利用低軌衛星負載之定軌資料測定高精度之軌道及地球位模式

Abstract

本文主要的內容：從衛星定軌資料的前期處理、各座標轉換資料庫的建立、軌道積分參數與條件的設定，GEODYN II軟體積分計算，線性軌道理論數學關係式與程式的建立，到各項實例（如中華一、三號衛星、CHAMP）的應用等。 本文先從衛星運動方程與定軌問題的認識著手，驗證自行開發的座標轉換程式計算，與OASYS積分軟體相較，座標值經由程式在地固（CTS）與慣性（CIS）框架之間的轉換，其各軸最大誤差約在5、6公尺範圍以內。本文並對GEODYN軟體應用從事深入探討，同時藉由對該軟體之應用，建立各項星曆資料庫及積分參數的設定，以此為基礎，實際對衛星定軌數據做程序處理（如一號衛星的range rate 資料、GPS資料和 CHAMP模擬資料等）。同時提出推論：如以都卜勒資料測定中華一號衛星軌道時，推論中華一號衛星之距離變化率觀測中誤差應該約在1 cm 等級，而本研究計算求得中華一號衛星軌道位置及速度之精度為35.17m和3.76 cm 上下。 本文利用Kaula(1966)之線性軌道理論及平差理論，以先前處理過之人造衛星定軌數據，求得衛星之位置擾動，再由其位置擾動反推求得地球重力位之球諧係數差值，從事各項案例的試驗：如計算中華一號衛星的range rate 資料、GPS資料在徑向、沿軌跡方向、橫向三方向擾動分量，發現其最大最小值，與設定的最大階數成正比，且在橫向方向的擾動分量，震幅幅度最大；沿軌跡方向的擾動，圖形變化最激烈。如一年份之一號GPS資料分兩部分處理，一為原始狀態，一為以OSU91A地位模式等擾動力為改正考量，求出的軌道積分資料，兩者經由線性軌道理論的計算，正可求出相對於OSU91A球諧係數的差值，由此差值與各月份繪製的圖表，正可研判重力球諧係數之時間變化。如對分組CHAMP模擬資料試驗，利用線性軌道理論推導之估算係數與EGM96係數(設為真值)相較，計算兩組係數展開至各階繪製之大地起伏網格差之RMS值，以驗證該軌道理論之精度及可行性。如以Kaula 的解析理論推導中華三號衛星之地位球諧係數，利用EGM96球諧係數分析大地位模式對於三號400公里與800公里兩個時期之軌道誤差。三分量的誤差皆以沿軌跡方向最大，徑向次之，而橫向方向最小，其量級主要受衛星高度影響，在總誤差量上，RMS值則分別為64.091公尺與1.691公尺，誤差量的大小亦與高度成反比關係。 本文之貢獻歸納成以下幾點： 一、實際對低軌衛星之定軌資料作程序處理。 二、建立球諧函數與衛星軌道參數之數學觀測方程式，並由其方程式推導求得估算之係數，作為日後改進地球重力場的參考。 三、則是將此觀測方程式實際應用於各項案例試驗，驗證線性軌道理論的可行性。

This work includes preparing tracking data of satellite , establishing coordinate transformation database, setting up orbit integral parameters, experimenting with GEODYN II software, writing linear orbit theory programs and testing various cases ( ROCSAT-1, ROCSAT-3 and CHAMP ) in gravity recovery. This work primarily investigates the theory of equations of motion ( EOM ) and orbit determination. A set of programs are applied to coordinate transformation between CTS ( conventional inertial system ) and CIS ( conventional terrestrial system ). Compared with the result from OASYS software, the largest differences are about 5-6m . Then, the work studies the structure of the NASA/GSFC orbit determination software-- GEODYN II, and use this software as a basis to process satellite tracking data and to determine orbits of various satellites. For three-day arc, the result of the solutions indicates that the accuracy of ROCSAT-1 of range rate is about 1 cm . For orbit passes near Taiwan, the RMS discrepancies at one-day overlapping arcs are 35.17m and 3.76 cm , which are about the standard errors of ROCSAT-1 orbit determined with range rate. The orbit perturbation theory of Kaula (1966) was used to derive an approximate analytical formula for near circular orbit and the order-zero formula which is suitable for assessing perturbation in the radial, along-track and cross-track directions. With this theory, we experiment with different cases of gravity recovery and tests; for example, computing perturbation components in the radial, along-track and cross-track directions, distinguishing time variation of geopotential coefficients, exploring gravity field ( geoid ) determination from orbit perturbations and using linear theory to estimate geopotential model error. The RMS orbit errors due to the EGM96 model error are estimated to be 64.091m for ROCSAT-3 at a 400-km altitude, and 1.691m for ROCSAT-3 at a 800-km altitude, respectively. In conclusion, the work contributes to: (1) Practically processing the tracking data of low-earth-orbiting satellites ( range rate and GPS data of ROCSAT-1 and simulated data of CHAMP et al.). (2) Establishing the relationship of the geopotential coefficients and satellite orbit parameters. (3) Applying the linear orbit theory to various cases.