Evaluate and Design the Method of A Solution to the Ill-conditioned GPS Positioning Problem

一般GPS接收機定位時，需要至少能夠觀測到四顆衛星。但若環境高樓遮蔽，造成衛星訊號不佳的問題，使得最低需求無法滿足，則可能造成接收機無法使用的情況。 為解決此病態定位問題，本文使用多種方式，諸如高度固定輔助法、鐘差預測法與虛擬距離預估器等，解決病態定位下的問題。再進一步精準的定位，我們考慮最小平方法、卡爾曼濾波器、約束濾波器等，並用最好的方式求得定位解。 不同衛星數目的情況下，使用不同方式處理，有使用的時間限制與約束條件；因此除了整合各種演算法，成功完成病態定位外；再利用模擬器設計靜態與動態實驗，針對衛星不足情況發生時，評估在容忍誤差範圍內，各方法可使用的時間。For normal positioning of using GPS receiver, it is required that there are at least four GPS satellites in view. However, due to the blockage of the tall buildings and receive unhealthy satellites signal, it is sometimes not able to reach that minimum requirement so that the operation of GPS receiver may be interrupted.n dealing with such ill-conditioned problems, different algorithm such as altitude-hold method, clock bias predictor and pseudorange predictor are used in this thesis. In order to attain more accurate positioning, we consider different methods to find the best positioning solution : LS(Least Squares), WLS(Weighted Least Squared), KF(Kalman Filter), RKF(Robust Kalman Fitler) and CF(Constraint Filtering).or different number of visible satellites, the applicability of different methods depends on the capability of the adopted method. In addition to solving the ill-conditioned problem, static and dynamic experiments were conducted by using the simulator SimGen to evaluate the duration of usage of various schemes for acceptable errors.致謝……………………………………………………………………....i要………………………………………………………………...…....iibstract…………………………………………………………….…..iii錄……………………………………………………………………..iv表目錄……………………………………………………………......vii一章 緒論………………………………………………………….….1.1內容簡介與研究動機………………………………………….………1.2文獻回顧…………………………………………………………….…2.3論文架構……………………………………………………….………3二章 GPS定位法簡介………………………………………….…….4.1座標系統簡介…………………………………………………….……4.1.1直角座標系統…………………………………………….……4.1.2地理座標系統………………………………………………….5.1.3座標系統轉換………………………………………………….6.2 GPS定位原理…………………………………………………………8.2.1虛擬距離觀測量表示式…………………………….…………9.3最小平方法LS(Least squares method) …………………………..…..11.4 權重之最小平方法WLS(Weighted least squares)…………..…....…12.5 卡爾曼濾波器KF(Kalman filter)……………………………………132.5.1方程式………………………………………………………...132.5.2 狀態方程式模型……………………………………………..14.6 強健濾波器RKF(Robust Kalman filter) ……………………………17.7 約束濾波器CF(Constraint filtering) ………………………………..192.7.1 方程式………………………………………………………..19 2.7.2 方程式轉換求解……………………………………………..20三章 衛星不足時之定位演算法……………………………………23.1 高度固定輔助定位法………………………………………………..233.1.1 實驗結果……………………………………………………..27.2 高度固定輔助定位與鐘差預測法…………………………………..29.2.1 實驗結果………………………………………………..……31.3 虛擬距離預估器……………………………………………………..33.3.1 實驗結果……………………………………………………..35四章 方法設計與可靠性評估………………………………………37.1精度因子分析………………………………………………………...37.2 定位方法比較………………………………………………………..40.2.1 WLS與LS……………………………………………………40.2.2 KF與WLS……………………………………………………42.2.3 RKF、KF與WLS……………………………………………44.2.4 CF與RKF……………………………………………………46 4.3 可靠性評估…………………………………………………………..47 4.4 架構與流程圖………………………………………………………..49 4.4.1 虛擬距離判斷器……………………………………………..49 4.4.2 虛擬距離預估器……………………………………………..50 4.4.3 定位…………………………………………………………..51 4.4.4 實際路測(I) ………………………………………………….53.4.5 實際路測(II) …………………………………………………54.4.6 實際路測(III) ………………………………………………..55.4.7 實際路測(IV) ………………………………………………..57五章 結論與未來工作………………………………………………59.1 結論…………………………………………………………………...59.2 未來工作……………………………………………………………...60考文獻…………………………………………………………………………...6