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
generalized matrix inverses and free network adjustment
- estimation of
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.
students in KTH's master programme "Geodesy and Geoinformatics",
the prerequisite for this course is course AH2921
A complete description
of the course's aim, contents, requirements, etc can be found at KTH:s online Study
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:
L.E. (1984a). Lecture Notes on General Matrix Calculus, Adjustment and
Component Estimation. Nordiska forskarkurser “Optimization of
Norges Geogr. Oppm. Publ. 3/1984.
Rao, C.R. (1973). Linear Statistical Inference and Its
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
matrix inverses. Free network adjustment
of gross systematic errors.
Information on individual project work.
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:
- 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.
- Estimate the variance components for angles and distances, respectively,
using the Best Quadratic Unbiased Estimator (BQUE).
- 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.
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
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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