两种SINS惯性系四元数粗对准算法等价性分析

针对捷联惯导系统惯性系粗对准两种四元数算法的等价性进行了详细分析。首先,根据姿态矩阵的分解原理将初始对准问题转化为多矢量定姿的Wahba问题,并根据重力矢量连续变化的特点建立了积分形式的优化目标函数。然后,根据基于四元数的坐标变换原理,将目标函数变换为关于姿态四元数的函数,进而根据四元数运算性质分别导出最优四元数的两种求解形式,并根据矩阵特征值和特征向量的性质证明了两种算法的等价性。最后,通过仿真和试验数据进一步验证了理论分析的正确性。

Equivalence analysis between two quaternion based coarse alignment algorithms for SINS with inertial frame

The equivalence between two quaternion based coarse alignment algorithms for strapdown inertial navigation system (SINS) with inertial frame is carefully analyzed. Firstly, the alignment of SINS is transformed into the Wahba problem in attitude determination based on the decomposition principle of the attitude matrix, and an integral form objective function to be optimized is established according to the fact that the gravity vector changes continuously. Then the objective function is transformed into the function of attitude quaternion on the basis of coordinate transformation rules in the quaternion form, and two algorithms are derived to acquire the optimal attitude quaternion. Finally the equivalence between the two algorithms is demonstrated based on the properties of matrix eigenvalues and eigenvectors, with further verification conducted with data from both simulation and field experiment.