Adjustment of observations and least squares estimation theory
| Title | Συνορθώσεις παρατηρήσεων και θεωρία εκτίμησης / Adjustment of observations and least squares estimation theory |
| Code | 03YA017 |
| Faculty | Engineering |
| School | Rural and Surveying Engineering |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Christoforos Kotsakis |
| Common | No |
| Status | Active |
| Course ID | 600025729 |
Programme of Study: PPS Tmīmatos Agronómōn kai Topográfōn Mīchanikṓn (2025-sīmera)
Registered students: 61
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core Courses | Core Courses | 3 | 2 | 5 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 4 |
| Class ID | 600267785
|
Type Of Offer
- Disciplinary Course
Course Type 2021
General Foundation
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600267785
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=16159
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
Prerequisites
General Prerequisites
Linear algebra and matrices, Calculus, Statistics, Basic Surveying.
Learning Outcomes
The aim of this course is to provide, at an introductory level, the necessary background for performing least squares adjustments of surveying, geodetic and geospatial observations, and assessing the internal and external accuracy of their results. The course is especially focused on theoretical and practical aspects of error theory and observation modeling, and the study of optimal estimation techniques in linear (or linearized) models with erroneous data.
The objective is to provide students with the following competencies at the completion of the course:
- Understand the main principles and related concepts of error theory and optimal estimation techniques in linear models.
- Basic knowledge of least squares algorithms for data adjustment in different types of observation models.
- Apply the least squares method for data adjustment and parameter estimation in several problems related to surveying engineering applications.
- Usage of statistical tools for precision and accuracy assessment of least squares adjustment results.
- Interpret, in a critical way, the results from least squares adjustments and provide concrete conclusions for their quality level.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Advance free, creative and causative thinking
Course Content (Syllabus)
The course content is organized in the following sections:
1) Introduction – Course description
2) Types of observation errors – Precision and accuracy
3) Random errors and their propagation law – Stochastic modeling of observations
4) Mathematical models and their basic characteristics
5) Least squares principle and data adjustment with the observation equations model
6) Best linear unbiased estimation and Gauss-Markov models
7) Assessment of precision in least-squares adjustment results
8) Accuracy analysis of least-squares solutions and statistical tests
9) Least-squares adjustment with the mixed equations model
10) Least-squares adjustment with the condition equations model
11) Least-squares adjustment with constraints
12) Practical examples from Surveying and Geodesy
Keywords
observation errors, modeling, least squares principle, data adjustment, parameter estimation, linear models, precision, accuracy, statistical testing
Educational Material Types
- Notes
- Slide presentations
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Laboratory Teaching
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 40 | ✓ | |||
| Laboratory Work | 20 | ✓ | |||
| Reading Assigment | 35 | ✓ | |||
| Tutorial | 25 | ✓ | |||
| Exams | 3 | ✓ | |||
| Total | 123 |
Student Assessment
Description
Final exam (weighting 100%)
Student Assessment methods
- Written Exam with Multiple Choice Questions (Summative)
- Written Exam with Short Answer Questions (Summative)
- Written Exam with Extended Answer Questions (Summative)
- Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [11103]: Μέθοδοι και εφαρμογές συνόρθωσης παρατηρήσεων, Δερμάνης Αθανάσιος Α., Φωτίου Αριστείδης Ι., Εκδόσεις Ζήτη, Θεσσαλονίκη, 1992
Βιβλίο [11291]: Συνορθώσεις παρατηρήσεων και θεωρία εκτίμησης, Τόμος 2, Δερμάνης Αθανάσιος Α., Εκδόσεις Ζήτη, Θεσσαλονίκη, 1987
Additional bibliography for study
Σημειώσεις διδάσκοντα
Ghilani C.D. (2010) Adjustment computations and spatial data analysis, fifth edition, John Wiley & Sons, Inc., Hoboken, New Jersey.
Koch K-R (1987) Parameter Estimation and Hypothesis Testing in Linear Models. Springer-Verlag.
Δερμάνης A. (1987) Συνορθώσεις παρατηρήσεων και θεωρία εκτίμησης, Τόμος 1, Εκδόσεις Ζήτη, Θεσσαλονίκη (Εύδοξος: 11290)
Strang G., Borre K. (1997) Linear algebra, Geodesy and GPS. Wellesley-Cambridge Press, Wellesley, MA.
Last Update
21-02-2025
