Course Details
Theory of errors and adjustment I
Academic Year 2023/24
GE04 course is part of 1 study plan
B-P-C-GK / GI Summer Semester 1st year
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.
Credits
5 credits
Language of instruction
Czech
Semester
summer
Course Guarantor
Institute
Forms and criteria of assessment
course-unit credit and examination
Entry Knowledge
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.
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.
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).
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).
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)
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)
Kubáčková, L.: Metódy spracovania experimentalnych údajov. Veda, Bratislava, 1990. (sk)
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
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
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.
Specification of controlled instruction, the form of instruction, and the form of compensation of the absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
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
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
13 weeks, 2 hours/week, compulsory
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.
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.