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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Interpolation of GPS Receiver Clock Errors Using Least-Squares Collocation

Least-Squares Collocation을 이용한 GPS 수신기 시계오차 보간

  • Hong, Chang-Ki (Dept. of Geoinformatics Engineering, Kyungil University) ;
  • Han, Soohee (Dept. of Geoinformatics Engineering, Kyungil University)
  • Received : 2018.12.06
  • Accepted : 2018.12.24
  • Published : 2018.12.31
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Abstract

More than four visible GPS (Global Positioning System) satellites are required to obtain absolute positioning. However, it is not easy to satisfy this condition when a rover is in such unfavorable condition as an urban area. As a consequence, clock-aided positioning has been used as an alternative method especially when the number of visible satellites is three providing that receive clock error information is available. In this study, LSC (Least-Squares Collocation) method is proposed to interpolate clock errors for clock-aided positioning after analyzing the characteristics of receiver clock errors. Numerical tests are performed by using GPS data collected at one of Korean CORS (Continuously Operating Reference Station) and a nearby GPS station. The receiver clock errors are obtained through the DGPS (Differential GPS) positioning technique and segmentation procedures are applied for efficient interpolation. Then, LSC is applied to predicted clock error at epoch which clock information is not available. The numerical test results are analyzed by examining the differences between the original and interpolated clock errors. The mean and standard deviation of the residuals are 0.24m and 0.49m, respectively. Therefore, it can be concluded that sufficient accuracy can be obtained by using the proposed method in this study.

GPS (Global Positioning System)를 이용하여 위치를 결정하기 위해서는 4개 이상의 가시위성이 있어야 한다. 하지만 도심지역과 같은 환경에서는 이러한 조건을 만족하기 어려운 경우도 있다. 특히, 가시위성이 3개뿐인 경우 외부로부터 위치결정에 필요한 시계오차정보를 활용하는 측위기법이 대안으로 사용되기도 한다. 본 연구에서는 먼저 수신기 시계오차특성을 분석한 후 시계오차의 보간에 적합한 방법으로 LSC (Least-Squares Collocation)을 제안하였다. 실험을 위해 국내 상시관측소와 상시관측소 근처에 설치된 수신기로부터 수신된 GPS 데이터를 이용하였다. DGPS (Differential GPS)기법을 통해 먼저 시계오차를 계산했으며 효율적인 보간을 위해 구간을 나눈 후 보간하는 방법을 적용하였다. 시계오차의 계산이 불가능한 epoch에 대해 LSC 보간법을 적용함으로써 시계오차를 계산하였다. 실험결과를 분석하기 위해 원래 데이터로부터 계산된 시계오차와 보간된 시계오차와의 차이인 잔차를 계산하였다. 계산결과 잔차의 평균은 0.24m 그리고 표준편차는 0.49m로 충분한 정확도의 확보가 가능한 것으로 판단된다.

Keywords

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Fig. 1. Flowchart of data processing

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Fig. 2. Azimuth and elevation angles of GPS satellite (T007)

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Fig. 3. Number of GPS satellites and DOPs (T007)

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Fig. 4. Estimated receiver clock errors; (a) TEGN and (b) T007

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Fig. 5. Absolute positioning results (T007)

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Fig. 6. DGPS positioning results (T007)

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Fig. 7. Number of satellites after data removal

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Fig. 8. Estimated receiver clock errors after data removal

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Fig. 9. Receiver clock offsets detected with discriminant criterion (T007)

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Fig. 10. Change rate of receiver clock errors with respect to time (TEGN)

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Fig. 11. Results of interpolation using LSC; (a) original clock errors (b) interpolated clock errors  

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Fig. 12. Differences between the original and interpolated clock errors

Table 1. Station informations used in this study

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Table 2. Statistical characteristics of DGPS positioning results (T007)

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Table 3. Data spans with number of satellites information

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