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| Title: | 利用不同目標函數之演算法進行粗差偵測之研究
The study of using different objective functions with algorithm in gross error detection |
| Authors: | 張宏嘉
Chang, Hung-Chia |
| Contributors: | 甯方璽
Ning, Fang-Shii
張宏嘉
Chang, Hung-Chia |
| Keywords: | 粗差定位
最小一乘法
權迭代法
最佳化權矩陣
Gross error
LAD
OWM
Reverse weight matrix of LAD |
| Date: | 2018 |
| Issue Date: | 2018-08-27 14:56:28 (UTC+8) |
| Abstract: | 在測量領域中，最小二乘法為最常被使用的平差方法，然而最小二乘法建立於觀測量僅含有偶然誤差的前提之下，當觀測量含有粗差時，最小二乘法的成果容易受到影響。因此，本研究透利用不同演算法對不同目標函數進行計算，並以統計檢定量分析各方法偵測粗差的能力。
本研究所使用的方法分別為等權最小二乘法、權迭代法、最小一乘法及最佳化權矩陣。此外，本研究提出最小一乘法的反求權矩陣的概念，藉此解決最小一乘法缺乏統計檢定量的問題。並以權重、標準化殘差及多餘觀測分量分析各方法之成果。
在模擬實驗中，當多餘觀測量較少時，最佳化權矩陣及最小一乘法的反求權矩陣具有較佳的粗差定位能力，並降低含有粗差的觀測量之權重；當觀測量越來越多時，則是權迭代法具有較佳的成果。在實測資料的部分，各方法之成果容易受到多餘觀測分量及後驗中誤差的影響，導致各方法皆無法順利定位粗差，而最佳化權矩陣及最小一乘法的反求權矩陣能夠使含有粗差的觀測量具有較大的標準化殘差，以利使用者後續對該觀測量優先進行檢核。
In the field of surveying, Least Square (LS) methods are often used in adjustment. However, LS built on observations usually show with random errors. If observations have gross errors, the solution of LS will be effected easily. So this study uses different objective functions to calculate with different algorithms, and analyzes the ability of gross errors detection with test statistic.
The methods in this study are equal weight LS、Iteratively Reweighted LS (IRLS)、Least Absolute Deviation (LAD) and Optimal Weight Matrix (OWM). This study proposes a concept “inverse weight matrix of LAD” to solve the problem that LAD lacks test statistics. And assess the different methods’ results with weight value、 standardized residual and redundant observation component.
In simulated data, when observations have less redundant observations, OWM and “inverse weight matrix of LAD” have better ability of gross error detection, and them make the gross errors have lower weight value. With more observations, the IRLS has better result. In real data, the posteriori variance will be effected easily, and lead to every methods can’t locate the gross error. However, OWM and “inverse weight matrix of LAD” can enlarge the standardized residual of gross errors and help user to check the observations. |
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| Description: | 碩士
國立政治大學
地政學系
105257032 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0105257032 |
| Data Type: | thesis |
| DOI: | 10.6814/THE.NCCU.LE.016.2018.A05 |
| Appears in Collections: | [地政學系] 學位論文
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