從過去十幾年前開始，使用多個全球定位系統天線判定載具姿態一直是個熱門的研究題目，而許多關於多天線全球定位系統的研究都展示了豐碩的成果。然而，將全球定位系統姿態判定運用於導航系統上仍然是一個具有挑戰性的題目。問題的關鍵在於在某些特殊的情況，如全球定位系統衛星訊號遭受遮蔽或是電離層閃爍等情況下，全球定位系統姿態判定系可能會輸出誤差很大的姿態估計值。如果導航系統使用了這些姿態估計值，導航系統的效能可能會大幅降低甚至引發災難性的後果。全球定位姿態系統姿態估計值誤差是解決這個問題的關鍵。如果能夠計算出可靠的姿態估計值誤差上限，導航系統則以針對誤差上限為依據做出適當的反應。一般而言，最小平方法中觀測量的數目多於未知數的數目。這些觀測量的一致性可以做為全球定位姿態系統姿態估計值品質的依據。接收器自主完整性監測就是一個檢查觀測量一致性的重要應用。接收器自主完整性監測計算出全球定位系統水平與垂直定位誤差保護極限以做為水平與垂直誤差上限提供不同的導航系統使用。因此，本篇論文希望將接收器自主完整性監測應用於全球定位姿態判定系統上並計算出對應的姿態保護極限。本篇論文將會介紹最小平方法全球定位姿態判定與接收器自主完整性監測的基本理論，說明如何將接收器自主完整性監測方法應用於小平方法全球定位姿態判定上並且以實驗資料來驗證計算出的姿態保護極限。

Attitude determination using multiple Global Positioning System (GPS) has been investigated extensively in the past decades and has demonstrated its capability in several researches. However, it is still challenging to incorporate multiple antennas GPS attitude determination system into real navigation systems. The problem is that bad attitude estimates might result from, for example, signal blockage of ionosphere scintillation for multiple antennas GPS attitude determination. If the bad attitude estimates are used, degradation of navigation system performance might result. Lack of reliability makes GPS attitude determination impractical and dangerous for safety of life application. One possible solution to this problem is to prevent navigation system from use of the multiple antennas GPS attitude estimates when they are not of sufficient quality or to take proper actions. It is thus crucial for navigation systems to identify the bad attitude estimates or to know a reliable error upper bound. Detection of the bad attitude estimate is possible for least squares estimation because there are generally more measurements than required. Consistency of these redundant measurements can be checked and the goodness of the estimate is judged. An important application of this consistency check is the Receiver Autonomous Integrity Monitoring (RAIM). In addition to consistency check, RAIM further calculates vertical and horizontal protection levels as confidence bounds on the vertical and horizontal errors. In this thesis, a method is proposed to calculate protection levels for the least squares GPS attitude determination. The protection levels will serve the upper bound on the attitude errors. The analytical background of multiple antennas GPS attitude determination and RAIM are also introduced. Data is collected and the proposed method is applied to validate the effectiveness of the proposed protection level calculation method.

[1] M. Abramowitz, and I. Stegun, Handbook of Mathematical Function, Dover Pub. Inc., 1992.
[2] S. Alban, Design and Performance of a Robust GPS/INS Attitude System for Automobile Applications, Ph.D. Dissertation, Stanford University, June 2004.
[3] R. G. Brown, “A Baseline GPS RAIM Scheme and a Note on the Equivalence of the Three RAIM Methods,” Navigation, Vol. 37, No. 3. Fall 1992.
[4] C. Cohen, Attitude Determination Using GPS, Ph.D. Dissertation, Stanford University, December 1992.
[5] A. Conway, P. Montgomery, S. Rock, R. Cannon and B. Parkinson, “A New Motion-Based Algorithm for GPS Attitude Integer Resolution,” Navigation, Vol. 43, No. 2, 1996.
[6] M. Dumaine, “High Precision Attitude Using Low Cost GPS Receivers,” Proceedings of the ION GPS-96, September 1996.
[7] P. Enge, T. Walter, S. Pullen, C. Kee, Y-C. Chao and Y-J. Tsai, “Wide Area Augmentation of the Global Positioning System,” Proceedings of the IEEE, Vol. 84, No. 8, 1996.
[8] P. Enge, “Local Area Augmentation of GPS for the Precision Approach of Aircraft,” Proceedings of the IEEE, Vol. 87, No. 1, 1999.
[9] H. Euler, and C. Hill, “An Optimal Ambiguity Resolution Technique for Attitude Determination,” Proceedings of the 1996 IEEE Position Location and Navigation Symposium (PLANS), April 1996.
[10] J. Gautier, GPS/INS Generalized Evaluation Tool (GIGET) for the Design and Testing of Integrated Navigation System, Ph.D. Dissertation, Stanford University, June 2003.
[11] S. Gleasson, D. Gebre-Egziabher, et al, GNSS Applications and Methods, the Artechhouse Press, 2009.
[12] F. van Graas and M. Braasch, “GPS Interferometric Attitude and Heading Determination: Initial Flight Test Results,” Navigation Vol. 38, No. 3, 1991.
[13] D. Knight, “A New Method of Instantaneous Ambiguity Resolution,” Proceedings of the ION GPS-94, September 1994.
[14] P. Misra and P. Enge, Global Positioning System: Signals, Measurements, and Performance, second edition, Ganga-Jamuna Press, 2006.
[15] P. Teunissen, “A New Method for Fast Carrier Ambiguity Estimation,” Proceedings of the IEEE Position, Location and Navigation Symposium (PLANS), April 1994.
[16] T. Walter and P. Enge, “Weighted RAIM for Precision Approach,” Proceedings of ION GPS-95, September 1995.
[17] P. Ward, “The Natural Measurements of a GPS Receiver,” Proceedings of ION 51st Annual Meeting, 1995.