Course detail

Theory of errors and adjustment I

FAST-GE04Acad. year: 2022/2023

Classification of errors, laws of distibution errors, accuracy and precision, simple analysis of measurements, weight and cofactors, laws of propagation of errors, weights and cofactors, inverse formula, least squares method and adjustment, adjustment of direct observations, pairs of measurement, adjustment by elements, observation equations, residuals equations, normal equations and solution, standard deviations.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

Ing. Radim Kratochvíl, Ph.D.

Department

Institute of Geodesy (GED)

Learning outcomes of the course unit

Student gets practical knowledge of teorie of errors, analysis and classified sources of measurement errors (instrumental errors, natural errors and personal errors). Student will manage laws of error propagation and principle of adjustment by last squares metod (adjustment direct observations and adjustment by elements).

Prerequisites

Surveying and computing of measurements on the plane, Linear algebra - fundaments of matrix calculus, Analytic geometry, Derivative of a function, Taylors expansion of a function.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. History of subject. Theoretical base. Probability and statistic
2. Definition errors of measurements and their classification.
3. Distribution of random quantities and their specification in theory of errors
4. Standard deviation and simple analysis of precision
5. Weight, cofactors, covariance matrix, cofactor matrix
6. Laws of error propagation, law of weights propagation, inverse formula
7. Principle of least squares method, types of adjustment
8. Adjustment of direct observations, 9. Principle of adjustment by elements, observation equations
10. Residuals equations, normal equations and their solution, standard deviation of unit weight
11. Standard deviation, computed quantities

Work placements

Not applicable.

Aims

After completing the course, the students should be able touse the basics necessary to deal with terms as precision and accuracy, laws of errors propagation and principle of adjustment.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Böhm, J., Hampacher, M., Radouch, V.: Teorie chyb a vyrovnávací počet. Kartografie Praha, 1990. (CS)
Hampacher, M., Radouch, V.: Teorie chyb a vyrovnávací počet 10. ČVUT Praha, 1997. (CS)
WEIGEL, Josef: Teorie chyb a vyrovnávací počet I. VUT, 2009. (CS)
Wolf, P.R., Ghilani, Ch.D.: Adjustment Computation. John Wiley, New York., 1997. (EN)

Recommended reading

Kubáčková, L.: Metódy spracovania experimentalnych údajov. Veda, Bratislava, 1990. (SK)
Vykutil J.: Teorie chyb a vyrovnávací počet. VUT Brno, 1981. (CS)

Classification of course in study plans

  • Programme B-P-C-GK Bachelor's

    branch GI , 1 year of study, summer semester, compulsory

  • Programme B-K-C-GK Bachelor's

    branch GI , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Radim Kratochvíl, Ph.D.

Syllabus

1. History of subject. Theoretical base. Probability and statistic 2. Definition errors of measurements and their classification. 3. Distribution of random quantities and their specification in theory of errors 4. Standard deviation and simple analysis of precision 5. Weight, cofactors, covariance matrix, cofactor matrix 6. Laws of error propagation, law of weights propagation, inverse formula 7. Principle of least squares method, types of adjustment 8. Adjustment of direct observations, 9. Principle of adjustment by elements, observation equations 10. Residuals equations, normal equations and their solution, standard deviation of unit weight 11. Standard deviation, computed quantities

Exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Radim Kratochvíl, Ph.D.

Syllabus

1. Introduction, basic of probability 2. Distribution of random quantities, Normal distribution 3. Errors of measurements and their classification, random errors 4. Standard deviations, precision, accuracy 5. Confidence intervals 6. Weight, cofactors, cofactors matrix, covariance matrix 7. Examples of law propagation of errors 8. Examples of law propagation of standard deviations 9. Inverse problems of errors 10. Law of propagation of weight and cofactors 11. Adjustment of direct observations 12. Pairs of measurements. Final test 13. Check of fulfilling the credit conditions,granting of credits.