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Lecturer(s)
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Pospíšil Martin, doc. Ing. PhD.
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Aubrecht Jan, prof. Ing. PhD
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Mašek Marek, doc. Ing. PhD.
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Course content
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Basic definitions and terminology. Classification of mathematical models. Deterministic and stochastic parts of the model. General methods for solution of mathematical models. Linearization of non-linear mathematical models. Metric tensors, distances and lengths of vectors. Geometric meaning of the least-squares adjustment. Theory of probability. Random event, variable and samples. Statistical hypothesis and its testing. Errors of hypothesis tests. Tests of observations for consistency and gross errors. Testing observations in the context of mathematical models. Tests of solved parameters. Design problems. Models with the a priori knowledge about unknown parameters. Models with conditions. Models with singularities.
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Learning activities and teaching methods
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Task-based study method, Self-study of literature, Lecture, Practicum
- Preparation for comprehensive test (10-40)
- 20 hours per semester
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
- Contact hours
- 26 hours per semester
- Practical training (number of hours)
- 13 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| to explain fundamentals of land surveying |
| to explain fundamentals of the adjustment calculus |
| to explain fundamentals of the mathematical analysis |
| to explain fundamentals of algebra |
| to explain fundamentals of goniometry |
| Skills |
|---|
| to derive an uncertainty of observable |
| programming at the beginner level |
| to make a plot or a map |
| to interpret results and their uncertainties |
| Competences |
|---|
| N/A |
| N/A |
| learning outcomes |
|---|
| Knowledge |
|---|
| to resolve among data processing methods and apply them |
| critically assess the results of processing |
| Skills |
|---|
| to practically realise the variance-covariance law |
| to practically process observables in geodesy |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Lecture |
| Practicum |
| Task-based study method |
| Skills |
|---|
| Practicum |
| Task-based study method |
| Competences |
|---|
| Lecture |
| Practicum |
| Task-based study method |
| assessment methods |
|---|
| Knowledge |
|---|
| Oral exam |
| Written exam |
| Combined exam |
| Test |
| Skills |
|---|
| Oral exam |
| Written exam |
| Combined exam |
| Test |
| Competences |
|---|
| Oral exam |
| Written exam |
| Combined exam |
| Test |
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Recommended literature
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K-R. Koch. Parameter estimation and hypothesis testing in linear models. Springer, Berlin, 1999. ISBN 3-540-65257-4.
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M. Hampacher, M. Štroner. Zpracování a analýza měření v inženýrské geodázii. ČVUT, Praha, 2011. ISBN 978-80-01-04900-6.
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P. J. G. Teunissen. Adjustment Theory: an introduction. VSSD, 2000. ISBN 978-9040719745.
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P. J. G. Teunissen. Network Quality Control. VSSD, 2009. ISBN 978-9071301988.
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P. J. G. Teunissen. Testing Theory: an introduction. VSSD, 2009. ISBN 978-9040719745.
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