Course Details

Theory of errors and adjustment 1

Academic Year 2022/23

BEA006 course is part of 1 study plan

BPC-GK Summer Semester 1st year

Basics of combinatorics, theory of probability, repeated experiment, random variable - it's distribution and characteristics of position and variability, classification of measurement errors, Normal distribution, two- and more-dimensional random variable - covariance and correlation coefficient, laws of propagation of errors, weights and cofactors, adjustment of redundant measurements, Least squares method, adjustment of direct observations, pairs of measurement.

Course Guarantor

doc. Ing. Josef Weigel, CSc.

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. Purpose and content of the subject, requiements for obtaining the credit and passing the exam, information sources. Basics of combinatorics, prior and statistical probability, total and compound probability, independent and dependent repeated experiment.
2. Random variable discrete and continuous, probability distribution of random variable, probability density and cumulative distribution function, types of distribution, characteristics of position and variability.
3. Classification of measurement errors, Normal distribution, primary and selective characteristics of random variable array.
4. Two- and more-dimensional random variable – covariance, correlation coefficient, covariance and correlation matrix. Law of true errors propagation.
5. Law of standard errors propagation, application to sum/difference and mean, matrix notation.
6. Inverze task of law of standard errors propagation, principle of equal influence, law of standard errors propagation on function array.
7. Variable accuracy measurement, weights and cofactors, weight and cofactor matrix, law of weigths propagation.
8. Adjustment of redundant measurements, adjustment methods, Least squares method and it's applications.
9. Direct observations adjustment of equal and unequal accuracy.
10. Measurement pairs of equal and unequal accuracy.

Prerequisites

Geodetical surveying and computation of measurements on the plane, linear algebra – fundaments of matrix calculus, analytical geometry, derivative of functions, Taylors expansion of a function, use of calculator and table processors.

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/254860

Lecture

13 weeks, 2 hours/week, elective

Syllabus

1. Purpose and content of the subject, requiements for obtaining the credit and passing the exam, information sources. Basics of combinatorics, prior and statistical probability, total and compound probability, independent and dependent repeated experiment.
2. Random variable discrete and continuous, probability distribution of random variable, probability density and cumulative distribution function, types of distribution, characteristics of position and variability.
3. Classification of measurement errors, Normal distribution, primary and selective characteristics of random variable array.
4. Two- and more-dimensional random variable – covariance, correlation coefficient, covariance and correlation matrix. Law of true errors propagation.
5. Law of standard errors propagation, application to sum/difference and mean, matrix notation.
6. Inverze task of law of standard errors propagation, principle of equal influence, law of standard errors propagation on function array.
7. Variable accuracy measurement, weights and cofactors, weight and cofactor matrix, law of weigths propagation.
8. Adjustment of redundant measurements, adjustment methods, Least squares method and it's applications.
9. Direct observations adjustment of equal and unequal accuracy.
10. Measurement pairs of equal and unequal accuracy.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

1. Introduction, envelope, exercise Prior and statistical probability.
2. Test, exercise Repeated experiment.
3. Test, examples random variable, Normal distribution, Normal normed distribution.
4. Test, exercise Normal distribution.
5. Consultation of the exercise Normal distribution, spare.
6. Test, exercise Laws of errors propagation.
7. Test, exercise Law of standard errors propagation on function array.
8. Test, exercise Adjustment of direct observations and pairs of measurement.
9. Test, consultation and correction of all the exercises, spare.
10. Checking fulfilment requirements and granting credits.