Theory of Errors and Adjustment Calculus 2

Garant předmětu:

Martin Štroner

Lecturer:

Tutor:

Supervisor:

Department of Special Geodesy

Synopsis:

Alignment of intermediaries, repetition of measurement errors and basic procedures. The law of the accumulation of weights. General law of accumulation of standard deviations. Robust methods of compensation. Finding outlying measurements. Special procedures in alignment: Elimination of unknowns. Sequential equalization. Errors in the initial quantities. Approximation of relationships. Regression and correlation analysis. Equating line and plane. Approximation by empirical polynomial. Harmonic analysis. Fourier transform. Equalization of conditionals with unknowns. Statistical hypothesis testing 2. Reliability. Optimization of geodetic measurements. Methods for solving normal equations. Direct solution, inversion, pseudoinversion.

Requirements:

no

Syllabus of lectures:

1. Alignment of intermediaries, repetition of measurement errors and basic procedures.

2. Robust alignment methods. Finding outlier measurements.

3. Methods for solving normal equations. Direct solutions, inversions, pseudoinversions.

4. Special procedures in equalization: elimination of unknowns. Sequential equalization. Errors in the initial variables.

5. Law of accumulation of weights. General law of accumulation of standard deviations.

6. Approximation of relations. Regression and correlation analysis.

7. Equating line and plane. Approximation by an empirical polynomial.

8. Harmonic analysis. Fourier transform.

9. Equalization of conditionals with unknowns.

10. Statistical hypothesis testing 2.

11. Reliability.

12. Optimization of geodetic measurements.

13. Overview of the design and processing of geodetic network measurements.

Syllabus of tutorials:

1. Linear regression.

2. GNU Gama - equating bounded and free networks.

3. General law of accumulation of standard deviations.

4. Test of the 3rd exercise. Testing statistical hypotheses.

5. Test of the 4th exercise. Testing repeated measurements.

6. Test from exercise 5. Robust methods of alignment.

7. Robust methods of alignment - completion.

8. Leveling plane - horizontal, general.

9. Approximation by empirical polynomial.

10. Test of exercises 8 and 9. Harmonic analysis. Fourier transform.

11. Equating conditionals with unknowns.

12. Reserve. Credit.

Study Objective:

mastering the subject content

Study materials:

[1] Hampacher, M. – Štroner, M.: Zpracování a analýza měření v inženýrské geodézii. 2. vyd., Praha: Česká technika – nakladatelství ČVUT, ČVUT v Praze, 2015. 336 s. ISBN 978-80-01-05843-5.

[2] Böhm, J. – Radouch, V. – Hampacher, M.: Teorie chyb a vyrovnávací počet. GKP, Praha 1990. ISBN 80-7011-056-2.

[3] Hampacher, M. – Radouch, V.: Teorie chyb a vyrovnávací počet 10, 20. Příklady a návody ke cvičení. ČVUT v Praze, 2000, ISBN 80-01-02250-1.

[4] Hampacher, M. – Radouch, V.: Teorie chyb a vyrovnávací počet 10. ČVUT v Praze, 1997, ISBN 80-01-01704-4

Note:

Further information:

https://k154.fsv.cvut.cz/vyuka/bc-geodezie/tcv2/

No time-table has been prepared for this course

The course is a part of the following study plans:

• Geodézie a kartografie (compulsory course)
• Geodézie a kartografie (compulsory course)