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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Precision GPS Orbit Determination and Analysis of Error Characteristics

정밀 GPS 위성궤도 결정 및 오차 특성 분석

  • 배태석 (세종대학교 공과대학 지구정보공학과)
  • Published : 2009.08.31
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Abstract

A bi-directional, multi-step numerical integrator is developed to determine the GPS (Global Positioning System) orbit based on a dynamic approach, which shows micrometer-level accuracy at GPS altitude. The acceleration due to the planets other than the Moon and the Sun is so small that it is replaced by the empirical forces in the Solar Radiation Pressure (SRP) model. The satellite orbit parameters are estimated with the least-squares adjustment method using both the integrated orbit and the published IGS (International GNSS Service) precise orbit. For this estimation procedure, the integration should be applied to the partial derivatives of the acceleration with respect to the unknown parameters as well as the acceleration itself. The accuracy of the satellite orbit is evaluated by the RMS (Root Mean Squares error) of the residuals calculated from the estimated orbit parameters. The overall RMS of orbit error during March 2009 was 5.2 mm, and there are no specific patterns in the absolute orbit error depending on the satellite types and the directions of coordinate frame. The SRP model used in this study includes only the direct and once-per-revolution terms. Therefore there is errant behavior regarding twice-per-revolution, which needs further investigation.

동역학적 방법을 이용한 GPS(Global Positioning System) 위성궤도 결정을 위해 양방향 적분이 가능한 multi-step 방식의 수치적분기를 개발하였으며, 이는 GPS 위성 고도에서 마이크로미터 수준의 정확도를 보였다. 가속도 모델링에서 달, 태양 이외의 천체에 의한 인력은 매우 작으므로 태양복사압에서 경험적 모델로 대체하였다. 위성궤도 미지수는 수치적분된 위성궤도와 IGS(International GNSS Service) 정밀궤도를 이용하여 최소제곱방법으로 결정했다. 이를 위해서는 수치적분기에서 가속도와 함께 미지수에 대한 편미분값을 동시에 적분해야 한다. 추정된 위성궤도 미지수를 이용하여 계산한 잔차의 RMS(Root Mean Squares error)로 부터 위성궤도의 정확도를 검증했다. 2009년 3월 한달의 평균적인 궤도오차 RMS는 5.2mm 였으며, 궤도오차의 절대적인 크기는 위성체의 종류 및 위성진행방향기준 좌표계 상에서 특별히 편향된 형태를 보이지는 않는 것으로 나타났다. 본 연구에서 적용한 태양복사압 모델은 상수항 및 궤도당 1주기에 대한 변화만을 포함하고 있으므로, 궤도당 2주기에 해당하는 궤도오차 양상을 크게 보이고 있으며 이에 대한 추가적인 연구가 필요할 것으로 판단된다.

Keywords

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