本論文探討了一種基於卡爾曼濾波與感測器融合的方法，以估計全球定位系統（GPS）失效時的移動軌跡重建，解決導航應用中因信號遮擋或干擾導致的定位中斷問題。GPS在戶外環境中提供高精度定位，但在城市峽谷、隧道或室內場景下易失效，而慣性測量單元（IMU）雖可獨立運作，卻受噪聲和漂移影響。本研究從多組實測數據中收集GPS和IMU數據（包括經緯度、速度、加速度、陀螺儀和羅盤數據），通過卡爾曼濾波技術對加速度進行修正，以實現連續且準確的軌跡重建。方法上，首先利用卡爾曼濾波平滑加速度數據以降低噪聲影響；接著通過互補濾波融合羅盤與陀螺儀數據，生成穩定航向角；在GPS失效後，基於初始速度和運動學積分估計 IMU 軌跡，並採用極座標標準化技術將GPS和 IMU軌跡與基準對齊。研究結果顯示，融合方法生成的軌跡與基準軌跡的均方根誤差（RMSE）接近基準值，優於單獨使用GPS或IMU的結果，驗證了其在短時失效場景下的有效性。相較於現有方法，本研究通過實測數據還原軌跡，計算效率高且無需大量訓練數據，具備較強的應用適應性。本方法為運動導航、無人機飛行等GPS失效場景提供了可靠解決方案，未來可進一步融入多感測器數據，提升長期失效下的軌跡精度。

This paper investigates a method based on Kalman filtering and sensor fusion to reconstruct movement trajectories during Global Positioning System (GPS) outages, addressing positioning interruptions in navigation applications caused by signal obstruction or interference. GPS provides high-precision positioning in outdoor environments but is prone to failure in urban canyons, tunnels, or indoor settings. In contrast, Inertial Measurement Units (IMU) can operate independently but are affected by noise and drift. This study collects GPS and IMU data (including latitude, longitude, velocity, acceleration, gyroscope, and compass data) from multiple real-world experiments and employs Kalman filtering to refine acceleration data for continuous and accurate trajectory reconstruction. The methodology first applies Kalman filtering to smooth acceleration data, reducing noise impact. Then, complementary filtering is used to fuse compass and gyroscope data, generating a stable heading angle. During GPS outages, IMU trajectories are estimated based on initial velocity and kinematic integration, with polar coordinate standardization aligning GPS and IMU trajectories to a reference. Results show that the fused method achieves a root mean square error (RMSE) comparable to the reference trajectory, outperforming standalone GPS or IMU, validating its effectiveness in short-term outage scenarios. Compared to existing methods, this approach reconstructs trajectories from real-world data with high computational efficiency and no need for extensive training data, demonstrating strong adaptability. The method provides a reliable solution for motion navigation, drone flight, and other GPS outage scenarios, with potential future enhancements through multi-sensor data integration to improve trajectory accuracy in long-term outages.

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