AH2917 Advanced Theory of Errors, 7.5c

Autumn semester 2010, period 1

Last updated by Huaan Fan on 2010-09-03.

This course deals with three advanced topics for error analysis of measurement data: 

  1. generalized matrix inverses and free network adjustment
  2. estimation of variance-covariance components 
  3. gross error detection using the method of data snooping

Participants of this course are assumed to have basic knowledge in theory of errors, especially on error propagation, least squares principle and adjutment by elements. For students in KTH's master programme "Geodesy and Geoinformatics", the prerequisite for this course is course AH2921 Adjustment Theory.

A complete description of the course's aim, contents, requirements, etc can be found at KTH:s online Study handbook.

Except 5 lectures, the course will be run mostly as a project work to be carried out during a period of about 4 weeks. Time schedule of the lectures is decided after consultation with students.

Lecturer and course examiner is Huaan Fan, while Uliana Danila will provide technical support to students during the project work.

1.  Course Literature

The required reading is: Fan, H. (2010). Theory of Errors and Least Squares Adjustment. In particular, chapters 4, 5 and 6 of the above textbook cover the main topics of the course.

Other suitable but non-obligatory literatures are listed below:

   Sjöberg, L.E. (1984a). Lecture Notes on General Matrix Calculus, Adjustment and Variance-Covariance
   Component Estimation
. Nordiska forskarkurser “Optimization of Geodetic Operations”. 
   Norges Geogr. Oppm. Publ. 3/1984.
   Rao, C.R. (1973). Linear Statistical Inference and Its Applications. John Wiley & Sons.
   Rao, C.R. and S.K. Mitra (1971). Generalized Inverses of Matrices and Its Apllications. John Wiley & Sons.

2.  List of lectures

L Date Time Room Topics Chapters
L1 100908 14-17 D4448 Generalized matrix inverses. Free network adjustment 4.1, 4.2
L2 100915 13-15 V21 Estimation of variance-covariance components 5.1, 5.2.1, 5.3.1
L3 100922 13-16 D4448 Detection of gross systematic errors. 
Information on individual project work.
5.1, 5.2.1, 5.3.1

3.  Project work

The project work concerns analysis of a simulated 2D geodetic network. Each student will first make a least squares adjustment of the network in the traditional way and then choose one of the following three analysis tasks:

  1. Treat the network as a free network without any fixed points. Calculate the least squares minimum-norm solution for the unknown coordinates. In particular, students are requested to numerically investigate: (a) the coordinates of the centre of the network before and after the free network adjustment; (b) the rotation of each radial vector as well as the total rotation of the network due to free network adjustment and (c) the scale change of each radial vector as well as the total scale change for the whole network after the adjustment.
  2. Estimate the variance components for angles and distances, respectively, using the Best Quadratic Unbiased Estimator (BQUE).
  3. Use data snooping to search for gross errors for three different situations: (a) only one big gross error, (b) several  "moderate" gross errors and (c) several big gross errors.

4.  Requirements

The project work should be documented in a project report, which should clearly describe the  input data sets, methods and formulas used, numerical results and analysis of the results.

Grade for the course will be based on the student's performance including project work and the written report.

 In case two persons work together and submit the same report, then they should submit also a short declaration which states clearly who has done what in the project, and who has written which chapters/sections.

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