在本篇論文中，波束成型 (beamforming) 輔助之合作式定位被提出，用於修正低軌道衛星 (LEO satellites) 之衛星定位結果。在波束成型中，具有單一方向性之主波束可以用於角度估計。一個有限大小的波束候選 (beam candidate) 集合由多個波束組成，也被稱作碼本 (code book)。每一個波束候選代表一個特定的角度，稱作尋找表 (lookup table)。經過波束搜索 (beam search) 後，根據尋找表，波束候選對應的角度可以被找出。此外，一個用於投影估計的角度在定位座標系上的座標系被定義。根據估計的角度和參考點的位置 (精確的位置或是有誤差的衛星定位結果) ，可以計算估計點的位置，稱作波束成型輔助之合作式定位。其中，角度和位置等資訊根據全等三角形的定義結合。由於衛星的分布位置會影響定位的效能 (誤差傳播效應)，量測誤差必須由低軌衛星和接收器的位置來產生。低軌衛星和接收器位置的等效距離 (考量大氣層和時鐘誤差等因素) 被稱作偽距 (pseudorange)。一種實際被使用的低軌衛星的軌道系統被應用於本篇論文的模擬。

為了評估合作式定位和角度估計的效能，一個車輛定位的情境被設定。根據模擬結果，本篇論文提出的波束成型方法可支持低訊雜比 (low SNR, 0dB) 的情況。合作式定位中需要的參數 (例如迭代次數) 由數值模擬得出，其結果會被波束成型中的波束候選和偽距的量測誤差影響。模擬條件考慮最差的情況，只有衛星定位的位置資訊被使用 (所有定位結果皆有誤差)。如果參考點為正確位置，效能會更好。因為波束成型的解析度限制，合作式定位只有在量測誤差的變異數很大時才會被開啟。和衛星定位座標相比，波束成型的結果為更可靠的資訊 (從比較近的距離量測)，因此將波束成型的結果結合衛星定位的座標可以達到修正誤差的效果。從模擬的結果可以看出如果合作式定位被使用，定位誤差可以被降低。在本篇論文中，量測雜訊 (measurement noise) 代表偽距的量測雜訊，量測誤差 (measurement error) 代表定位結果和正確位置的差距。

In this thesis, a beamforming assisted cooperative positioning is proposed to correct result of LEO (Low Earth Orbit) satellite positioning. Beamforming with directional beam can be used to estimate angle. A finite set of beam candidates is composed of directional beams. Each beam candidate represents a specific angle, called lookup table. After beam search, angle is estimated by finding angle according to beam candidate in lookup table. A frame is defined to map estimated angle to coordinate of positioning. Based on estimated angle and position of reference points, position can be estimated, called beamforming assisted cooperative positioning. In proposed method, information is combined according to definition of congruent triangle. Because distribution of satellite position affects performance of positioning (error propagation), measurement error has to be generated by position of LEO satellites and receiver. A real orbit system of LEO satellites is used for simulation in the thesis.
To evaluate performance of proposed beamforming assisted cooperative positioning, a scenario of vehicular localization is set. According to simulation result, low SNR (0dB) is supported by proposed method of angle estimation. Parameters of cooperative positioning such as number of iteration are determined by numerical simulation, which are related to beam candidates of beamforming and variance of measurement noise (for pseudorange). Owing to resolution of beamforming, cooperative positioning is switched on when variance of measurement noise is large. Comparing to satellite positioning, result of beamforming is more reliable (measured in closer range). Therefore, proposed beamforming assisted cooperative positioning can improve performance of satellite positioning. It is shown that error of positioning is reduced if cooperative positioning is applied. Note that term measurement noise is for measurement of pseudorange and term measurement error is for result of positioning in this thesis.

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