对偶四元数导航的简化算法

摘要： 针对原始对偶四元数导航算法计算量大的问题推导了一种简化算法，对原始算法的矢量求解进行数学化简，使引力速度、非引力速度和位置矢量的求解变得简单明了，物理意义明确清晰. 通过近似将简化算法中的非引力速度公式再次化简而得到近似算法. 仿真导航显示，简化算法与原始对偶四元数法解算的位置精度相同，均高于传统捷联导航算法，而简化算法计算量最小；近似算法的位置精度与简化算法相比无明显下降.

Simplified Dual-Quaternion Navigation Algorithm

Abstract: The original dual-quaternion navigation algorithm involves many complex operations and requires a large amount of computation. A implified algorithm is proposed for dual-quaternion navigation to make extraction of gravitational velocity and position vectors easier. The notation of the simplified algorithm is unambiguous. After that, the formula for extracting non-gravitational velocity is further simplified. Simulation shows that the simplified method provides the same precision as the original dual-quaternion algorithm, both being better than the traditional strap-down navigation algorithm. The computation complexity of the proposed method is the least among the three, while position error of the approximate algorithm is close to that of the original dual-quaternion algorithm.