Course detail

Theory of errors and adjustment I

FAST-GE04Acad. year: 2018/2019

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.

Department

Institute of Geodesy (GED)

Learning outcomes of the course unit

Basic knowledge of students about theory of errors. Basic information of precision of measurements and adjustment.

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

Basic knowledge of surveying methods, Precise measurements of distances and angles, Mathematics - partial derivative

Planned learning activities and teaching methods

The course is taught through lectures, practical classes and self-study assignments. Attendance at lectures is optional, but attendance at classes is compulsory.

Assesment methods and criteria linked to learning outcomes

Attendance, submission and acceptance of single tasks protocols, 4 test, passing the final written test. The exam is composed from test examples, exercise and oral part. 30% of the points are generated from the exercise evaluation. 20% from test examples and 50% oral part of exam. The total number of points is 100, for the successful completion of the exam 50% of points

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

Do not required

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

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

Classification of course in study plans

  • Programme B-K-C-GK Bachelor's

    branch G , 1. year of study, summer semester, compulsory

  • Programme B-P-C-GK Bachelor's

    branch G , 1. year of study, summer semester, compulsory

  • Programme B-K-C-GK Bachelor's

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

  • Programme B-P-C-GK Bachelor's

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

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

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.