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.     

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).     

LAPLACE POINTS IN MODERATE AND HIGH LATITUDES

Abstract

A method of applying azimuth control to a survey is given in which the precision with which the astronomical position must be determined is proportional to tan (altitude) instead of tan (latitude) as in the orthodox method. By using the method with stars of low altitude the observational difficulties are greatly reduced, especially in high latitudes. Methods of observation and reduction are discussed which make it possible to avoid altogether special observations to determine the astronomical position.     

THE APPLICATION OF TRANSFORMATION FACTORS TO THE ADJUSTMENT OF AIR PHOTOGRAPHS COVERING NARROW LAND AREAS AND COASTLINES

Abstract

1. This new method of adjusting air photographs numerically to a uniform scale on a final map grid has already been described by the writert, where it concerns a large block-adjustment. The method to be described in this paper is the application of the same principle to the adjustment of photographic strips, covering narrow land areas and coastlines.     

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.     

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.     

A NOVEL METHOD OF MEASURING THE COEFFICIENT OF THERMAL EXPANSION OF INVAR

Abstract

In a letter published in a recent issue of Nature, Prof. L. F. Bates and Mr J. C. Wilson, of University College, Nottingham, have described a new and novel method of determining the coefficient of thermal expansion of invar. Although this method is hardly likely to be applied to the measurement of the coefficient of expansion of long invar tapes, such as are used by surveyors, yet it is so novel and ingenious in itself that a short reference to it may not be out of place in this Review. One extremely interesting thing about it is that no measurements of a length, or of changes of length, are involved.     

RELAXATION AND THE CO-ORDINATE METHOD OF TRIANGULATION ADJUSTMENT

Abstract

Few, most certainly, will dispute the value of Mr Black's paper describing a method of “Systematic Relaxation”, which appeared in a previous number of this Review. At the same time, however, it seems to the writer to be only fair to readers to point out that the application of the method to triangulation adjustment is really a treatment, from a slightly different aspect, of methods that have long been established.     

ADJUSTMENT OF A TRAVERSE BY RELAXATION

Abstract

1. The condition of least squares for survey adjustments is generally accepted as providing the best set of corrections, and the method might be more universally used were it possible to avoid the solution of as many simultaneous equations as there are independent unknowns. The method of correlatives effects a simplification where the number of conditions relating the unknowns is small, notably in Traverse Survey.     

DETERMINATION OF LATITUDE AND AZIMUTH FROM OBSERVATIONS OF AN UNKNOWN STAR

Abstract

Mr. Sanjib K. Ghosh, of the Survey of India, has recently described in these pages a method in geodetic astronomy which, although not of wide application, appears to have possible uses in field operationst. As Mr. Ghosh has only given a direct solution of the problem, it would appear of value to adapt to it the method of using a first approximation to the correct answer (method of approximate position), the more so as the set of observation equations can be treated by a graphical method which not only results in a gain in the simplicity and rapidity of calculation but also enables the conditions under which the method is applicable to be examined easily.     

The use of atmospheric dispersion in optical distance measurement

The development of lasers, new electro-optic light modulation methods, and improved electronic techniques have made possible significant improvements in the range and accuracy of optical distance measurements, thus providing not only improved geodetic tools but also useful techniques for the study of other geophysical, meteorological, and astronomical problems. One of the main limitations, at present, to the accuracy of geodetic measurements is the uncertainty in the average propagation velocity of the radiation due to inhomogeneity of the atmosphere. Accuracies of a few parts in ten million or even better now appear feasible, however, through the use of the dispersion method, in which simultaneous measurements of optical path length at two widely separated wavelengths are used to determine the average refractive index over the path and hence the true geodetic distance. The design of a new instrument based on this method, which utilizes wavelengths of6328 ? and3681 ? and3 GHz polarization modulation of the light, is summarized. Preliminary measurements over a5.3 km path with this instrument have demonstrated a sensitivity of3×10 ⁻⁹ in detecting changes in optical path length for either wavelength using1-second averaging, and a standard deviation of3×10 ⁻⁷ in corrected length. The principal remaining sources of error are summarized, as is progress in other laboratories using the dispersion method or other approaches to the problem of refractivity correction.     

POINT TO POINT COMPUTATION OF GEOGRAPHICAL COORDINATES OF LONG LINES

Abstract

The computation of geographical coordinates in a geodetic triangulation is usually carried out using Puissant's method, in which the assumption is made the sphere radius ν (the radius of curvature of the spheroid perpendicular to the meridian) not only touches the spheroid along the whole small circle of latitude ?,but also, since ρ (the radius of curvature in meridian) is very nearly equal to ν it makes such close contact with the spheroid that the lengths of sides and angles of a geodetic triangle may be considered identical on both sphere and spheroid.     

DETERMINATION OF AZIMUTH AND LATITUDE FROM OBSERVATIONS OF A SINGLE UNKNOWN STAR BY A NEW METHOD

Abstract

The purpose of this paper is to describe a new and easy method of determining the (astronomical) latitude and azimuth at any place and to explain the line of approach and the formulae. It will be seen that the method should be useful to a wide circle of land surveyors. One of its principal advantages is that identification of the star is not necesssary and it can be used when no star chart or star catalogue is available.     

A COMPARISON OF THREE METHODS USED FOR CALCULATING THE LONGITUDE FROM A PAIR OF WELL BALANCED STARS

Abstract

Because it was necessary to calculate the longitude many times from observed ex-meridian zenith distances, it was considered advisable to examine the various methods for achieving this in order to find which method was the most efficient.     

THE CLARKE FORMULÆ FOR LATITUDE,LONGITUDE AND REVERSE AZIMUTH,WITH CORRECTIVE TERMS FOR USE ON VERY LONG LINES

Abstract

This extremely simple and elegant method of computing geographical co-ordinates, given the initial azimuth and length of line from the standpoint, was published by Col. A. R. Clarke in 1880. There is no other known method giving the same degree of accuracy with the use of only three tabulated spheroidal factors. Clarke himself regarded this as an approximate formula (vide his remark in section 5, p. 109, “Geodesy”); but as this article demonstrates, it is capable of a high degree of precision in all occupied lati tudes when certain corrections are applied to the various terms. These corrections are comparatively easy to compute, require no further spheroidal factors, and some of them may be tabulated directly once and for all.     

COMPENSATION OF TRAVERSES WHEN LENGTHS ONLY ARE CORRECTED

Abstract

If it be assumed that the linear measurements of traversing are alone afflicted with error, the method of distribution of error demands consideration. In the present paper the notation of Wright and Hayford will be followed (“Adjustment of Observations”, 1906 edn., p. 156).     

SOME NOTES ON COMPUTING

Abstract

Probably the most important matter connected with computing is checking. Far more time is wasted by an incorrect result which has been passed as correct by the checker than by any other fault in computing. It is not necessary that a computer should always be perfectly accurate, but it is necessary that the method of checking used should always detect his errors. If the computer is sure that his accidental errors will be picked up he is relieved of anxiety and his work will be quicker and eventually more accurate for that reason.     

ADJUSTMENT OF THE SECONDARY TRIANGULATION OF SOUTH AFRICA

Abstract

The Secondary Triangulation of South Africa consists of a uniform network of triangles of from 5- to 10-mile sides, enmeshed in the Geodetic and Primary Triangulations. As a rule the Primary Triangulation is rigorously adjusted by least squares, and the Secondary made to conform to it by an approximately rigorous method which was introduced into the Trigonometrical Survey in 1920 by the late Dr van der Sterr.