基於Sumner位置線概念的天文定位創新求解方法-MSM

New Computational Approaches to Determine the Astronomical Vessel Position Based on Sumner Line Concept-Modified Sumner Method

翁國祐(Guo-Yu Weng)

指導教授 ： 許添本

國立臺灣大學/工學院/土木工程學研究所/博士(2017年)

https://doi.org/10.6342/NTU201702254

摘要

對於大洋中航行的船舶，測天解算是一項不可或缺的定位方法。本研究基於Sumner位置線的概念，首先建立了Sumner-GC法及Sumner-SL法，用以檢視採用大圈或直線近似位置圈的差異。其中，Sumner-GC法以球面三角學中的大圈取代位置圈，而Sumner-SL法則利用平面幾何中的直線取代位置圈。無論以大圈或直線近似位置圈，均隱含了試誤的性質，因此引入迭代機制，配合假設緯度區間，來求得真實的天文定位(real AVP)；繼而，為解決Sumner法在中天或近中天觀測時，無法使用的缺陷，本研究應用天文球面三角形的幾何特性，提出適應性邊界技巧(adaptive boundaries technique, ABT)。本研究提出的修正Sumner法(modified Sumner method, MSM)，以Sumner法為基礎，結合適應性邊界技巧(ABT)及迭代法，可成功地求解天文定位。此外，本研究引入航進定位的概念，使上述發展的方法能用於不同時觀測天體的情境(non-simultaneous sights)。最後，值得一提的是，確保Sumner法能夠成功求解天文定位之關鍵，在於決定假設緯度時，應考慮天體的赤緯與高度，而並非觀測者的推算船位。以上研究成果，均以實務例題檢驗之。

關鍵字

天文航海 ； 天文定位 ； Sumner位置線 ； 航進定位 ； 迭代法

並列摘要

The sight reduction method is indispensable for ocean-going vessels. On the basis of the Sumner line concept, this research first developed two approaches, Sumner-GC method and Sumner-SL method, to find out the difference between using the great circle and using straight line to approximate the circle of position (COP). Because this approximations imply trial-and-error property, the iteration method is introduced to obtain the real astronomical vessel position (AVP). Furthermore, to deal with problems resulting from ex-meridian or meridian sights, an adaptive boundaries technique (ABT) yielded by geometrical properties of celestial triangles is used. Combining the ABT and iteration method into Sumner method, the modified Sumner method (MSM) is then developed. By implemented middle-latitude sailing concept, the developed methods are capable to determine the real AVP while non-simultaneous sights condition encountered. Finally, it should note that the key to solve AVP successfully by Sumner method is considering the declination and altitude of celestial body instead of using dead reckoning position of the vessel while setting the assumed latitudes. All of the proposed methods are demonstrated and verified by practical examples.

並列關鍵字

celestial navigation ； astronomical vessel position ； Sumner line ； running fix ； iteration method

參考文獻

Hsu, T. P., G. Y. Weng and C. L. Chen (2017). A Modified Sumner Method for Obtaining the Astronomical Vessel Position. Journal of Marine Science and Technology, 25(3), 319-328.

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Chen, C. L., Hsu, T. P., and Weng, G. Y. (2014). New Computational Approaches to determine the Astronomical Vessel Position Based on the Sumner Line. Polish Maritime Research, 21(4), 3-11.