今天，車輛導航系統已經成為一個很受歡迎的產品了，在這些系統裡面，全球定位系統(GPS)和方位推估法(Dead Reckoning; DR)的技術被廣泛地用來提供車輛即時定位和方向判定。本篇論文研究的架構為將一個由兩個GPS天線所組成的GPS指北針和DR感測器整合在一台車子上以便全時都能提供車子的即時位置和方向等資訊供導航系統使用。雖然以GPS為基礎的多天線三維姿態判定系統(three-dimensional attitude determination system)已經被廣泛地研究，特別是在飛機的應用上，不過，對於商用的車輛，基於安裝空間或是建置成本的考量，通常只在車子上安裝兩個GPS天線形成一個單基線向量判定系統(single baseline vector determination system)，這様的系統又被稱為GPS指北針，當這樣的一輛車子在平坦的地面上行駛時，該基線向量(baseline vector)將對應到一個”趨近平面”(quasi-planar)的運動，也就是該基線向量的運動近乎於平面運動但又不完全是平面運動。先前也有一些學者的研究集中在單基線向量判定系統，但是他們的研究結果都有一些限制，那就是該基線向量相對於任意兩個垂直軸必須都有大角度的旋轉或者是該基線向量的運動必須被完全限制在一個平面上。這些研究結果都不太適合於一般陸用車輛的應用。另外，因為GPS衛星所發送的訊號傳送到地球時已經太微弱了，以致於無法通過建築物而被遮蔽，因此，GPS衛星訊號在建築物內是收不到的，在這樣的情況下，GPS虛擬衛星(GPS pseudolite)可以被用來取代GPS衛星的配置並廣播定位訊號供室內車輛的定位和方向判定來使用。相對於GPS衛星而言，虛擬衛星與接收機的距離很近，因此當接收機移動時將產生不同於GPS衛星的幾何運動關係。因此，那些應用在GPS載波相位訊號的車輛定位和方向判定的演算法必須適當的修改以適合建築物內車輛定位和方向判定之應用。
本篇論文的研究集中在移動載波相位定位與GPS指北針之方向判定及其在陸用車輛、室內和磁性羅盤校準的應用。首先，本篇論文將GPS指北針方向判定的問題重新公式化為限制總最小二乘方(Constrained Total Least Square; CTLS)的非線性最佳化問題，並發展一個以牛頓法(Newton’s method)為基礎的數值演算法來疊代計算這個問題的最佳解。電腦數值模擬的結果顯示採用CTLS方法所得到的解其精確度比傳統的最小平方法(Least Square; LS)所得到的解更好。接下來，本篇論文提出一個正規化的限制總最小二乘方法(Regularized Constrained Total Least Square; RCTLS)來處理當GPS指北針被安裝在陸用車輛時其基線向量對應到”趨近平面”運動所產生的惡劣情況(ill-conditioned)現象，這個方法釋放了先前學者對於單基線向量判定系統的研究所做的限制，電腦數值模擬的結果顯示採用RCTLS方法所得到的解其精確度比CTLS和LS所得到的解更好，而且相較之下，RCTLS方法更強韌且收斂速度比CTLS和LS更快。
接下來，本篇論文利用一個室內的GPS虛擬衛星定位系統(GPS pseudolite positioning system)來取代GPS衛星的配置並廣播定位訊號供室內車輛定位與方向判定來使用，並且提出一個室內移動載波相位定位演算法以達成室內精準定位與方向判定，另外也提出一個完整性檢核法則來檢驗估測的載波相位整數周波未定值是否已收斂到真值。
最後，本篇論文提出兩種不同的線上磁性羅盤量測誤差校準方法，一個叫做參數適應演算法(Parameter Adaptive Algorithm; PAA)，另一個叫做函數學習演算法(Functional Learning Algorithm; FLA)，兩種方法均利用GPS指北針所量測到的方向作為校準訊號。PAA透過使用GPS指北針所量測到的方向來估測磁性羅盤量測值的旋轉橢圓模型的參數，當磁偏角很小且磁性羅盤量測誤差可以完全被這些參數描述的時候，PAA校準的方法極其有效，而當磁偏角很大或者當磁性羅盤量測誤差無法透過只調整旋轉橢圓模型的參數來校準的時候，可以改用FLA的方法來校準，FLA校準學習的函數必須具有週期性的特性，而磁性羅盤量測誤差剛好是週期性函數。透過電腦數值模擬和實際實驗的結果顯示兩種演算法均可有效校準磁性羅盤量測誤差且適合被用在商業用途的導航設備並實現即時誤差校準性能。

Today, land-vehicle navigation systems have already become a popular subject. In these systems, GPS and Dead Reckoning (DR) technologies are widely used to determine the vehicle positions and headings for navigation. In this dissertation, integration of a GPS Compass and DR sensors on a vehicle to determine the vehicle positions and headings seamlessly for navigation is considered. Although, three-dimensional GPS-based attitude determination system with multiple GPS antennas onboard has been extensively studied, especially in aircraft applications, however, due to the cost consideration or spaces available on commercial land-vehicles, it is beneficial to use only two antennas mounted on a vehicle forming a single baseline vector (heading) determination system, which is known as GPS Compass. When such a vehicle traveling on flat terrains, the baseline corresponds to a “quasi-planar” motion situation where the baseline motions nearly, but not exactly, confine to a horizontal plane. Some of the prior researches focused on single baseline vector determination system but have the limitations that the baseline must have large-angle rotations about any two arbitrary but perpendicular axes or