Course Details

# Theory of errors and adjustment I

GE04 course is part of 2 study plans

B-P-C-GK Summer Semester 1st year

B-K-C-GK 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.

Course Guarantor

Institute

Institute of Geodesy

Objective

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.

Knowledge

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).

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

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.

Language of instruction

Czech

Credits

5 credits

Semester

summer

Forms and criteria of assessment

course-unit credit and examination

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

https://www.vut.cz/en/students/courses/detail/254863

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

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