GLONASS衛星軌道演算及其定位方法

Abstract

全球導航衛星系統(Global Navigation Satellites System; GNSS)乃泛指所有以衛星為基礎之導航系統。目前發展較為成熟之導航衛星系統包括美國的GPS(Global Positioning System)以及俄羅斯的GLONASS(Global Navigation Satellites System)。 隨著科技的演進，不同領域的應用對於導航與定位之精度需求越加精細。提升定位精度最直接之方法即為提升可視衛星數目，而整合GPS 及GLONASS 可達此目的。由於GPS 及GLONASS 兩系統不可完全兼容，在整合前需對各別系統有相當程度之了解。因此，吾人對GLONASS 進行研究，嘗試運用該系統作定位，並觀察其結果。 在本文中，吾人從能量之觀點推導GLONASS 衛星軌道模型，找出衛星運動方程式，並將該系統之廣播星曆代入求解，藉龍格-庫塔數值積分法取得準確之衛星位置。其後，利用衛星位置與偽距於偽距觀測量定位法進行定位。偽距觀測量定位法中，需修正電離層延遲誤差，才能使定位精度提高，而GLONASS 並無廣播電離層模型之參數予以修正誤差，故吾人將GPS 廣播之電離層模型參數應用於GLONASS 定位之上。最後，引入高度限制條件式於定位方程中，而定位精度與穩定度均有相當改善。 本文除顯示運用GLONASS 定位之結果外，也詳細描述整個定位過程。從接收到廣播星曆開始直至定位完成，期間計算所需注意之部分皆於本文當中。此舉將便於未來相關應用。

In general, GNSS (Global Navigation Satellites System) is described as the satellites-based navigation system. Presently, the available systems include GPS (Global Positioning system) of United States and GLONASS (Global Navigation Satellites System) of Russia. With more available satellites, the accuracy of positioning could become more precise, and the combination of GPS and GLONASS could easily reach it. Although GPS and GLONASS are similar to each other, the both systems are not entirely compatible. Before combining these two systems, it is important to be familiar with each system in great details. Therefore, we made a study of GLONASS and attempted to specify the position by means of only GLONASS. In this paper, we determine the satellite position through GLONASS ephemeris by using Runge-Kutta Method, and then obtain the receiver position with pseudorange measurement. To correct ionosphere delays on GLONASS satellites, we applied Klobuchar Model with little modification. Afterward, we also applied altitude-hold constraint to positioning equations, and consequently, the results of positioning point have become more precise and stable. It shall be noted that we not only demonstrated the results but also elaborated on the whole process of positioning. This will benefit the future studies and some relative applications.