that the baseline motions need to be exactly confined to a plane. These results are not easily applicable to land-vehicle applications. Furthermore, GPS satellite signals are unavailable indoors since they are too weak to be blockaded by obstacle. In that situation, GPS pseudolites can be used to replace GPS satellite constellation and broadcast ranging signal for indoor positioning and heading determination. Hence, the algorithms for outdoor carrier phase positioning and heading determination should be adequately modified and developed for indoor applications.
The study of this dissertation focuses on the motion-based differential carrier phase positioning, GPS Compass heading determination and its applications to land-vehicles, indoors and magnetic compass calibration. First, the GPS Compass heading determination problem is properly reformulated as Constrained Total Least Square (CTLS) nonlinear optimization problem and a numerical solution algorithm based on Newton’s method is developed to compute the solution iteratively. The accuracy of the CTLS solution is shown to be better than that of the conventional Least Square (LS) solution. Next, a modified CTLS approach based on Tikhonov’s regularization, which is called Regularized CTLS (RCTLS) approach, is proposed to address the ill-conditioned problem occurred in land-vehicle applications. This approach releases the limitations of the prior researches on single baseline vector determination. The results show that the accuracy of RCTLS solution is better than that of CTLS and LS solution. Moreover, the approach is more robust and converges at a faster rate than CTLS and LS approach.
Following, an indoor pseudolite positioning system is introduced to replace GPS constellation in a space where GPS satellite signals are unavailable and broadcast ranging signals. A motion-based indoor carrier phase positioning algorithm is proposed to achieve accurate positioning and heading determination indoors. Also, a suitable integrity check criterion is proposed to determine when the estimated ambiguity values have converged to the true values.
Finally, two different online magnetic compass calibration methods, one based on the Parameter Adaptation Algorithm (PAA) and the other based on the Functional Learning Algorithm (FLA), are developed to achieve online self-calibration function for a flux-gate compass using GPS heading as reference signals. PAA estimates parameters of the compass magnetic ellipse by using GPS headings as references, and it is extremely effective when compass errors can be modeled by these parameters and the magnetic declination is small. In the case when the magnetic declination is large or when the compass are subjected to non-parameterized errors and cannot be calibrated by adjusting the parameters of the rotated ellipse model only, FLA can be used instead due to it only requires the compass bias function to be periodical. Both algorithms are shown to be suitable in commercial navigation devices and can be implemented in real time.

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