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研究生: 黃敬傑
Huang, Jing-Jie
論文名稱: 具迭代權重式IMU校正與互補濾波航姿系統開發實務驗證
Development and Verification of IWLMA Calibration Method and AHRS Algorithm Based on IMU
指導教授: 彭兆仲
Peng, Chao-Chung
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2018
畢業學年度: 106
語文別: 中文
論文頁數: 93
中文關鍵詞: 慣性量測元件迭代具權重之萊文貝格-馬夸特校正方法互補濾波器之航姿參考系統演算法光流與加速規速度融合演算法
外文關鍵詞: IMU, IWLMA calibration method, Complementary filter based AHRS algorithm, Optical flow and accelerometer velocity fusion algorithm
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  • 近年來微機電系統之慣性測量單元(MENS-IMU)的運用越來越廣泛,IMU被運用於智慧型手機等隨身裝置,也被運用於感知人肢體即時的姿態。為了能更精準估測姿態,校正IMU成為一項不可或缺的程序。然而,校正程序通常在無擾動環境下進行。由於無擾動環境情況的建構困難度較高。因此,在本論文中,考慮到外部環境擾動的校正。提出迭代具權重的萊文貝格-馬夸特方法(Iterative Weighted Levenberg-Marquardt Algorithm, IWLMA)以克服外部環境擾動問題,並透過實際的實驗數據驗證所提出IWLMA方法的適用性。另外,本論文亦提出以9自由度為基底的互補濾器之姿態航向參考系統(Attitude Heading Reference System, AHRS)演算法,互補濾波器演算法相較卡爾曼濾波器演算法需求更少的計算量,因此適合實現於微處理器,所提出AHRS演算法使用四元數來計算載具的姿態,相較於使用尤拉角描述姿態,以四元數描述姿態不具有奇異性問題。根據所估測的姿態資訊,再結合加速規量測的數值進行積分可估測載具速度,並將加速規估測的速度值與光流法模組PX4FLOW所估測的速度值透過速度融合演算法進行資料融合,提升速度估測之正確性。本研究通過設計三軸旋轉平台(Gimbal)驗證所提出AHRS演算法的精度。

    Implementation of low-cost Microelectromechanical Systems Inertia Measurement Unit (MENS-IMU) has been more and more popular over the past few years. Recently, IMU has been used for wide varieties of consumer electronics, including smartphones, smart watches and so on. Under some situations IMU has been also used to detect the gesture of the human limbs. To precisely estimate the motion information, the calibration process of the IMU is indispensable. In general, the calibration procedures are usually conducted under a clean and perturbation free environment. However, such a perfect situations may not always be available. As a result, in this paper, the calibration subject to external perturbation is considered. An iterative weighted Levenberg-Marquardt algorithm (IWLMA) is proposed to cope with the perturbation issue. Experiment data are conducted to verify the proposed IWLMA method under the imperfect situations. The 9 degree of freedom (DOF) complementary filter based attitude heading reference system (AHRS) algorithm method will be introduced. Complementary filter consumes less computation effort than Kalman filter, as a result, it is suitable to implemented on the microprocessor. Quaternion is used in the proposed AHRS algorithm to calculate the attitude of a vehicle, unlike Euler angles, quaternion can describe the attitude of a vehicle without singularity problem. According to the estimated attitude information, the velocity can be calculated by using integration of the data from accelerometer. The estimated velocity from accelerometer and the estimated velocity from optical flow module PX4FLOW will be fused together by using the velocity fusion algorithm, thus improve accuracy of the estimated velocity. Three axis rotational platform (Gimbal) has been designed and built to verify the performance the proposed AHRS algorithm.

    中文摘要 i Extended Abstract ii 誌謝 ix 表目錄 xiii 圖目錄 xiv 第1章、 緒論 1 1.1. 前言 1 1.2. 研究動機 1 1.3. 文獻回顧 1 第2章、 IMU校正 3 2.1. 感測器精度誤差 3 2.2. 微處理器及感測器元件 3 2.2.1. 微處理器 3 2.2.2. 加速規 4 2.2.3. 陀螺儀 4 2.2.4. 磁力計 5 2.3. 感測器誤差數學模型建立 5 2.3.1. 座標系統非正交 5 2.3.2. 位移偏差及比例誤差 7 2.4. 感測器校正步驟 8 2.4.1. 加速規及磁力計校正步驟 8 2.4.2. 陀螺儀校正步驟 9 2.5. 感測器校正硬體 10 2.5.1. 加速規校正硬體 10 2.5.2. 陀螺儀校正硬體 11 2.6. 感測器校正演算法 12 2.6.1. 感測器成本函數建立 12 2.6.2. 萊文貝格-馬夸特方法(LMA) 13 2.7. 具有權重萊文貝格-馬夸特演算法(IWLMA) 14 2.7.1. IWLMA驗證 16 第3章、 互補濾波器之航姿參考系統與位移估測演算法 18 3.1. 航姿參考系統 18 3.2. 座標系統定義 18 3.2.1. 地球座標系統(Earth frame) 18 3.2.2. 地磁當地座標系統(Local magnetic NED frame) 19 3.2.3. 體座標系統 20 3.3. 姿態描述之數學方法 20 3.3.1. 方向餘弦矩陣(DCM) 21 3.3.2. 羅德里格旋轉公式 26 3.3.3. 四元數 28 3.3.4. 尤拉角 37 3.4. 方向餘弦矩陣計算四元數 40 3.5. 陀螺儀四元數積分姿態計算 43 3.6. 參考四元數計算 44 3.7. 九軸互補濾波器之航姿參考系統計算流程總攬 46 3.8. 互補濾波器融合演算法 48 3.8.1. RC濾波器 49 3.8.2. 互補濾波器之差分方程式推導 50 3.8.3. 參考四元數符號補正 53 3.9. 加速規速度估測 53 3.10. 速度融合演算法 56 3.10.1. 光流法模組演算法 56 第4章、 速度估測與航姿參考演算法模擬 60 4.1. 模擬環境建置 60 4.1.1. 速度融合演算法模擬驗證環境 60 4.1.2. 航姿參考演算法模擬驗證環境 62 4.2. 模擬結果與討論 64 4.2.1. 速度融合演算法模擬結果 64 4.2.2. 航姿參考演算法模擬結果 68 第5章、 速度估測與航姿參考演算法實驗驗證 75 5.1. 實驗平台建置 75 5.1.1. 速度演算法實驗驗證環境 75 5.1.2. 航姿參考演算法實驗驗證環境 76 5.2. 實驗結果與討論 77 5.2.1. 速度融合演算法實驗結果 77 5.2.2. 航姿參考演算法實驗結果 79 第6章、 結論與未來研究方向 90 6.1. 結論 90 6.2. 未來研究方向 91 參考文獻 92

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