Ana María Domingo Preciado
Professor, School of Topographic Technical Surveying
Polytechnic University of Madrid

ABSTRACT

This paper focuses on the teaching guidelines around which the contents of the subject “Adjustment of Observations” are structured in the School of Surveying, Madrid. The paper states the need of those contents in view of the new professional requirements Surveyors are to meet. Some recommendations are also made to upgrade and update those contents.

CONSIDERATIONS

We may start this paper with a very general idea: it is a fact that no measurement or observation may be deemed as accurate. As a consequence we may derive that every observation, no matter how carefully we make it, contains some error. Both are basic and fully accepted facts.

Since the main task of an engineer —specially, a Surveyor — is to make observations, understanding and knowing error behaviour is evidently of paramount significance. Surveyors, therefore, no matter where they develop their careers in the future, are to have a deep knowledge of different kinds or errors, their sources, their expected magnitudes and their forms of dissemination or transmission. This will allow them adopt and resort to adequate procedures to reduce the impact of errors while making the observation and still afterwards. Also, they will have to learn state-of-the-art statistical techniques to deal with errors.

On the other hand, it is important to highlight how closely linked observation sciences are, in particular, Geodesy, Topography and Photogrammetry. Any set of captured data, no matter how accurate they may be, if treated by traditional methods and without being subject to a final adjustment, will not deliver optimum results.

The above-mentioned facts together with the present availability of modern calculation tools resulted in Adjustment of Observations, a subject incorporated to the Curricula in 1990. It is a fact that modern tools allow the practical application of what used to be only theory. D. Nicolás Serrano, a member of our faculty, fully convinced of the facts above mentioned and supported by the experiences lived in other universities, successfully suggested the incorporation of these topics. Since 1993, I have the pleasure of sharing with him the teaching of these subjects.

This subject is to be supplemented by another course, optional in nature. Basically, we focus on the strengthening of these topics and, particularly, the use of Adjustment Techniques by Least Squares.

Technology has introduced many changes in Surveying. Not only in the instruments but also in the data processing.

Computers allow dealing with great numbers of data, adjustment procedures have become programmable and automatised routines. These capabilities lead to a very rigorous treatment of calculation errors and also provide for a statistical analysis of the final precisions of the adjusted magnitudes.

Going back to teaching, we would like to point out that the current Curriculum includes two subjects, as above mentioned:
A compulsory subject, Adjustment of Observations with three hours for theory and two hours for practice every week, to be followed for a half term during the second course.
Adjustment of Observations II, an optional subject structured around three areas: Statistics and Operational Research, Cartography Engineering, Geodesy and Applied Photogrammety and Mathematics.

We will now specify the objectives of Adjustment of Observations. The main objective is to teach one of the most fundamental tools in topography: the application of Adjustment Methods based on the Least Squares, which will be used by students until they graduate and during their professional careers.

Therefore, we might point out the following specific objectives:
1) Laying out the Mathematical Model relative to a specific topographic problem
2) Determining the number of observations necessary to solve the problem, by optimising the observation process and by setting the redundancy value
3) Setting the normal equations system and their resolution
4) Using indistinctly the two adjustment techniques applicable in any set problem
5) Deducing the values of estimates and residuals
6) Calculus of the Accuracy Matrixes associated to the adjusted values
7) Construction of Error Ellipses and Results Analysis

The theory suggested to meet the teaching objectives has been structured in such a way that the student is gradually taken from the most basic, simple concepts and techniques to the most general ones. However, focus is always made on the practical applications of this subject. Each topic is supplemented with a set of practical problems to be discussed and solved during class work. Students are also pushed to design some informatics program to add agility to the required calculations.

Concerning the second subject, Adjustment of Observations II, it was born to be a perfect supplement to the previously described subject. It is designed to increase knowledge and expertise on areas and aspects not thoroughly explained before, since time was short. Focus is made on statistical analysis issues, on the design of geodesic or topographic networks, on detection of distortions, elements that are crucial when students of Topography are looking forward the best possible professional training for their future careers.

I would also like to make some short reference to the texts used in teaching these subjects. First, let us remember we face the absence of texts in Spanish that may suit our objectives. We overcame this problem by writing our own textbook once the subject was consolidated in its approach. Our students are now benefiting from the second edition. Anyway, we believe it is advisable for students to read other textbook, which approach these topics from different standpoints, though we understand the difficulty of reading and fully grasping a text written in a foreign language. A very complete bibliography that can be found at the School’s Library is always suggested.

In order to conclude this paper and always considering technological advances, I would like to mention some ideas concerning possible changes and improvements applicable to these two subjects. On the one hand, it would be very interesting to incorporate — as a new subject or may be as a seminar— a course on the new Métodos de Estimación Robusta, an alternative to the Traditional Method that may solve, for instance, the anomalous behaviours when initial observations have type I errors, turning traditional solutions inapplicable. On the other hand, the study of methods to apply the Adjustment Methods in new and different contexts of data processing found by the modern Surveyor, for instance, GPS in Digital Photogrammetry.

Just to conclude, I may insist on the significance of teaching these subjects and on teaching guidelines that should lead us, teachers, to clearly differentiate two aspects: the every day upgrading and updating that must be transferred to students and the interdisciplinary nature of this subject which is a “big box of tools”, powerful tools that will help and be with Surveyors all along their careers.

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