LEAST-SQUARE ADJUSTMENTS OF TRIANGULATION DIRECTIONS VERSUS ANGLES

Abstract

IT has been assumed in the past that because angles for triangulation are usually observed by the direction method, therefore it must be more correct theoretically to perform the least-square adjustments by directions rather than by angles. It is fairly obvious that an adjustment of the same figure by directions will not give the same result as an adjustment by angles: the unknowns in each case are different and the number of directions is usually about 25 per cent. greater than the number of angles for the same figure. Strictly, the least square method is only applicable to observations from which all systematic errors have been eliminated, and in which the remaining errors are truly accidental. It is generally safe to assume that most survey errOlS consist of a random and a systematic part. Rarely, if ever, is it possible to state that all systematic error has been eliminated, strive how we may to take all precautions against it.     

Problems of mapping a nature reserve: Aberlady Bay LNR and SSSI

Abstract

A new five-colour map of Aberlady Bay Local Nature Reserve and Site of Special Scientific Interest at 1:7,500 scale is published as a loose insert with the June 1993 issue of The Cartographic Journal. This accompanying paper describes the problems of producing the map at minimal cost, considers some of the cartographic issues particular to the site, and provides specification details of the compilation.

Such individual map sheets, which are used for environmental planning, research and teaching, have in the past been produced mainly by universities with the support of conservancy and countryside agencies. Future production costs at universities will inevitably rise although some economies may be possible by the use of digital database methods of cartography.     

'Be Map Aware: Cutting-edge…Not Close to the Edge'

Abstract

An assessment is made of the accuracy of the map and written survey, which is essentially a list of land-holders and the areas held by each, and of their mutual consistency. The geometry of the map is compared quantitatively with that of the first edition (1852) Ordnance Survey 6-inch (1 : 10 560) map. The Saxton map is found to have a scale of 1 : 5140, leading to the conclusion that the perch used in the scale bar represents 7¹/₉ yards or thereabouts. The areas quoted in the written survey are consistent with acres based on this value. The positional accuracy of points on the map is found to be ～20 m, and areas of typical plots determined from the map are uncertain by between about 4 and 12%. The relationship between these two facts can be understood through a detailed study of the statistics of the errors in separations of points on the map. The written survey is found to omit a substantial number of plots of land from its listings. The map thus appears to be more reliable overall than the written survey.     

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.     

DIRECTIONS AND ANGLES IN A SIMPLE CHAIN

Abstract

Mr. Rainsford's article on “Least Square Adjustments of Triangulation: Directions versus Angles” in the Empire Survey Review No. 78, Vol. x, October 1950, leads to many speculations and interesting results. I try to show here, how, by assuming artifices to simplify the results, weights may be assigned to angles derived from directions so that the results of adjustment by angles, with these weights, will be the same as the adjustment by directions, all of equal weight.     

THE READABILITY OF THE MAP: THEORETICAL PRINCIPLES

An effort is made at developing a theory of map readability, defined as the process of the user's representation of the information of the map in his/her own mind. This can be estimated quantitatively by surrogate measures, which include the speed of map comprehension and accuracy of map interpretation. Levels of psychological representation of map information are incorporated to determine at what stage particular aspects of map knowledge are understood. Thus what readability entails, and the approaches used to measure it (what types of things are comprehended, how fast, and how accurately) will depend upon the level of representation. Translated from: Vestnik Leningradskogo Universiteta, seriya 7 [geologiya, geografiya], 1988, No. 1, pp. 32-37.     

Use of Artificial Neural Networks for Selective Omission in Updating Road Networks

Abstract

An important problem faced by national mapping agencies is frequent map updates. An ideal solution is only updating the large-scale map with other smaller scale maps undergoing automatic updates. This process may involve a series of operators, among which selective omission has received much attention. This study focuses on selective omission in a road network, and the use of an artificial neural network (i.e. a back propagation neural network, BPNN). The use of another type of artificial neural network (i.e. a self-organizing map, SOM) is investigated as a comparison. The use of both neural networks for selective omission is tested on a real-life road network. The use of a BPNN for practical application road updating is also tested. The results of selective omission are evaluated by overall accuracy. It is found that (1) the use of a BPNN can adaptively determine which and how many roads are to be retained at a specific scale, with an overall accuracy above 80%; (2) it may be hard to determine which and how many roads should be retained at a specific scale using an SOM. Therefore, the BPNN is more effective for selective omission in road updating.     

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.     

LEAST SQUARES ADJUSTMENTS OF TRIANGULATION: DIRECTIONS VERSUS ANGLES

Abstract

This paper continues the discussion started in an article of the same title (E.S.R., ×, 78, :353-66), on which a further letter was written in October, 1952. The amount of computation required originally was very considerable, and it was obviously impossible to publish it all. The recent letter was necessary to answer the suggestion that the agreement between errors put in and corrections obtained from the L.S. solution was not very close. It seemed sufficient to give the list of errors and corrections, leaving readers to judge for themselves. The correlation coefficient from the two sets of figures was 0.78, which looked quiteg90d. Unfortunately, it was not realized before that corrections from a L.S. solution cannot, legitimately, be compared with errors put in on directions unless a station correction is first applied to the errors to make the sum of the errors at each station equal to zero. This is one of the points about the direction method of adjustment which is not very easy to understand.     

