第一代衛星導航系統GPS (Global Positioning System)已成為現今重要導航系統之一，亦廣泛應用於製圖、測量、商業用途及工程科學…等。近年全世界皆致力於發展自主之衛星導航系統，如：歐盟的伽利略衛星導航系统、中國大陸的北斗二代導航衛星系統、日本準天頂衛星系统、印度區域導航衛星系統及星基增強系統…等。因此，多星系衛星導航系統為未來衛星導航系統發展趨勢。本論文發展並應用演算法以探討多星系衛星導航系統之特點。
首先，在導航系統之高精度定位計算方面，一般係利用載波相位之二次差量測方程式，進行載波相位整數未定值求解及基線解算，文中提出特徵分解法作為一整數未定值搜尋方法，經由實際基線解算依計算量及可靠度來評估其性能。此外，下一代衛星導航系統將提供三頻之觀測量，CAR (Cascading Ambiguity Resolution)方法利用線性組合之載波觀測量來解算整數未定值以提升解算效率，且利用模擬之觀測量來評估其效能。
於多星系衛星導航系統之定位求解問題，由於各衛星導航系統之時間不同步，定位求解問題將不只是計算接收器位置，亦須同時計算接收器於各衛星導航系統之時間差。本論文發展一解析方法探討單一星系及多星系衛星導航系統之定位求解問題，在單一星系導航系統定位計算可轉換成二次方程式來解算定位，而多星系衛星導航系統定位計算則可轉換成一組二次方程式或四次方程式來解算，因此，多星系衛星導航系統之定位問題可透過解析方法求解，而二次或四次方程式的係數及判別式正負將決定衛星導航系統解的存在與否。
未來飛航所需之位置、速度和時間訊息將倚賴全球導航衛星系統提供，然而目前單一衛星導航系統無法提供符合需求的精度(accuracy)、整體性(integrity)、妥善率(availability)及持續性(continuity)。藉由發展星基增強系統以提供一完善導航服務，在本論文中，收集實際GPS資料及星基增強系統修正訊息，針對台北飛航情報區的星基增強系統作性能評估，並應用適應性權重方式提升妥善率以改善飛航需求之性能。

The first generation satellite based navigation system, GPS (Global Positioning System), has become one of the most important navigation systems today. GPS is also a useful tool for mapping, land surveying, commerce, and scientific uses. In addition to GPS and GLONASS, several satellite based navigation systems including Europe’s Galileo system, China’s Beidou-2 system, Japan’s QZSS (Quasi-Zenith Satellite System), India’s IRNSS (Indian Regional Navigation Satellite System), and regional Space Based Augmentation Systems (SBASs) are being developed worldwide. As a result, future satellite based navigation system will be a multi-constellation system. In this dissertation, several algorithms will be developed and applied to explore the features of multi-constellation satellite based navigation systems.
In high precision positioning, the linear double difference carrier phase equations are employed for ambiguity resolution and baseline determination. An eigen-decomposition method is proposed to solve the integer least squares problem and several experiments are performed to evaluate the proposed method in terms of computational load and reliability. In addition, a triple frequency linear combination is formulated to the CAR (Cascading Ambiguity Resolution) method for ambiguity resolution. The virtual measurements are also generated to assess the performance of the CAR method.
Since two different constellations may not be time-synchronized, the navigation problem needs to solve the position and the clock bias with respect to each constellation. An analytic approach is developed to investigate the solvability and solutions of the single-constellation and multi-constellation navigation problems. It is shown that the single-constellation navigation problem can be reduced to the solving of a quadratic equation. In contrast, the multi-constellation navigation problem could be transformed as the solving of a set of two simultaneous quadratic equations or a quartic equation. Through the analytic approach, all solutions to the multi-constellation navigation problem are parameterized. In addition, the solvability is governed by the zero-crossover of the leading coefficient and the sign of the discriminant of the quadratic/quartic equation.
Future air navigation will rely mainly on GNSS (Global Navigation Satellite System) for the determination of position, velocity, and time. However, the single-constellation GNSS positioning service falls short of the accuracy, integrity, availability and continuity. SBASs have been developed for enhancing the services to meet aviation requirement. Both GPS and SBAS (MSAS and GAGAN) are collected and assessed in terms of the required navigation performance at different phases of flight. An adaptive weighting strategy is further proposed to meet the PA required navigation performance in Taipei FIR (Flight Information Region).

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