摘要
GPS接收機經過長時間關機之後，再開機時所花的定位時間可能因為衛星軌道資訊取得的困難而較長，為了解決這個問題而達到快速開機定位的效果，本研究中，我們利用GPS衛星位置的預估器來延長GPS衛星星歷的可用時間，使得GPS接收機維持在類似熱開機的狀態之下。 我們將用積分牛頓運動方程式的方法來預估衛星位置，衛星的運動在太空中不只受到地球的重力影響，還會受到其他擾動力的影響，因此若是要精確的預估衛星位置，就必須加入擾動項的修正。本論文所加入的擾動力修正項有地球非正球體之擾動項(Non–spherical Earth)、太陽及月球重力之擾動項(Solar and Lunar Gravitational Effect)以及太陽輻射壓擾動項(Solar Radiation Pressure)，並且探討了衛星姿態運動(Attitude Motion)對軌道的影響。 此外，GPS接收機中的星曆資料為在WGS-84座標系統下表示，但是牛頓運動方程式卻只能在慣性座標下計算，因此我們需要做WGS-84座標系統和慣性座標系統的轉換。而這兩個座標系的轉換必須相當精確，地球之進動、章動、極動的影響都必須納入考慮。 我們所使用的數值積分方法為四階的Runge Kutta method，由解算的結果可知，使用本論文的方法可以成功地將一天內軌道預估誤差由未加任何修正時的數十公里降至數十至數百公尺，使得預估結果和真實衛星位置相當接近。
並列摘要
After GPS receivers being shot down for a long time, the time of booting may be too long due to the difficulty in obtaining the satellite’s position. In order to solve the problem and reduce the booting time, we use the GPS satellites positions prediction in this research to extend the useable time of GPS ephemeris such that the GPS receivers can be maintained in the condition of hot start. The Newton’s equation is integrated to predict the position of satellite since forces acting on the satellite in space do not only contain the Earth’s gravitational force. If we want to predicate the position of satellite precisely, we have to consider the other forces. The forces include the non–spherical Earth effect, Solar and Lunar gravitational effect, and Solar radiation pressure in this thesis. Moreover, the effect of attitude motion to the orbital prediction is discussed. The ephemeris data in the GPS receivers is in the frame of WGS-84, but the Newton’s equation is calculated in an inertial frame. Therefore, we have to adopt the appropriate coordinate transformation between the two frames by including the effect of the precession, the nutation, and the polor motion of the Earth. The forth-order Runge Kutta method is used to solve the Newton’s equation. The numerical results show that the prediction error of the satellites positions in one day can be reduced from ten of kilometers to ten or hundreds of meters after the perturbations being included. The designed prediction successfully predict the positions of GPS satellites very close to the actual positions.
參考文獻
延伸閱讀
- 黃子銘（2011）。GPS衛星軌道預測方法之研究〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2011.10117
- 羅逢源（1998）。GPS全球定位系統之時間問題研究。海運研究學刊，(5)，31-52。https://doi.org/10.7093/MRJ.199804.0031
- 林老生（2009）。GPS精密單點定位在地籍測量之應用。臺灣土地研究，12(2)，1-25。https://doi.org/10.6677/JTLR.200911_12(2).0001
- 陳詩經（1992）。衛星定位系統。船舶科技，(9)，93-101。https://doi.org/10.30037/MT.199204.0010
- 陳志偉（2005）。Positioning Algorithm for Insufficient GPS Satellites〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2005.02988