人造衛星或天體之軌道狀態 (orbital state)定義為該物體在某時間點的位置速度向量或是軌道參數 (orbit elements)。在知道某衛星的初始狀態 (initial state)後，便可運用軌道推算器 (orbit propagator)來推算該衛星在未來的軌道狀態，也因此其成為人造衛星星載導航功能的重要元件。軌道推算器之演算需考慮到簡化二體運動 (Keplerian)，以及在真實太空環境出現的其他受力，如：地球重力場分布不均、空氣阻力、三體重力場、太陽輻射壓力等。前述非克卜勒受力統稱為軌道擾動 (orbit perturbations)，會導致衛星實際的軌跡偏離理想的克卜勒軌道。 軌道推算器的選擇與設計需考量到準確度與運算效率兩種對立因素。軌道推算器若以數值積分的方式解衛星的運動方程式，便可以較準確的方式模擬軌道擾動之影響，但與解析解軌道推算器相比同時增加了所需計算資源與時間。本論文將探討以MATLAB為基礎自製之UPOP (UPperair Orbit Propagator)數值解軌道推算器：由最初始的座標轉換問題、積分器誤差容忍度乃至於受力模型應用，並與福衛五號之原始飛行資料進行比對。旨在建立一種於一週內無軌道測定 (orbit determination)資料輸入最終推算誤差仍能小於10公里之軌道推算器。 ;The orbital state of the satellite or celestial body is defined as its position and velocity vectors or orbit elements during a specific epoch. After knowing the initial state of the satellite, we can use an orbit propagator to propagate the future ephemeris of the satellite, which makes it an important function inside the navigation filter of an artificial satellite. The algorithm of an orbit propagator should consider not only the simplified Keplerian problem but also other forces in the real space environment: e.g. the aspherical gravitational forces from the Earth, drag, third-body effect, solar radiation pressure, etc. The non-Keplerian forces above are called orbit perturbations, which will make the real trajectory of the satellite differ from the ideal Keplerian orbit. One should consider the accuracy and computational efficiency when it comes to the choice and design of an orbit propagator, especially if intended for onboard use. The effect of orbit perturbations can be simulated more accurately using a numerical integration approach, but will cost more computationally compared to the analytical solution. This thesis presents and examines the sensitivities of our self-made, MATLAB-based UPOP (UPperair Orbit Propagator) orbit propagator: from the tasks of coordinate transformations, integrator tolerance, the implementations of force models, and finally compares propagated trajectories with the raw flight data of FORMOSAT-5. Our goal is to create an orbit propagator which has the propagational error less than 10 km after 7-days of propagation without orbit determination data inputs.
