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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Accuracy Improvement of GPS/Levelling using Least Square Collocation

Least Square Collocation에 의한 GPS/Leveling의 정확도 개선

  • 윤홍식 (성균관대학교 토목환경공학과) ;
  • 이동하 (성균관대학교 토목환경공학과)
  • Published : 2005.12.01
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Abstract

This paper describes an accuracy analysis of newly developed gravimetric geoid and an improvement of developed geoid using GPS/Levelling data. We developed the KGEOID05 model corrected with the correction term. The correction term is modelled using the difference between GPS/Levelling derived geoidal heights and gravimetric geoidal heights. The stochastic model used in the calculation of correction term is the least squares collocation technique based on second-order Markov covariance function. 373 GPS stations were used to model the correction term. The standard deviation of KGEOID05 is about 11 cm and it indicates that we can be determined accurate heights ($2{\sim}3\;cm$) when we made precise modelling using KGEOID05 and a few GPS measurements for the local area.

본 논문에서는 중력데이터를 사용하여 중력지오이드모델을 개발하고, GPS/Leveling데이터를 사용하여 개선한 KGEOID05모델을 계산하였으며, 그 정밀도를 분석하였다. KGEOID05는 중력지오이드모델에 보정항을 더하여 계산하였으며, 보정항은 GPS/Levelling에 의하여 구한 지오이드고와 중력지오이드고의 차이를 사용하여 모델링 하였다. 모델링을 위한 통계학적 함수는 Markov 2차공분산 함수에 기초한 least squares collocation방법을 사용하였다. 총 373점의 GPS관측점을 보정항 모델링에 사용하였으며, 정밀도분석결과 KGEOID05의 정밀도는 11cm로 계산되었다. $2{\sim}3$점의 수준점에 대한 GPS관측데이터를 사용하여 지역적으로 KGEOID05모델에 대한 fitting을 실시할 경우에 GPS관측에 의한 $2{\sim}3cm$ 정밀도의 표고측정이 가능하다.

Keywords

References

  1. 최재화, 윤홍식, 이석배 (1996), FFT에 의한 한반도 일원에서의 중력지오이드 결정, 한국측지학회지, 제14권, 제1호, pp. 49-58
  2. Arabelos, D. and C. C. Tscherning (1998), The Use of Least Suqares Collocation Method in Global Gravity Field Modeling Phys. Chem. Earth, Vol. 23, No. 1, pp. 1-12 https://doi.org/10.1016/S0079-1946(97)00234-6
  3. Benahmed Daho S.A. and S. Kahlouche (1998), The gravimetric geoid in Algeria: First Results. Geodesy on the Move. IAG Scientific Assembly, Rio de Janeiro, September 3-9
  4. Forsberg R., C. C. Tscherning and P. Knudsen (2003), An Overview Manual of the GRAVSOFT, Kort & Matrikelstyrelsen
  5. Forsberg, R. (1985), Gravity field terrain effect computations by FFT, Bull. Geod., 59, pp. 342-360
  6. Forste C., F. Flechtner, R. Schmidt, U. Meyer, R. Stubenvoll, F. Barthelmes, R. Konig, K.H. Neumayer, M. Rothacher, Ch. Reigber, R. Biancale, S. Bruinsma, J.M. and Lemoine, J.C. Raimondo (2005), A New High Resolution Global Gravity Field Model Derived From Combination of GRACE and CHAMP Mission and Altimetry/Gravimetry Surface Gravity Data, EGU General Assembly 2005, Vienna, Austria, pp. 24-29
  7. Heiskanen, W.A. and H. Moritz (1967), Physical Geodesy, W.H. Freeman and Co., San Fransisco
  8. Henning, W. E., E. E. Carlson and D. B. Zilkoski (1998) Baltimore County, Maryland, NAVD 88 GPS-derived Orthometric Height Project, Surv. Land Info. Sys., Vol. 58, No. 2, pp. 97-11
  9. Kearsley, A.H.W. (1988), The determination of the geoid-ellipsoid separation for GPS levelling, The Australian Surveyor, 34(1), pp. 11-18 https://doi.org/10.1080/00050326.1988.10438999
  10. Omang, O. C. D. and R. Forsberg (2000), How to handle topography in practical geoid determination: three examples, Bull. Geod., 74, pp. 458-466 https://doi.org/10.1007/s001900000107
  11. Tschering C. C., A Radwan, A. A. Tealab, S. M. Mahmoud, M. Abd EL-Monum, Ramdan Hassan, I. EI-Syad and K. Saker (2001), Local geoid determination combining gravity disturbances and GPS/Levelling: a case study in the Lake Nasser area, Aswan, Egypt, Bull. Geod., 75, pp. 343-348 https://doi.org/10.1007/s001900100185
  12. Tscheming, C. C. (1994), Gravity field modelling with GRAYSOFT least-squares collocation. Lecture Notes, International School for the Determination and Use of the Geoid, Milano, Oct. 10-15. International Geoid Service, pp. 101-134
  13. Yun, H. S. (1994), Determination of Gravimetric Geoid Solution in South Korea, Gravity and Geoid, International Association of Geodesy, Symosia. 113, IUGG and IAG, Springer, Berlin
  14. Yun, H. S. (1999), Precision geoid determination by spherical FFT in and around the Korean peninsula, Earth Planets Space, 51, pp. 13-18 https://doi.org/10.1186/BF03352204
  15. Zilkoski, D. (2001), Vertical Datums. In Digital Elevation Model Technologies and Applications: The OEM User Manual, Published by American Society for Photogrammetry and Remote Sensing, MAUNE, D. Eds. Bethesda, MD. pp. 35-60