Course detail

Theory of errors and adjustment 2

FAST-BEA013Acad. year: 2025/2026

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

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Josef Weigel, CSc.

Department

Institute of Geodesy (GED)

Entry knowledge

Geodetical surveying and computation of measurements on the plane, similar for heights, linear algebra – matrix calculus and processing systems of linear equations, analytical geometry, derivative of functions, Taylors expansion of a function, characteristics of position and variability of random variable, covariance matrix, laws of error propagation, weigth matrix, Least squares method, use of calculator, table processors and matrix oriented programming environment.

Rules for evaluation and completion of the course

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Aims

After completing the course, the students should be able touse the complicated types of adjustment and fitting.
Student gets knowledge of ways of principle of conditions adjustment and solutions the other complicated types of adjustment problems, regression analysis and analysis of correlation.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BPC-GK Bachelor's 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Josef Weigel, CSc.

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

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Josef Weigel, CSc.
Ing. Ladislav Bárta, Ph.D.

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.