A Study of the Point Positioning Influence by Chebyshev Polynomial Fitting on Broadcast Ephemeris -A Case Study of Taichung Monitoring Network

• Main Authors: Chien-An Hsu, 許建安
• Other Authors: 高書屏
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/4j59q8

碩士 === 國立中興大學 === 土木工程學系所 === 98 === In GPS satellite positioning, the satellite coordinates require to be continuously updated to obtain coordinates of ground single-point positioning by using determined coordinates and method of backward intersection. Real-time satellite coordinates are determined by broadcast ephemeris. The broadcast ephemeris forecasts the data every two hours. If the data are used to calculate satellite coordinates, the data would be enormous and calculation is complex. Therefore, this study applied Chebyshev polynomials fitting method to reduce computation process and save data memory space. This study analyzed satellite data from the TC02 GPS base station in Taichung City, applied Chebyshev polynomials to fit broadcast ephemeris, and discusses impacts of sampling time and fitting order on 3D components and precision results of satellite coordinates for ground point-positioning after fitting. In selection of fitting order, this study applied the 12th order Chebyshev polynomials to fit experimental fitting order, because too many orders may require longer sampling time and cannot be used in calculation of real-time satellite positioning. Thus, the 12th order was selected to balance sampling time and fitting precision. The fitting results showed that the fitting precision of 3D coordinate components is lower than ±2m when using satellite coordinates of Chebyshev polynomials fitting. The satellite coordinates after fitting were used to calculate single-point positioning results of TC02 GPS base station. Errors of the coordinate components were less than ±6m. The precision of fitting results were 0.2~0.5m higher than that of satellite coordinates obtained from original equation. These findings can be used to reduce the computation procedure of satellite coordinates needed for GPS satellite single-point positioning. This study can improve the shortcomings in the equations of computing satellite coordinates using broadcast ephemeris to lift the speed of single-point positioning.