Course Details

Theory of errors and adjustment 2

Academic Year 2025/26

BEA013 course is part of 1 study plan

​ BPC-GK Winter Semester 2nd year

Course Guarantor

doc. Ing. Josef Weigel, CSc.

Institute

Institute of Geodesy

Language of instruction

Czech

Credits

5 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289958

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. Geodetic task, conditions of resolvability, kinds and types of adjustment.
  • 2. Procedure of indirect observations adjustment.
  • 3. Indirect observations adjustment - quality assessment.
  • 4. Procedure of conditional observations adjustment.
  • 5. Conditional observations adjustment - quality assessment.
  • 6. Solution of conditional observations adjustment by conversion to indirect observations adjustment, adjustment of given sum, indirect observations adjustment with conditions.
  • 7. Conditional observations adjustment with unknowns, adjustment of heterogenous observations.
  • 8. Regression analysis, approximation by a polynom.
  • 9. Linear regression, regression plane, harmonic analysis.
  • 10. Testing of statistical hypotheses.
  • 11. Testing of systematic errors.
  • 12. Testing of outliers, law of total errors propagation.
  • 13. Analysis of variance, correlation analysis, error ellipses and ellipsoides.
  • 1. Principle of condition Adjustment.
  • 2. Condition, misclosure, and linearization condition equations.
  • 3. Solution of normal equations, correlates, standard deviations.
  • 4. the other types of adjustment, mixed adjustment.
  • 5. Test of observations, simple statistic tests.
  • 6. Test of normal distribution of sample.
  • 7. Analysis of systematic errors in observations.
  • 8. Analysis of parameters.
  • 9. Linear regression - line fitting.
  • 10. Regression analysis - regression curves.
  • 11. Harmonic functions.
  • 12. Analyssis of corelation, physical and mathematical corelation.
  • 13. Helmert curve, error ellipsis, error ellipsoides. Laws of propagation corelation observations.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Introduction and base theory, matrix computation in theory of errors.
  • 2. Test, examples of indirect observations adjustment up to residual equations.
  • 3. Indirect observations adjustment - classical notation.
  • 4. Test. Exercise Indirect observations adjustment - matrix notation.
  • 5. Test, examples of conditional observations adjustment up to linearized condition equations.
  • 6. Exercise Conditional observations adjustment - classical notation.
  • 7. Test, exercise Conditional observations adjustment - matrix notation.
  • 8. Exercise Conditional observations adjustment - heterogenous observations.
  • 9. Test, consultation of the exercise Conditional observations adjustment - heterogenous observations, spare.
  • 10. Exercise Regression analysis.
  • 11. Test, exercise Testing of statistical hypotheses and systematic errors.
  • 12. Consultation and correction of all the exercises, spare.
  • 13. Checking fulfilment requirements and granting credits.