在飛行中如何獲得精確的姿態資訊對於飛機的導航與控制是非常重要的，本論文中研究以實驗室自行設計的微機電飛行資訊量測系統為基礎的姿態計算方法，本研究提出了三種基於四元數的非線性濾波器來整合導航四元數與重力場分量這兩種飛行姿態計算方法，包括擴展式卡曼濾波器、無跡卡曼濾波器以及粒子濾波器。
該演算法利用導航四元數計算姿態的演算法中四個元素的更新矩陣作為濾波器的動態模型，以四個元素作為濾波器的狀態。將由重力場分量以及由電子羅盤得到的姿態角視為濾波器的量測，另外，將導航四元數法中四個元素的約束條件視為完美的量測，並加入到濾波器的設計中。並且詳細的推導建立了量測訊號的隨時間變化的雜訊變異數之近似值。該演算法成功地通過一組由本實驗室自行設計的姿態量測系統所收集的飛行測試數據的驗證。

Obtaining precise attitude information is essential for aircraft navigation and control. This thesis presents the results of the attitude determination using an in-house designed low-cost MEMS-based flight information measurement unit. This study proposes three quaterni-on-based nonlinear filters to integrate the traditional quaternion and gravitational force de-composition methods for attitude determination algorithm, include extended Kalman filter, unscented Kalman filter, and particle filter. The proposed nonlinear filter utilizes the evolu-tion of the four elements in the quaternion method for attitude determination as the dynamic model, with the four elements as the states of the filter. The attitude angles obtained from the gravity computations and from the electronic magnetic sensors are regarded as the measurement of the filter. The immeasurable gravity accelerations are deduced from the outputs of the three axes accelerometers, the relative accelerations, and the accelerations due to body rotation. The constraint of the four elements of the quaternion method is treated as a perfect measurement and is integrated into the filter computation. Approximations of the time-varying noise variances of the measured signals are discussed and presented with de-tails through Taylor series expansions. The algorithm is intuitive, easy to implement, and reliable for long-term high dynamic maneuvers. Moreover, a set of flight test data is utilized to verify the success and practicality of the proposed algorithm and the filter design.

目錄
目錄	iii
圖目錄	vii
符號定義	x
第一章 緒論	1
第二章 飛行資訊量測組件	7
第三章 卡曼濾波器	10
3.1卡曼濾波器演算法	10
3.2離散卡曼濾波器	14
第四章 飛行姿態角計算	17
4.1 航向角計算	18
4.2 重力場三軸分量計算姿態角	20
4.3 透過四元數計算姿態角	25
4.4 卡曼濾波器計算姿態角	29
4.5 地面實驗室測試	30
第五章 雜訊特性	34
5.1 系統雜訊	34
5.2 量測雜訊	35
第六章 擴展式卡曼濾波器設計	40
6.1 應用EKF於姿態計算	41
6.2 地面實驗室測試	46
6.3 實際飛行數據測試	47
6.3.1 爬升(1420秒～1430秒)	50
6.3.2 下降(2340秒～2380秒)	51
6.3.3 平飛(2745秒～2755秒)	52
6.3.4 左轉彎(1106秒～1130秒)	53
6.3.5 右轉彎(2600秒～2675秒)	54
6.3.6 S型轉彎(2810秒～2900秒)	55
6.4 應用EKF於姿態計算2	56
6.5 實際飛行數據測試2	59
6.5.1 爬升(1420秒～1430秒)	60
6.5.2 下降(2340秒～2380秒)	61
6.5.3 平飛(2745秒～2755秒)	62
6.5.4 左轉彎(1106秒～1130秒)	63
6.5.5 右轉彎(2600秒～2675秒)	64
6.5.6 S型轉彎(2810秒～2900秒)	65
第七章 無跡卡曼濾波器設計	67
7.1 無跡變換	67
7.2 應用UKF於姿態計算	69
7.3 地面實驗室測試	73
7.4 實際飛行數據測試	74
7.4.1 爬升(1420秒～1430秒)	76
7.4.2 下降(2340秒～2380秒)	77
7.4.3 平飛(2745秒～2755秒)	78
7.4.4 左轉彎(1106秒～1130秒)	79
7.4.5 右轉彎(2600秒～2675秒)	80
7.4.6 S型轉彎(2810秒～2900秒)	81
第八章 粒子濾波器設計	83
8.1 貝式狀態估測	84
8.2 粒子濾波器(The particle filter)	88
8.3 應用粒子濾波器於姿態計算	92
8.4 地面實驗室測試	95
8.5 實際飛行數據測試	96
8.5.1 爬升(1420秒～1430秒)	98
8.5.2 下降(2340秒～2380秒)	99
8.5.3 平飛(2745秒～2755秒)	100
8.5.4 左轉彎(1106秒～1130秒)	101
8.5.5 右轉彎(2600秒～2675秒)	102
8.5.6 S型轉彎(2810秒～2900秒)	103
第九章 結論與未來展望	106
參考文獻	107
附錄一	113
 
