steps towards developing a model of how blind people comprehend tactile graphics. In the first half of the paper we set out the aims of the model, and then consider other key issues such as the nature and scope of the model, the information it must incorporate and the outcomes it should provide. In the second half of the paper we present our ideas for the model itself, outlining the four facets that make it up — perceptual processing, cognitive skills, knowledge and cognitive development. Throughout the paper we raise questions for open debate and invite feedback on our ideas.     

A FIFTY-YEARS RETROSPECT

Abstract

The Ordnance Survey after the War.—I might class the four years after the War, during which I remained at the head of the Ordnance Survey, as interesting but troublesome. As is well known, an entirely unreasonable impression was spread about that, now that the War was over, there would be a period of great prosperity, and that we should all live like fighting cocks. Well, things did not work out like that. There was a Select Committee on National Expenditure (1918), and this Committee recommended a lengthening of the period of revision of the large-scale maps of the United Kingdom and a consequent, ultimate, reduction of establishment by 500 men. The Treasury later on insisted on a reduction by 600, including Ireland.     

A framework for user-generated geographic content acquisition in an age of crowdsourcing

ABSTRACT

Obtaining useful geographic information from the flood of user-generated geographic content (UGGC) data is of significant interest, but comes with challenges in an age of crowdsourcing. To address this issue, we adopt Maslow’s model of human needs to frame UGGC. Synthesizing across literature about volunteered geographic information and participatory GIS, we present a conceptual framework for characterizing collection of UGGC. The framework is composed of multiple dimensions and levels that include perspectives about motivations, participatory methods, and participants. We also articulate four levels of participants (stakeholders, core-engaged participants, semi-core-engaged participants, and engaged citizens) together with four work principles (communication, cooperation, coordination, and collaboration). Finally, a case study describes an example we use to evaluate the conceptual framework for its suitability in design of a UGGC system. We conclude by reflecting on how and why this framework offers a valuable perspective for deriving useful geographic information and offer future research directions.     

A generalisation of the least-squares method for the adjustment of free networks

Summary The system of normal equations for the adjustment of a free network is a singular one. Therefore, a number of coordinates has to be fixed according to the matrix. The mean square errors and the error ellipses of such an adjustment are dependent on this choice. This paper gives a simple, direct method for the adjustment of free networks, where no coordinates need to be fixed. This is done by minimizing not only the sum of the squares of the weighted errorsV ^T PV=minimun but also the Euclidean norm of the vectorX and of the covariance matrixQ X ^T X=minimum trace (Q)=minimum This last condition is crucial for geodetic problems of this type.