具有督卜勒效應補償之GPS追蹤迴路控制器設計與分析

Abstract

本論文先對全球衛星定位系統作一個概略的敘述，接著介紹系統中接收機處理信號的流程，描述各個步驟的分工與合作狀況，再針對處理流程中的信號追蹤步驟加以討論，最後設計一個追蹤迴路控制器去完成整個信號追蹤的過程。 信號追蹤的過程中，首先是加上一個督卜勒效應補償器，讓衛星信號在太空中傳遞時受到督卜勒效應的影響減小，以方便後續處理衛星信號中電碼相位漂移的部份。經過督卜勒補償之後將信號分段，分成長度一到二十個毫秒不等的訊框與本地產生之不同延遲的C/A碼複製版本作相關係數的運算。每個訊框的運算結果中，將最高相關係數絕對值對應的相位其延遲量記為此訊框所對應的相位漂移。在每一段時間中，將訊號切割成數十到數百個訊框並作上述相位判定的工作之後，可以得到相位漂移的特徵，也就是相位會隨著時間慢慢改變。而依照相位漂移與督卜勒效應的關係，可以用找出相位漂移所對應的最小方差直線以求出此時的督卜勒效應的估計值，以利進行下一次追蹤迴路。 最後，本論文分析了本追蹤迴路在選取不同訊框長度時，對於雜訊強度的承受度。在整理六種不同訊框長度對應的雜訊承受極限後，得出一個可以概估兩者關係的式子，並且探討其意義。最後也對於不同訊框長度下，所需要的計算量作一個比較。

This thesis starts by making a brief description about the Global Positioning System (GPS), and introduces how the signal processing task in GPS receivers is divided into sub-tasks and accomplished as a whole. Then, the tracking loop in the GPS signal processing sub-system is particularly addressed. Finally, a tracking loop controller is designed specifically for the signal processing purpose. In the tracking loop, a Doppler effect compensator is added first to suppress the Doppler effect on signals transmitting in the outer space. This makes it easier to deal with the signals subsequently, such as the phase shift of C/A code in the satellite signal. The step taken after Doppler compensation is to divide a signal into frames with different lengths, from 1 to 20 milliseconds, and to compute the correlation coefficients between frames and locally generated C/A code copies with different phase delays. In every computation result, the phase shift is recorded according to the highest absolute value of correlation coefficient, so that the trace of phase shift can be obtained, which represents phase changes as time passing. Based on the relationship between code phase shift and Doppler effect, the estimated value of Doppler effect can be counted by finding the least-square line from the code phase shift and time, and can be used in tracking loop for the next iteration. The thesis finishes with the analysis of noise margin using different frame lengths. After summarizing the relation between all six kinds of frame length and noise margin, an equation can be obtained to estimate one with the other. Besides, the total calculation effort with different frame length is discussed.