Theory of Errors and Adjustment Calcullus

Garant předmětu:

Martin Štroner

Přednášející:

Martin Štroner

Cvičící:

Lenka Línková, Martin Štroner

Předmět zajišťuje:

katedra speciální geodézie

Anotace:

Measurement errors and their division, two and multidimensional errors. Measurement properties, characteristics of random variables. Probability distributions. Law of accumulation of real errors, standard deviations. Characteristics of precision. Equalization of measurements. Least squares method (equating measurements of intermediate, conditional, intermediate with conditions). Alignment of bound and free geodetic grids. Regression and correlation analysis - linear regression. Basics of statistical hypothesis testing.

Požadavky:

no

Osnova přednášek:

1. Introduction to the subject. Measurement errors and their division, measurement properties.

2. Characteristics of random variables (position, accuracy, slope and peak). Total measurement error.

3. Probability distribution. Normal distribution, Chi-square distribution, Student's distribution, Fisher distribution, point and interval estimates. Testing the fit of the distribution.

4. Law of accumulation of true errors, standard deviations.

5. Bivariate and multivariate errors. Accuracy characteristics. Helmert curve. Measurement equalization. Equalization of straight measurements. Pairs of measurements.

6. Least squares method. Adjustment of intermediate measurements. Problem formulation, calculation procedure, unit standard deviation, standard deviations, weights, linearisation.

6. Adjutment of intermediate measurements - examples.

7. Adjustment of intermediate measurements - overview of alignment procedure, checks.

8. Adjustment of conditional measurements.

9. Adjustment of intermediate measurements with conditions.

10. Adjustment of a geodetic network. Alignment of a free, bound network.

11. Regression and correlation analysis 1. Linear regression.

12. Statistical hypothesis testing 1.

Osnova cvičení:

1. Introduction to the subject. Matlab - repetition of basic procedures. Definitions of constants, functions, scripts, matrices.

2. Characteristics of random variables

3. Test from the 2nd exercise. Testing the consistency of the distribution.

4. Law of the accumulation of standard deviations

5. Test from exercise 4. Aligning the measurements of the direct. Pairs of measurements.

6. Test from exercise 5. Alignment of intermediate measurements - elevation grid.

7. Adjustment of intermediary measurements - free position.

8. Adjustment of conditional measurements.

9. Adjustment of the tied network.

10. Adjustment of the free network.

11. Test of exercises 6 - 10. Alignment of tied and loose nets - completion.

Cíle studia:

Mastery of course content.

Studijní materiály:

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. Koch, K. R.: Parameter Estimation and Hypothesis Testing in Linear Models. Springer Verlag, Berlin, 1999, ISBN 978-3-540-65257-1.

4. 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

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

Poznámka:

Rozvrh na zimní semestr 2023/2024:

Rozvrh není připraven

Rozvrh na letní semestr 2023/2024:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů: