中文摘要：

以微小型捷联航姿参考系统为研究对象,建立基于对偶四元数的导航系统姿态更新解算参数模型。该方法区别于描述刚体纯旋转变换的四元数方法,将载体系与地理系之间坐标转换的旋转与平移过程进行统一、融合,通过建立最小方差目标方程,求解最优的姿态更新矩阵。构建Kalman滤波方程,最终确定载体姿态,航向角实时信息。仿真表明,对偶四元数所建姿态四元数误差的均值与均方差均小于0.002。Kalman滤波器构造符合实际系统要求,在传感器测量精度有限的情况下,可使俯仰角、横滚角、航向角误差分别减小到0.1°,0.1°,0.2°。

英文摘要：

The parameter model for attitude updating in the field of micro-strapdown attitude and heading reference system （AHRS） was established based on the dual quaternion （DQ） algebra. Differing from the quaternion （Q） solution adopted to express the pure rotation transition of rigid body, DQ scheme described the coordinates transition between body frame and geographical frame by fusing the measurements of rotation and translation process, computed the optimized attitude updating matrix by constituting the least squares cost function as well. Moreover, the Kalman filter functions were designed, which then defined the real-time attitude and heading estimates. Simulation indicates that the mean and root mean square of attitude quaternion error based on DQ technique are both below 0.002. The modeling of Kalman filter accords with the requirements for practical applications, the pitch, roll, and heading angles error never exceed 0.1°, 0.1°, 0.2° respectively, even if the accuracy of the sensors is modest.