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).     

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.     

THE ADJUSTMENT OF A FIRST-ORDER LEVELLING NETWORK

Abstract

In the E.S.R. January and April numbers of 1955, Vol. xiii, Nos. 95 and 96, Mr. Hsuan-Loh Su described the “Adjustment of a Level Net by Successive Approximations and by Electrical Analogy”. It does not seem to be as generally known as it should be that the rigid least square solution can be greatly simplified by utilizing the electrical analogy and solving by Kirchhoff's method. The method as detailed below has been in use for over 40 years.     

The Oblique Zenithal Equidistant Projection

Abstract

The idea of constructing an equidistant map centred on Glasgow originated as a school project. The amount of calculation required meant that it was necessary to use a computer to calculate the co-ordinates for the projection on a 15° graticule. Subsequently it was decided to write a program to instruct another computer, equipped with a graph plotter, to plot the same graticule automatically. The basic mathematical constructions and the procedure for programming the computer for automatic plotting are fully explained.     

NUMBER ONE HUNDRED

Abstract

Readers will notice that this issue of the Review is numbered 100 and, as it has always been published quarterly, this means that it has now been in existence for 25 years and so celebrates its silver jubilee.     

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.     

PRACTICAL SAG CORRECTION IN CATENARY TAPING

Abstract

When a line is being measured with a steel tape suspended in catenary but standardized on the flat, the correction for sag is usually computed from the weight of the tape. It can, of course, be determined by actual measurements on the ground, if these are made both on the flat and in catenary, but this is not usually done as it is a tedious process in the absence of a proper standardizing base.     

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.     

MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

1. Computation of a minor triangulation as if it were executed on a plane surface of course ignores spherical excess, an omission not strictly rigorous so far as azimuths are concerned. Further the reduction of such a triangulation to a system of plane coordinates again assumes that the earth's surface is a plane.     

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 CADASTRAL MAP

Abstract

In the Empire Survey Review for April 1934 (No. 12, pp. 382–4), the Editor has raised the question of the function of the cadastral map. As he remarks, the question is not simple, but it is easier to say what the function of the map is than to decide of what the map should consist in order that it may fulfil its function. Broadly speaking we may state that the function of the map is to record the boundaries of landed property in such a manner as not only to afford a pictorial representation but also to supply data for the identification of these boundaries on the ground when occasion requires. Apart from this the map should show the areas of properties, as this information may be required for taxation purposes.     

MAPPING OUT OF CROWN LANDS IN CEYLON

Abstract

13. As mentioned earlier (xi, 83, 199) the “Final Village Plan”, which is evolved from the 4-chains-to-an-inch (1:3,168) “Block Survey” village plan after inquiry and settlement of claims as between the Crown and private parties, provides a sound basis for mapping-out and for the subsequent administration of the Crown estate. But as (in all cases) the development of Crown land could not await Block Survey and “Settlement”, it was also necessary to undertake mapping out in areas which had not been systematically surveyed, and for which no continuous large-scale plans were available.     

The Potential of the Lenticular Foil Technique for Thematic Cartography

Abstract

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Lenticular visualisation methods are innovative advancements of modern presentation media in cartography. Owing to the mainly three-dimensional perception of people, this technique, in print as well as on screen, offers the possibility to introduce autostereoscopic, i.e. three-dimensional views in cartography. On the basis of true 3D, it has already found its way into the visualisation of relief relations. Moreover, it also opens perspectives for the more widespread products of thematic cartography (thematic maps). Multi-layered representation becomes possible on the basis of three-dimensional or sequentially differentiated depictions of spatial phenomena. Thus, several parameters or dimensions of cartographic content can be displayed at the same time. This essay discusses some potential applications of the lenticular foil technique for thematic cartography on a theoretical basis.     

Minimum mean squared error (MSE) adjustment and the optimal Tykhonov–Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE)

In a linear Gauss–Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov–Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result. The delay in publishing this paper is due to a number of unfortunate complications. It was first submitted as a multi-author paper in two parts. Due to some miscommunication among the original authors, it was reassigned to one of the J Geod special issues, but later reassigned at this author’s request to a standard issue of J Geod. This compounded with a difficulty to find willing reviewers to slow the process. We apologize to the author.     

INFLUENCE OF GEOIDAL TILT ON AZIMUTH

Abstract

If the horizontal circle of a theodolite is tilted, the azimuth of a point in the field will be affected. The tilt may be a mere question of dislevelment but it may be also due to a deviation of the vertical which the level on the instrument cannot measure. In either case the effect on azimuth or bearing is of the same nature, which is worth consideration for more than one reason. That it has previously been investigated elsewhere is no valid reason against renewed consideration here, particularly as the consequences are probably unknown to some readers.