變形測量理論
Deformation Surveying
| 節 | 週五 |
|---|---|
2 09:00–09:50 | 變形測量理論 EB404（光復） 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
Deformation monitoring, in a generalized point of view, can be interpreted as the technique to locate and analyze elusive signals obscured in environmental or observational noises. This course will place emphasis on geodetic applications either in engineering or scientific researches. Statistical theorems associated with the titled issue will be introduced to the details so that students can have the clear picture conceptually to handle the task of stochastic data processing, and the ability to develop decent tool to deal with the problems encountered in the future. Meanwhile, several examples will be presented in the class as well to serve as the supplementary guide helping students get a better idea about this subject. As the technology evlolutes, constantly monitored deformation data are possible nowadays. Time series analysis would be the tool to elaborate small signals hidden in noise over a significant long period temporal interval. This lecture will adress some introduction for radndom process including the topics of optimal prediction such as Kriging/ collocation, spectrum techniques/Fourier series.
fundamental adjustment linear algebra
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Review of Gauss Markov Model, Least squared parameter estimation, and relevant theorems
range space, null space of design matrix in Gauss Markov model. The orthogonality of four subspaces. The principle of least squared approach for parameter estimation
- 講授：
- 3
Best linear uniformaly unbiased estimator
Derive linear estimator for Gauss Markov model which features the unbiasedness while optimize the mean squared error
- 講授：
- 3
error ellipse, confidence ellipse
discuss the concept of error ellipse. elaborate the confidence ellipse based on the dispersion matrix of estimated parameters
- 講授：
- 1
datum deficiency
Deal with the datum deficiency problem by split the parameter vector in Gauss Markov model where the selected datum parameters are collected in a sub vector. Parameter estimation is carried out in the sense of least squared approach for the modified Gauss Markov model
- 講授：
- 2
Gauss Markov model with constraints
Elaborate on the BLUUE of unknown parameter vector and BLUP of error vector for the determinstic constrained GMM. The statistical inference based on the hypothesis test. The measure to deal with the inversion for a rank deficient equation system.
- 講授：
- 6
| 週次 | 主題 |
|---|---|
| 第 1 週 | review of Gauss Markov model Feb 19 |
| 第 2 週 | Best linear uniformly unbiased estimator Feb 26 |
| 第 3 週 | Error ellipse, confidence ellipse datum deficiency and split of parameter vector March 4 |
| 第 4 週 | review March 11 |
| 第 5 週 | Gauss Markov Model with constraints (full rank design matrix) BLUUE of unknown vector, unbiased predictor for error vector, and their dispersion. March 18 |
| 第 6 週 | Rank deficient Gauss Markov model with constraints. General Inverse Symmetrical general inverse Reflexive general inverse March 25 |
Parameter Estimation and Hypothesis Testing in Linear Models by K.R. Koch, Springer 1997 Concepts of Network and Deformation Analysis by W. F. Caspary, School of Surveying, the University of New South Wales, Australia (1988).
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