模擬中華三號追蹤資料精密定軌及測定重力場

Abstract

本研究係利用低軌衛星精密定軌法中的兩步法進行參數估算，其基本原理為衛星運動方程加上測量平差方法。目前考慮地球非球體引力位擾動、大氣阻力擾動、太陽輻射壓擾動、經驗公式等四項擾動模式進行變數方程的程式編譯求解。以EGM96大地位模式為真值、OSU91A大地位模式為計算初值，分別針對五階、十階大地位模式進行求解，期能回復EGM96模式。目前計算結果，一天五階模式之相對誤差為5×10-7、三天五階模式之相對誤差為3×10-7、一天十階模式之相對誤差為1.5×10-5、三天十階模式之相對誤差為6.6×10-6。在軌道回復部分，當設定衛星軌道傾角i為90度，確保衛星軌道資料幾何條件沒有問題情況下，此時三天五階模式衛星軌道誤差RMS值約為0.16cm、一天十階模式衛星軌道誤差RMS值約為0.55cm，且軌道誤差不隨時間增加而發散。若以華衛三號軌道設計（衛星軌道傾角i為72度），衛星觀測資料無法有效覆蓋全球的先天性缺陷狀況下，則必須加入約制條件以克服球諧係數法方程式矩陣產生奇異，此時一天五階模式衛星軌道誤差RMS值約為2cm、三天五階模式衛星軌道誤差RMS值約為9cm、一天十階模式衛星軌道誤差RMS值約為1.9m、三天十階模式衛星軌道誤差約為2.1m，誤差均隨時間增加而發散。未來工作將針對程式精度提昇以及程式執行效率進行修改，期能發展出一套國人自行開發之高精度衛星定軌軟體。

In this study, a ’two-step’ approach is used to compute precise orbits and estimate parameters of satellite perturbing forces. The approach is based on satellite equations of motion (EOM) and parameter estimation theory. The perturbing forces under consideration are the earth’s non-sphericity, air-drag, solar radiation and empirical accelerations. Programs for precise orbit and gravity determinations in this work are coded in Fortran 90. In the experiments, the EGM96 geopotential model is regarded as the true field, and the OSU91A geopotential model as the initial field in the parameter estimations. In terms of the accuracy of the recovered geopotential coefficients, the results from the simulations show that: (1) in a degree-5 solution with one day of tracking data the RMS relative error (RRE) is 5×10-7, (2) in a degree-5 solution with three days of tracking data the RRE is 3×10-7, (3) in a degree-10 solution with one day of tracking data, the RRE is 1.5×10-5, and (4) in a degree-10 solution with three days of tracking data the RRE is 6.6×10-6. To assess the accuracy of the computed satellite orbits, we experimented with two different orbital inclinations. The cases with a 90°-inclination are to validate the computer programs, and the results show that: (1) in a degree-5 solution with three days of tracking data the RMS orbit error (ROE) is 0.16 cm, (2) in a degree-10 with one day of tracking data the ROE is 0.55cm. The cases with a 72°-inclination are for the ROCSAT3/COSMIC mission, and the results show that: (1) in a degree-5 solution with one day of tracking data the ROE is 2 cm, (2) in a degree-5 solution with three days of tracking data the ROE is 9 cm, (3) in a degree-10 solution with one day of tracking data the ROE is 1.9 m, and (4) in a degree-10 solution with three days of tracking data the ROE is 2.1 m. Future work will be to improve the accuracy and precision of the computer package in precise orbit and gravity determinations.