Recursive Computation of Great Elliptic Sailing Distance with Discretionary Precision

瀏覽統計 Email 通知 RSS Feed

簡歷

基本資料

Project title

Code/計畫編號

NSC100-2410-H019-018

Translated Name/計畫中文名

基於大橢圓航法任意精確度航行距離的遞迴演算法

Project Coordinator/計畫主持人

Wei-Kuo Tseng

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Merchant Marine

Website

https://www.grb.gov.tw/search/planDetail?id=2348764

Year

2011

Start date/計畫起

01-08-2011

Expected Completion/計畫迄

31-07-2012

Bugetid/研究經費

520千元

ResearchField/研究領域

管理科學
交通運輸

"早期內建於衛星航行接收器裡基本的航行軟體，因為簡化及其他的理由這些航行的軟體使用有限精確度的計算方法，一個令人吃驚的現象是現在即使現代的航行軟體還是仍然使用這些鬆散的計算方法，忽略一些基本的原則及採用過份簡化的假設及錯誤的數學方法運算，例如在計算恆向線航法時誤將球體模型與旋轉橢球體混合運用在不同的計算步驟，由於缺乏對於精度及計算方法的官方的標準，全球航行衛星系統（Global Navigation Satellite System, GNSS）航行接收器及電子海圖顯示系統(Electronic Chart Display and Information, ECDIS)或電子海圖系統(Electronic Chart System ENS)的航行系統在進行航行計算的過程如同黑箱作業，因此有學者建議徹底檢視航行系統及全球衛星航行接收器的航法計算的問題。為了降低海上航行計算複雜性，地球模型簡化為正圓球形，因此傳統實務上；航行規劃或航海者利用大圓航法計算得到相關航行數據標示在紙本海圖上，以利完成整個航程，隨著時代的變遷電子海圖顯示系統(ECDIS, Electronic Chart Display And Information System)為了安全的緣故要求高精度及連續地定位, 全球定位系統(Global Positioning System, GPS)的定位功能可以達到ECDIS 的要求，全球定位系統的參考座標系統為WGS 84(World Geodetic System 1984)，雖然GPS 定位非常精準；如果航路不準確地規劃將會造成較大航行的誤差，以致於航行中需要常常不經濟及不斷的修正航向，甚至航行到誤區產生船舶航行安全上的威脅，對於時間性要求強及耗油量大的高速船舶其經濟性就有較大的損失。因為全球定位系統使用橢球體為參考座標，傳統上大圓航法的參考座標系統使用正圓球體，因此航程規劃所得的數據將會導致較大的誤差，如果將規劃航程使用的座標系統轉換成WGS 84 參考座標系統，航路的規劃的精確性將會大大的提高。本研究將利用已知出發點及航向或終點建立大橢圓航線，同時建構已知經緯度求解航向及距離，對於已知距離反求解經緯度及航向的函數也進行推導並建立計算程序，本文發現事實上大圓(Great Circle, GC)航線上的經緯度的關係與大橢圓(Great Ellipse, GE)航線上的經緯度關係是一樣的，但在進行距離與航向相關計算時需要考慮地球的扁率(eccentricity)，因此大圓航法計算所得的數據會有較大之誤差，利用向量分析及距離積分式可以求得大橢圓航行的距離、航向及位置，由於大橢圓距離積分式缺乏反積分式，因此可以使用數值積分或被積函數之二項級數展開逐項積分求取航點間的距離，本文發展出一套可以達到任何要求精確度的航行距離的遞迴演算法，利用向量分析建立大橢圓不僅僅有上述的優點，已知航行距離求解經度及緯度的數學方可以使用本文發展的迭代的數學方法，計算收斂的速度很快，通常只要2,3 次就足夠精確。對於電子海圖或地理資訊系統(Geographic Information System)軟體設計者編寫程式語言及航行人員使用商業數學軟體計算航行問題時會有很大的助益，本研究也將撰寫相關的Javascript 程式將成果顯示在Google Map 上，另外也會開發 Matlab 程式、EXCEL 增益集相關航海問題，計畫所撰寫程式集將會上載到作者的網頁上，提供程式設計者、航路規劃及相關研究人員參考。""This paper presents new algorithms for great elliptic sailing calculation for route planning and portrayal of sailing route on electronic chart. From the early days of the development of basic navigational software built into satellite navigational receivers, it has been noted that this navigational software is often based on methods of limited accuracy for the sake of simplicity and a number of other reasons. It is surprising that the method of navigational software is still used in loose manner even nowadays. The navigational software ignores basic principles and adopts oversimplified assumptions and errors such as the wrong mixture of spherical and ellipsoidal calculations in different steps of the solution of a particular sailing problem. The lack of official standardization on both the accuracy required and equivalent methods employed. The GNSS navigational receivers and navigational systems (ECDIS and ECS) provide the black solution. Therefore, it is necessary that that thorough examine the issue of sailing calculation for navigational system and GNSS recovers. The Earth is not a perfect sphere, so a great circle becomes a great ellipse. Among the ECDIS Requirements is the need for a continuous system with a degree of accuracy consistent with the requirements of safe navigation. At present, this requirement is best fulfilled by the Global Positioning System (GPS). The GPS system is referenced to World Geodetic System 1984 (WGS 84) Datum. Using the ellipsoid model for the spherical model, we can attain better accuracy for the calculated distances between two points on the Earth. Therefore, we construct a computation procedure for solving waypoints and courses along a great ellipse. The paper takes different scenario to produce the great ellipse Equation determining a great ellipse by a point and its course. The alternative solution of function of course and distance along great ellipse also are represented here. In this study, we found that the Great Circle (GC) equation is the same as the Great Ellipse (GE). This fact found in this paper presents that the formulae tackling relationship of latitude and longitude of the GC also can be suited for the GE excepting some problems of GE involving distance and azimuth. Applying vector methods to navigation problems gives some advantages to both syntax of computer algorithms and commercial mathematics software. We also give a recursive numerical algorithm attaining any requirement of accuracy for calculation of length of GE. Using the iterative calculation gives the position on a great ellipse when the distance is given. Normally two or three iterations are sufficiently accurate. The proposed formulas provide extremely high accuracies and are efficient to be exploited in the development of navigation software. Moreover, this paper was intended to appeal to the navigator or route planner who is interested in using more accurate mathematics for navigation and whose tools in use are personal computers and programming languages."

Keyword(s)

大圓
大橢圓
測地線
Great Circle
Great Ellipse
Geodesic

DSpace CRIS

Recursive Computation of Great Elliptic Sailing Distance with Discretionary Precision

基本資料

Description