國立臺灣大學電機工程學系暨研究所張帆人2006-07-252018-07-062006-07-252018-07-062004-07-31http://ntur.lib.ntu.edu.tw//handle/246246/7979姿態判定在載具的運動中是很重要的， 本文討論的主題就是從陀螺儀以及GPS 所提 供的資訊做姿態的判定。陀螺儀量到的角速度 能藉由姿態運動方程式求得表示姿態的單位 四元數；GPS 的載波相位二次差分模型則能利 用QUEST 的方法求得四元數，之後再利用濾 波器將兩者做一結合，以得到更準確的估測。 由於在姿態判定中所使用的狀態方程式 為非線性，所以一般會選用延伸型卡門濾波器 來整合資訊，但姿態四元數有單範的限制條 件，這會造成卡門濾波器中的協方差矩陣奇異 性問題，因而導致演算過程無法收斂。在本文 中，將利用修正式延伸型卡門濾波器解決此問 題。修正式延伸型卡門濾波器的概念是以四元 數的運算，並利用小角度的假設，減少協方差 矩陣的維數，因而避開奇異性的問題。 除了修正式延伸型卡門濾波器之外，本 文尚利用了球型線性內插法的觀念來做濾 波。球型線性內插法的優點有計算量較小且能 得到與卡門濾波器相若的效能；但是由於它無 法提供陀螺儀偏置值的資訊，因此在使用上有 任務時間的限制，此為其缺點。所以在選擇濾 波器的時候，必須在計算量、任務時間長短以 及陀螺儀偏置值標準差的大小做一衡量，選擇 最適合當時情況的演算法。The attitude determination is very important in the moving vehicles, the topic of this thesis is the attitude determination from the information that GPS and gyro provide. The unit quaternion which expressed the attitude can be derived from the angular velocity that gyro measures; also we can make use of the QUEST algorithm to obtain the unit quaternion from double difference of GPS carrier phase. These two data can be combined into a more accurate one by filters. Since the state equations are nonlinear, the linearization approaches may be used. The extended Kalman filter is an appropriate method for attitude determination. But unit norm constraint of quaternion vector results in the singularity of the error covariance matrix. To overcome this problem, we can use the modified extended Kalman filter. The modified extended Kalman filter adopts quaternion multiplication which preserves the unit norm of quaternion and reduces the dimension of error covariance matrix by an assumption of infinitesimal rotation. In addition to the modified extended Kalman filter, we propose the concept of spherical linear interpolation (SLERP) in the filter. The advantage of SLERP is less computation load and its performance is similar to that of Kalman filter. But the method of SLERP can not provide the measurement update of gyro bias, so using this method is restricted by mission duration. Therefore, when selecting the filter, we need consider a tradeoff among mission duration, computation load and gyro bias.application/pdf89205 bytesapplication/pdfzh-TW國立臺灣大學電機工程學系暨研究所卡門濾波器球形線 性內插法EKFSLERPIntegrationreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/7979/1/922213E002043.pdf