对偶四元数导航的简化算法

Simplified Dual-Quaternion Navigation Algorithm

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.

The original dual-quaternion navigation algorithm involves many complex operations and requires a large amount of computation.A simplified 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.