After the successful completion of this course, the students will be able to apply basic knowledge from least squares theory to resolve special types of data adjustment problems, such as:
(1) interpolation and predicition of unknown signals from discrete observations based on stochastic models,
(2) optimal parameter estimation in ill-conditioned linear models, and
(3) data adjustment problems with dynamic models based on Kalman filtering.
The students will learn essential techniques for the numerical solution of the above problems based on the use of Matlab programming language.
Course Content (Syllabus)
1) Review of basic principles from least-squares theory
2) Adjustment problems with extended models
3) Adjustment problems with weak or ill-conditioned models and regularized parameter estimation techniques
4) Adjustment problems with dynamical models via Kalman filtering techniques
5) Adjustment problems for determining "multivariate mean values" and optimal fitting of multiple spatial datasets
6) Adjustment problems for estimating unknown functions via stochastic modeling
7) Examples - Applications
Data analysis, parameter estimation, adjustment theory, inverse problems in surveying engineering applications
Additional bibliography for study
1) Strang G., Borre K. (1997) Linear algebra, Geodesy and GPS. Wellesley-Cambridge Press, Wellesley, MA.
2) Ghilani C.D. (2010) Adjustment computations & spatial data analysis. John Wiley & Sons, Inc., Hoboken, New Jersey.
3) Teunissen P.J.G. (2000) Adjustment theory: an introduction. Series on Mathematical Geodesy and Positioning, Delft University Press.
4) Teunissen P.J.G. (2000) Testing theory: an introduction. Series on Mathematical Geodesy and Positioning, Delft University Press.