圖目錄
圖2.1 飛行資訊量測組件系統架構圖(1)	7
圖2.2 飛行資訊量測組件系統架構圖(2)	9
圖2.3 慣性量測組件(a)與電子羅盤系統(b)	9
圖3.1 狀態估測及其誤差協方差時間關係	15
圖3.2 卡曼濾波器處理流程圖	16
圖4.1 歐拉角 [25]	17
圖4.2 地球磁場分量	18
圖4.3 航向角處理流程圖	20
圖4.4 重力場分量	21
圖4.5 由旋轉角速度造成的速度變化之分量	23
圖4.6 透過卡曼濾波器來計算姿態角流程圖	30
圖4.7 實驗平台架設圖	31
圖4.8 透過重力場分量計算之姿態	32
圖4.9 透過四元數法計算之姿態	33
圖6.1 EKF流程圖	41
圖6.2 應用EKF於姿態計算之流程圖	46
圖6.3 應用EKF於姿態計算之流程圖	47
圖6.4 飛行測試所用之輕航機	48
圖6.5 完整的飛行軌跡	49
圖6.6 姿態角變化	49
圖6.7 姿態角變化(1420秒～1430秒)	50
圖6.8 姿態角變化(2340秒～2380秒)	51
圖6.9 姿態角變化(2745秒～2755秒)	52
圖6.10 姿態角變化(1116秒～1140秒)	53
圖6.11 姿態角變化(2610秒～2680秒)	54
圖6.12 姿態角變化(2820秒～2910秒)	55
圖6.13 應用EKF於姿態計算之流程圖2	58
圖6.14 姿態角變化	59
圖6.15 姿態角變化(1420秒～1430秒)	60
圖6.16 姿態角變化(2340秒～2380秒)	61
圖6.17 姿態角變化(2745秒～2755秒)	62
圖6.18 姿態角變化(1106秒～1130秒)	63
圖6.19 姿態角變化(2600秒～2675秒)	64
圖6.20 姿態角變化(2810秒～2900秒)	65
圖7.1 UKF流程圖	69
圖7.2 應用UKF於姿態計算之流程圖	73
圖7.3 應用UKF於姿態計算之結果	74
圖7.4 姿態角變化	75
圖7.5 姿態角變化(1420秒～1430秒)	76
圖7.6 姿態角變化(2340秒～2380秒)	77
圖7.7 姿態角變化(2745秒～2755秒)	78
圖7.8 姿態角變化(1116秒～1140秒)	79
圖7.9 姿態角變化(2600秒～2675秒)	80
圖7.10 姿態角變化(2810秒～2900秒)	81
圖8.1 粒子濾波器流程圖	91
圖8.2 應用PF於姿態計算流程圖	95
圖8.3 應用PF於姿態計算之流程圖	96
圖8.4 姿態角變化	97
圖8.5 姿態角變化(1420秒～1430秒)	98
圖8.6 姿態角變化(2340秒～2380秒)	99
圖8.7 姿態角變化(2745秒～2755秒)	100
圖8.8 姿態角變化(1106秒～1130秒)	101
圖8.9 姿態角變化(2600秒～2675秒)	102
圖8.10 姿態角變化(2810秒～2900秒)	103

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