A TEST FOR THE RELIABILITY OF FIRST-ORDER TRIGONOMETRICAL OBSERVATIONS

Abstract

Generally speaking there is a tendency for observations to be judeged by the magnitudes of the triangular errors, although the misclosures of the side equations are equally important. This note explains how to formulate a compehensive criterion covering the two types of misclosure and given in terms of the mean traingular ? _m for which definite limits are usually laid down.     

INTERPRETATION AND ADEQUACY OF COMMONLY GIVEN INFORMATION ABOUT THE INSTRUMENTAL PRECISION OF AIR SURVEY EQUIPMENT

Abstract

Some difficulties in interpreting the specifications of instrumental accuracy are pointed out and traced to inadequate information. The paper discusses the possibility of amplifying this information for the benefit of the user and without over-burdening the inspection departments of the manufacturers.

It is suggested that the given information should include (1) estimates of all suspected errors and distortions, (2) the confidence limits relevant to (a) the errors incurred in any given measurements and (b) their point-to-point variation.

Confidencelimits for the effects of observational errors may be worked out from the t-distribution in the usual way, or more readily read from graphs given in this paper. Further research is however needed to investigate the statistical behaviour of other sources of variation in order to establish appropriate systems for the construction of corresponding confidence limits.     

NOTES ON THE GEODETIC SURVEY OF SOUTHERN RHODESIA

Abstract

Triangulation.—Apart from Simms' Geodetic Chain, Gordon's Chain, the Copper Queen Limb, and a section of the Victoria and Umtali Series, all the primary triangulation shown on the accompanying map has been executed since 1933. The work of Simms and Gordon has been remodelled, however, being greatly strengthened, and these chains are now called Simms' and Gordon's Series. For an explanation and plan of the above Series, see “A Note on the Trigonometrical Survey of S. Rhodesia”, in the Empire Survey Review, no. 27, vol. iv.     

On the night errors in astronomical determinations

Summary The discrepancy between precision and accuracy in astronomical determinations is usually explained in two ways: on the one hand by ostensible large refraction anomalies and on the other hand by variable instrumental errors which are systematic over a certain interval of time and which are mainly influenced by temperature.In view of the research of several other persons and the author’s own investigations, the authors are of the opinion that the large night-errors of astronomical determinations are caused by variable, systematic instrumental errors dependent on temperature. The influence of refraction anomalies is estimated to be smaller than 0″.1 for most of the field stations. The possibility of determining the anomalous refraction from the observations by the programme given by Prof. Pavlov and Anderson has also been investigated. The precision of the determination of the anomalous refraction is good as long as no other systematic error working in a similar way is present.The results, which are interpreted as an effect of the anomalous refraction by Pavlov and Sergijenko, could also be interpreted as a systematic instrumental error. It is furthermore maintained thatthe latitude and longitude of a field station can be determined in a few hours of one night if the premisses given in [3, p.68]are kept. It has been deplored that the determination of the azimuth has not been given the necessary attention. It is therefore proposed to intensify the research on this problem. The profession has been called upon to acquaint itself better with the valuable possibilities of astronomical determinations and to apply them in a useful and appropriate manner. At the same time, attention has been called to the possibility of improving astronomical determinations with regard to accuracy as well as effectiveness.     

AREAS BY EQUIDISTANT OFFSETS

Abstract

In chain and traverse surveys areas are frequently required between chain lines and crooked fences. Commonly these areas are computed from offsets measured at equal intervals, which are so much the shorter according as the sinuosity is the greater. Most frequently Simson's Rules are employed for this computation; for (2m+1) offset ordinates, Simson's First Rule may be used; for (3m+1) ordinates, Simson's Second Rule. The First Rule assumes that the fence is made up of arcs of ordinary parabolae; the Second Rule, of arcs of cubic parabolae.     

'Drawing the Coral Heads': Mental Mapping and its Physical Representation in a Polynesian Community

Abstract

Indigenous people throughout the world developed their own mapping skills and systems of knowledge. While Westerners are prone to overlook these communities' geographical knowledge and imagine their mapping activities to be primitive or non-existent, their mental maps are often impressive in sophistication and detailed even if based on cosmologies that are quite foreign to Western thinking. This article depicts a mental map of the ocean floor shared by Polynesians of Anuta, a remote community in the Solomon Islands. It situates Anuta's reef map in relation to academic discussions of indigenous cartography and describes the process that resulted in the map's physical representation.     

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.     

SPOT5城区影像几何精校正点位和面积精度研究

为深入研究二维多项式校正SPOT5城区影像(2.5m)的点位和面积精度,本文分别使用不同精度(GPS点和1∶10000地形图获取的点),不同数量(25和6)的地面控制点校正影像。并利用另外的10个GPS点作为检核点分别检核四种校正结果的点位和面积精度。