無GNSS資訊之行人定位系統研發與驗證

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劉世登(Shi-Deng Liu) 查詢紙本館藏

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機械工程學系

論文名稱

無GNSS資訊之行人定位系統研發與驗證

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至系統瀏覽論文 (2028-3-1以後開放)

摘要(中)

全球導航衛星系統(GNSS)的興起使得導航算法成為主流，但當全球定位系統(GPS)訊號受干擾或失效時，依賴GNSS的導航系統也會失效，因此不依賴GNSS的自主導航技術逐漸受到重視。研究旨在建立一行人定位系統，基於慣性導航理論，利用Madgwick與基於加速度計與磁力計之姿態估測快速演算法(SAAM)等姿態估算法，融合零速更新約束法(ZUPT)與高度資訊建立誤差狀態卡爾曼濾波(ESKF)，從而實現行人定位系統。
為驗證算法定位性能，首先透過建立模擬二維慣性訊號，以弦波與模擬行人步態訊號，建立矩形路徑，並比較經過ESKF算法濾波與未經濾波之慣性訊號定位精度，並透過誤差百分比(EP)與正規化之路徑RMSE(NP-RMSE)等指標分別對算法之定位目標精度與整體誤差進行評斷。從結果得知，EP自16.4%降至2.96%，而NP-RMSE自12.5%降至1.89%，代表ESKF算法具備有效過濾雜訊，令慣性訊號精準定位之能力；在實務實驗中，在直線、矩形與圓弧路徑實驗中結合無線定位量測系統進行實驗。結果根據不同姿態估算法建立系統之定位精度表示，Madgwick算法之EP與NP-RMSE分別為1.86%、3.1%、2.7%與7.63%、6.5%、2.7%，SAAM算法則為11.79%、3.8%、7.1%與15%、9.4%、4.5%。透過比較得知，Madgwick算法表現出較優的姿態精度，但無論使用哪種姿態估計算法，路徑結果都低估實際位移，這可能源於ZUPT狀態辨別精度不足所致。此外，兩種系統之高度RMSE分別為0.42m、0.21m、0.8m與0.42m、0.21m、0.85m,均呈現精準之高度定位精度；而系統之運算時間分別為4.85s、4.26s、62.84s與4.05s、3.65s、60.71s
，顯示出SAAM算法具備較高之運算效率，雖隨著運算量增加而逐漸減少差異，但對於實時定位之需求仍具潛力。
經過前述驗證實驗結果顯示：本系統已具備初步定位功能之雛形，但若要近一步實現實時定位，當行人處於不同狀態時，應令ZUPT與姿態估算法具備因應不同場合使用最適參數之適應能力，以提升系統定位精度，最終實現導航功能。

摘要(英)

The rise of Global Navigation Satellite Systems (GNSS) has made navigation algorithms mainstream. However, when Global Positioning System (GPS) signals are disrupted or fail, GNSS-dependent navigation systems also become ineffective. As a result, autonomous navigation technologies that do not rely on GNSS have gained increasing attention. This study aims to develop a pedestrian positioning system based on inertial navigation theory, utilizing attitude estimation algorithms such as the Madgwick filter and the SAAM (a fast attitude estimation algorithm based on accelerometers and magnetometers). By integrating the Zero Velocity Update (ZUPT) constraint method and altitude information, an Error-State Kalman Filter (ESKF) is constructed to enhance the pedestrian positioning system.
To verify the positioning performance of the algorithm, a simulated two-dimensional inertial signal was first established. Using sine waves and simulated pedestrian gait signals, a rectangular path was created, and the positioning accuracy of inertial signals processed by the ESKF algorithm was compared with unfiltered signals. The accuracy was assessed using indicators such as Error Percentage (EP) and Normalized-Path Root Mean Square Error (NP-RMSE). The results showed that EP decreased from 16.4% to 2.96%, while NP-RMSE reduced from 12.5% to 1.89%, demonstrating that the ESKF algorithm effectively filters noise and improves inertial signal positioning accuracy.
In practical experiments, the system was tested on linear, rectangular, and circular paths, integrating a wireless positioning measurement system. The positioning accuracy of different attitude estimation algorithms was evaluated, revealing that the Madgwick algorithm achieved EP and NP-RMSE values of 1.86%, 3.1%, and 2.7% and 7.63%, 6.5%, and 2.7%, respectively. Meanwhile, the SAAM algorithm yielded values of 11.79%, 3.8%, and 7.1% for EP and 15%, 9.4%, and 4.5% for NP-RMSE. The comparison indicates that the Madgwick algorithm provides better attitude accuracy. However, regardless of the attitude estimation algorithm used, the trajectory results underestimated actual displacement, likely due to insufficient accuracy in ZUPT state recognition.
Additionally, the altitude RMSE values for both systems were 0.42m, 0.21m, and 0.8m for the Madgwick algorithm and 0.42m, 0.21m, and 0.85m for the SAAM algorithm, demonstrating precise altitude positioning accuracy. The computation times were 4.85s, 4.26s, and 62.84s for the Madgwick algorithm and 4.05s, 3.65s, and 60.71s for the SAAM algorithm. Although the difference decreased with increasing computational load, the SAAM algorithm exhibited higher computational efficiency, making it a promising candidate for real-time positioning applications.
The experimental results indicate that the proposed system has successfully established a preliminary pedestrian positioning prototype. However, to achieve real-time positioning, the ZUPT and attitude estimation algorithms should be adapted with optimized parameters for different pedestrian states to enhance positioning accuracy and ultimately realize full navigation functionality.

關鍵字(中)

★ 自主式行人定位
★ Madgwick演算法
★ SAAM演算法
★ 零速更新法
★ 誤差狀態卡爾曼濾波

關鍵字(英)

論文目次

摘要 i
Abstract ii
目錄 iv
圖目錄 vi
表目錄 viii
第一章緒論 1
1-1 研究動機與目的 1
1-2 文獻回顧 2
1-3 研究範疇與章節內容 5
第二章慣性導航理論與步態分析 6
2-1 感測元件基本原理 6
2-1-1 加速度計 6
2-1-2 陀螺儀 7
2-1-3 磁力計 8
2-1-4 氣壓計 8
2-2 座標系統 9
2-2-1 慣性座標系 9
2-2-2 地心地固座標系 9
2-2-3 導航座標系 10
2-2-4 載體座標系 10
2-3 姿態表示法 11
2-3-1 歐拉角 11
2-3-2 方向餘弦矩陣 12
2-3-1 四元數法 14
2-4 行人步態分析 16
2-4-1 行人步態特性 16
2-4-2 零速更新法 17
第三章行人定位演算法 19
3-1 姿態估計算法 19
3-1-1 Madgwick算法 19
3-1-2 SAAM算法 25
3-2 定位狀態更新 29
3-3 誤差分析 37
3-3-1 擾動分析 37
3-3-2 訊號誤差建模 41
3-4 卡爾曼濾波 42
3-4-1 卡爾曼濾波基本方程式 43
3-4-2 誤差狀態卡爾曼濾波 44
3-4-3 模擬訊號驗證 46
3-5 演算法流程圖 49
第四章算法性能驗證實驗及結果分析 50
4-1 實驗量測系統 50
4-2 感測器靜態誤差校正 54
4-3 實驗設計 60
4-4 實驗結果與討論 61
第五章結論與未來展望 71
參考文獻 72

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指導教授

潘敏俊

審核日期

2025-3-13

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