对偶四元数导航算法的改进及仿真研究

针对对偶四元数导航算法计算量大,且没有对应的初始对准算法，研究了算法化简和初始对准问题。考虑速度和位置的求取运算复杂，通过研究对偶四元数代数，获取速度和位置矢量的简化算法。仿真表明，简化算法与原始算法具有相同的导航精度，而计算量显著下降。通过对偶四元数导航所需初始条件的研究分析，提出了对偶四元数导航基于传统捷联对准算法的初始对准方案。仿真显示,对准完成后导航解算300 s位置误差仅为1.5 m，证明此对准方案是可行的。简化算法的推导过程，揭示了对偶四元数导航物理本质，可为相关领域研究提供理论参考。

Improvement of dual-quaternion navigation algorithm and relevant simulation

The original dual quaternion navigation algorithm includes many complex operations and requires much more throughput. Moreover, dual quaternion navigation is lack of corresponding aligning algorithm so far. Therefore a simplification and aligning strategy are proposed for the dual quaternion navigation. Considering the velocity and position vectors is much complicated to extract, a straightforward solution is successfully achieved by the study of dual quaternion algebra. Simulation results display the simplified method reaches the same precision as the original one, while the operations cut down remarkably. Furthermore, the initial condition for the navigation method is studied to design an aligning scheme for dual quaternion navigation. As a result, an aligning strategy is proposed based on traditional strap down aligning technique. Simulation results reveal that the position error only 1.5 m for 300 s navigation after alignment, that is, the aligning strategy successful. Moreover, the deduction of the simplified algorithm unveils the dual quaternion algorithm’s physical hypostasis, which would provide an academic reference for relevant research.