一种四元数更新算法的推导及仿真研究

在捷联惯导系统中，可以四元数表示姿态矩阵，而姿态矩阵的计算是捷联惯导系统的关键问题之一，本文引入四元数三阶泰勒展开递推式作为四元数的更新算法，着重进行了公式的推导。并对某陆地捷联惯导系统的实际测量数据进行了仿真，仿真结果表明该算法的有效性。

Proof and Simulation for a Updating Algorithm of Quaternion

Attitude matrix is represented by quaternion and the calculation of attitude matrix is a key in Strapdown INS. In this paper three-order recursive Taylor expanded form of quaternion as the updating algorithm of quaternion is introduced. With the emphasis on the proof of the formula, the paper makes the corresponding simulation to the datum of a land vehicle strapdown INS that has been collected. The result proved that the algorithm is effective.