臺灣博碩士論文加值系統

傳統上衛星定位主要是使用最小平方法(Least Squares)，而使用者若是持有單頻接收機，則常結合精密單點定位(Precise Point Positioning, PPP)去提升定位精確度，本篇論文提出一種改良型Kaczmarz演算法(Modified Kaczmarz Algorithm)取代最小平方法，希望能夠更加提升PPP定位方法的精確度。Kaczmarz演算法是用來計算線性方程式的解的一種方法，但由於無法確定收斂速度，所以又發展出了隨機性Kaczmarz演算法(Randomized Kaczmarz Algorithm)，但隨機性Kaczmarz演算法的定位結果卻不如傳統上使用的最小平方法(Least Squares)，所以本篇論文改良了Kaczmarz演算法，使其定位精度相較於最小平方法，在定位誤差上有更好的效果。

For the GNSS receivers, usually the least-squares algorithm is used in positioning. In this paper, a modified Kaczmarz algorithm is proposed for single-frequency Precise Point Positioning (PPP) to improve positioning accuracy. Originally, Kaczmarz algorithm is a method which could be used to find the solution of a linear equations systems. When applying the traditional Kaczmarz algorithm in PPP, we find the results are not satisfactory. Therefore, we offer a modified Kaczmarz algorithm to improve the positioning accuracy. From the results of the experiments, the proposed method indeed outperform the least-squares and the traditional Kazmarz algorithms.

摘要……………………………………………………………………………………I
Abstract………………………………………………………………………II
目次…………………………………………………………………………………III
圖次…………………………………………………………………………………IV
表次…………………………………………………………………………………V
第一章 緒論……………………………………………………………1
1.1 前言……………………………………………………………………1
1.2 研究背景與動機………………………………………………1
1.3全球定位系統…………………………………………………………2
1.4本文架構…………………………………………………………………2
第二章 精密單點定位…………………………………………3
2.1 觀測量…………………………………………………………………3
2.2定位原理…………………………………………………………………4
2.3 觀測量誤差項…………………………………………………………6
2.3.1 衛星軌道誤差………………………………………………6
2.3.2 時鐘誤差……………………………………………………………7
2.3.3 電離層延遲…………………………………………………………7
2.3.4 對流層延遲…………………………………………………………9
2.3.5 相對論誤差………………………………………………………13
2.3.6 其餘誤差項………………………………………………………14
第三章 Kaczmarz演算法及改良………………………………16
3.1 Kaczmarz演算法………………………………………………………16
3.2 隨機性Kaczmarz演算法……………………………………………17
3.3 改良型Kaczmarz演算法……………………………………………21
第四章 實驗結果與分析…………………………………………………24
4.1 實驗環境與設備………………………………………………………24
4.2 實驗流程與設計………………………………………………………27
4.3 實驗結果………………………………………………………………28
第五章 結論與未來展望………………………………………38
5.1 結論……………………………………………………………………38
5.2 未來展望………………………………………………………………38
參考文獻……………………………………………………………………………39

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