Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography (한국측량학회지)

Korean Society of Surveying, Geodesy, Photogrammetry and Cartography (한국측량학회)
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The Accuracy Analysis of Methods to solve the Geodetic Inverse Problem

측지 역 문제 해석기법의 정확도 분석

  • 이용창 (인천대학교 도시과학대학 도시환경공학부)
  • Received : 2011.05.11
  • Accepted : 2011.07.29
  • Published : 2011.08.30
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Abstract

The object of this paper is to compare the accuracy and the characteristic of various methods of solving the geodetic inverse problem for the geodesic lines which be in the standard case and special cases(antipodal, near antipodal, equatorial, and near equatorial situation) on the WGS84 reference ellipsoid. For this, the various algorithms (classical and recent solutions) to deal with the geodetic inverse problem are examined, and are programmed in order to evaluate the calculation ability of each method for the precise geodesic determination. The main factors of geodetic inverse problem, the distance and the forward azimuths between two points on the sphere(or ellipsoid) are determined by the 18 kinds of methods for the geodetic inverse solutions. After then, the results from the 17 kinds of methods in the both standard and special cases are compared with those from the Karney method as a reference. When judging these comparison, in case of the standard geodesics whose length do not exceed 100km, all of the methods show the almost same ability to Karney method. Whereas to the geodesics is longer than 4,000km, only two methods (Vincenty and Pittman) show the similar ability to the Karney method. In the cases of special geodesics, all methods except the Modified Vincenty method was not proper to solve the geodetic inverse problem through the comparison with Karney method. Therefore, it is needed to modify and compensate the algorithm of each methods by examining the various behaviors of geodesics on the special regions.

본 연구의 목적은 WGS84 세계타원체를 기준으로 다양한 거리의 '표준측지선'은 물론, 극 및 적도와 그 주변을 지나면서 '특이영역에 위치하는 측지선'을 대상으로 측지 역 문제의 해석기법 별 정확도 및 특정을 비교 분석하는 것이다. 이를 위해 측지 역 문제를 해석할 수 있는 전통적인 방법은 물론 최근 제시된 방법 등 다양한 측지 역 문제 해석기법의 알고리즘, 총 18종을 분석하여 프로그래밍 하였다. 두 측점의 배치 상태에 따른 '표준 측지선' 및 '특이영역'에 위치한 측지선을 대상으로 거리 및 전방 방위각을 각기법별로 산출하고 Karney 해석법을 기준으로 비교하였다. 연구결과, 표준측지선에서 약 100km 이하의 단 측지선의 경우, 18가지 역 문제 해석 기법 모두, 매우 근접한 측지선의 길이를 나타낸 반면, 4,000km 이상의 중 장 측지선의 경우는 길이 및 전방 방위각에서 Karney, Vincenty 및 Pittaman 기법이 매우 근접한 결과를 보였다. 또한, '특이영역'에 대한 다양한 역문제의 해석결과, Karney 기법이 일관성 있는 종합적인 해석결과를 제시한 반면, 수정 Vincenty 기법을 제외한 다른 해석법들은 특이영역의 상황에 따라 좀더 면밀한 측지선의 거동분석과 함께 알고리즘의 수정 보완이 요망되었다.

Keywords

Acknowledgement

Supported by : 인천대학교

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