Theory Of Errors & Adjustment Of Observations I

LEARNING OUTCOMES

Main purpose of the course is the introduction to the theory of errors and of parameter estimation, and the familiarization with the processes of the adjustment of observations with the method of Least Squares.

After completing the course, the students:

• will have understood the basic principles of parameter estimation from multiple measurements of equal or unequal precision, the concept of error propagation as well as the search, by means of strict mathematical criteria, of optimal solutions which minimize the effect of observation errors;
• will know the concepts of precision, accuracy and reliability;
• will be in position to apply methods of statistical processing of equally and unequally weighted measurements and to handle, with the least squares method, simple linear and non-linear adjustment problems in the context of the activities of the surveying and geomatics engineer;
• will be capable of applying the acquired knowledge in the context of several other courses and exercises in our Department, but also for solving both basic and complex problems which involve computations based on actual measurements which inevitably contain errors.

 

General Competences

• Search for, analysis and synthesis of data and information, using the necessary technology
• Working independently
• Production of free, creative and inductive thinking
• Decision-making
• Working in an interdisciplinary environment

 

SYLLABUS

Error theory and its relation to other scientific topics. Areas of application of error theory in the fields of surveying and geoinformation. Measurements and errors. Error types. Element of probability theory and statistics. Random variables and observation errors. One dimensional random variables. Estimation from multiple measurements. Probability distributions for discrete and continuous random variables. The “normal” distribution. Confidence intervals. Observations of equal and unequal weight. Internal and external accuracy, reliability. Muti-dimensional random variables. Muti-dimensional normal distribution. Error ellipse and error ellipsoid. Propagation of variances-covariances. Parameter estimation and adjustment of observations. Method of observation equations. Least squares method for linear functions. Least squares method for non-linear functions. Examples of solved adjustments.

 

STUDENT PERFORMANCE EVALUATION

Language of evaluation: Greek
Methods of Evaluation:
• Written examination in the end of the semester (70%), which combines open-ended questions and numeric calculations.
• Evaluation of performance in the exercises (30%)

 

SUGGESTED BIBLIOGRAPHY

1. Agatza-Balodimou A.M., 2018. The Method of Least Squares and Applications. Tziola Editions, Athens (in Greek).
2. Darmanis A., 1997. Adjustment of Observations and Estimation Theory. Vols. I & II. Ziti Editions, Thessaloniki (in Greek)