本論文提出了一IMUPEN與一軌跡重建演算法。此IMUPEN包含了三軸加速度計，陀螺儀，微控制晶片，無線傳輸模組；而此軌跡重建演算法包含兩個部分：姿態估測程序以及位置估測程序。結合IMUPEN與此軌跡重建演算法，使用者能隨時地重建其空間中的三維動作軌跡，並藉此提供使用者遠離電腦時一個便利的人機互動方式。IMUPEN以無線的方式將其內建的慣性感測器原始量測值傳送到電腦端，進行軌跡重建演算；進行軌跡重建演算前，電腦端所接受之原始訊號先經過訊號前處理，訊號前處理包括了感測器校正和低通濾波。軌跡重建演算法中之姿態估測程序取用了經前處理之加速度及角速度，並利用兩種慣性訊號來計算IMUPEN之姿態。為了提高姿態估測準確性，本論文發展了一卡爾曼濾波器及一切換機制來提高姿態估測之準確性。軌跡重建演算法中之位置估測程序取用了經前處理之加速度訊號以及姿態估測程序所計算出的姿態資訊，並利用其來估測IMUPEN之位置。為了提高位置估測之準確性，本論文開發了一多軸動態開關來降低兩次積分之累積誤差。本軌跡重建演算法已透過動作軌跡重建及手寫數字辨識來驗證其實用性及準確度。

This thesis presents an inertial-measurement-based pen (IMUPEN) and a trajectory reconstruction algorithm. The trajectory reconstruction algorithm is capable of providing reconstructed trajectories on demand with the IMUPEN, composed of a triaxial accelerometer, two gyroscopes, a microcontroller, and an RF transmitter. The IMUPEN alone with the trajectory reconstruction algorithm can be used for off-desktop human computer interaction (HCI). The trajectory reconstruction algorithm comprises two constituent procedures: an attitude estimation procedure and a position estimation procedure. The signals collected from the inertial sensors are preprocessed before the trajectory reconstruction algorithm uses them. The signal preprocessing procedure includes a sensor calibration step and a low-pass filtering step. The attitude estimation employs both the preprocessed accelerations and angular velocities to produce attitude estimates. A Kalman filter and a switching mechanism have been developed and integrated into the attitude estimation procedure to make estimation more accurate. The position estimation procedure produces position estimates using the preprocessed accelerations and the attitude estimates. A multi-axes dynamic switch (MAD) has been developed to reduce position drift from double integration of accelerations. The accuracy of reconstructed trajectories is satisfactory for short-term motion trajectory reconstruction and handwritten digit recognition.

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