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研究生:林泰亨
研究生(外文):Lin, Tai-Heng
論文名稱:求解多天體天文船位問題的點斜方程組
論文名稱(外文):Point Slope Equations for Solving Multi-Body Astronomical Vessel Position Problems
指導教授:陳志立陳志立引用關係
指導教授(外文):Chen, Chih-Li
口試委員:許添本黃明居張建仁
口試委員(外文):Hsu, Tien-PenHwang, Ming-JiuChang, Jiang-Ren
口試日期:2020-01-10
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:商船學系
學門:運輸服務學門
學類:航海學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:70
中文關鍵詞:航海天文船位點斜方程組迭代機制航進定位
外文關鍵詞:NavigationAstronomical vessel positionPoint slope equationsIteration schemeRunning fix
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本文提出點斜方程組,以求解雙天體天文船位問題,進而延伸求解多天體天文船位問題。截距法因測天簡算表之設計,已成為天文觀測定位之主要方法,然而目前天文船位之計算方法,大多使用位置圈概念,導致方法過於複雜且難以使用。本研究係採用截距法之概念,即切線位置線建構點斜方程,由於截距法本質為「試誤法」,故必須引進迭代機制來改進天文船位的準確性。為了處理不同觀測時間的問題,以航進定位概念並採用平均緯度航法移動參考點,藉此計算求得定位時間的天文船位。值得注意的是,亦使用平均緯度航法求得切點,並轉至直角座標系統以代數法求解。另外,多天體天文船位的合理解集合應是天文船位及其誤差,故以統計學觀點以及截距法之概念求解多天體天文船位問題,並探討天文船位與誤差三角形之關係,發現天文船位即為重心。進而以點斜方程組開發計算雙天體及多天體天文船位的2AVP_PSE及nAVP_PSE程式。最後,將挑選數個標準計算實例驗證本研究方法的準確性與其廣泛的適用性。
A computational method, namely Point Slope Equations (PSE), is proposed to deal with the two-body astronomical vessel position (AVP) problem and further extended to resolve the multi-body AVP (nAVP) problems. Because the sight reduction tables was designed, the intercept method was main sight reduction method for navigator. However most conventional methods to determine the AVP are based on circles of position concept, they are too complicated and hard for use. This research adopts the lines of position (intercept method concept) to construct the PSE method. Due to the trial-and-error characteristic of the intercept method, an iteration scheme is introduced to improve numerical accuracy. For the non-simultaneous sights condition is encountered, the running fix concept and the mean latitude sailing will be adopted to translate reference points to the fix time for determining the AVP. It is noted that it’s also get the tangent point on circles of position by mean latitude sailing, transfer to Cartesian coordinates, and solve by algebra. Besides, the reasonable solution set of the nAVP problem should fall into the real AVP within an acceptable error range by using statistics and intercept method concept. Also, it can explore the relationship between astronomical vessel position and error triangle and find that the astronomical vessel position is the barycenter. Based on the PSE, two program namely 2AVP_PSE and nAVP_PSE were developed for solving two-body AVP and nAVP problems. Finally, several benchmark examples will be conducted to validate the accuracy and versatility of the novel approach.
目次
摘要 I
ABSTRACT II
圖次 V
表次 VIII
特殊符號說明 IX

第一章 緒論 1
1.1 背景目的與研究動機 1
1.2 天文船位概念說明 1
1.2.1 圖解法 2
1.2.2 航進定位 2
1.2.3 雙天體天文船位之計算方法 3
1.2.4 多天體天文船位之計算方法 3
1.3 天文船位問題描述與思考 4
1.4 論文架構 5

第二章 文獻回顧 11
2.1 雙天體計算法 11
2.1.1 雙位置圈 11
2.1.2 雙位置線 13
2.2 多天體計算法 13
2.3 小結 14

第三章 方法論暨計算程序 19
3.1 理論建構 19
3.2 點斜方程組程序建立 24
3.3 程式開發 26
3.3.1 程式開發工具 26
3.3.2 2AVP_PSE程式 27
3.3.3 nAVP_PSE程式 27
3.4 小結 27

第四章 實例驗證與評析 34
4.1 雙天體問題 34
4.2 多天體問題 37
4.3 小結 41

第五章 結論與建議 64
5.1 結論 64
5.2 建議 65

參考文獻 66
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