Course Details

Theory of errors and adjustment 2

Academic Year 2024/25

BEA013 course is part of 1 study plan

BPC-GK Winter Semester 2nd year

Geodetic task, base kinds and types of adjustment, indirect observations adjustment and it's quality assessment, conditional observations adjustment and it's quality assessment, combined adjustments, heterogenous observations adjustment, regression analysis, testing of statistical hypotheses and systematic errors, correlation analysis, error ellipses and ellipsoides.

Course Guarantor

Institute

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

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.