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对偶四元数是一种将平动与转动统一描述的运动参数,利用它求解捷联惯导系统(SINS)的速度参量,思路完全不同于传统的速度更新算法。对两种速度更新算法的解算过程进行了对比研究,从原理上明确了导致两种算法性能差别的原因,通过定义截断误差和近似积分误差,以二子样算法为例,对两种算法的精度差别进行了定性的分析,并作了定量的计算和推导,给出了定量的表征。研究结果表明:在高动态及大机动运动状态下,对偶四元数算法在精度上具有明显的优势。设置包含圆锥运动与划船运动的复杂、高动态测试条件,在理想情况下与实际情况下分别进行了仿真测试,测试结果验证了对偶四元数算法在整体性能上的显著优势。
Duality quaternion is a kind of motion parameter which is described by translation and rotation uniformly. Using it to solve the SINS speed parameter, the idea is totally different from the traditional speed update algorithm. The two speed update algorithms are compared and solved. The principle causes the difference between the two algorithms. By defining the truncation error and the approximate integral error, taking the two-sub-algorithm as an example, The difference of accuracy is qualitatively analyzed, and the quantitative calculation and derivation are made, and the quantitative characterization is given. The results show that the dual quaternion algorithm has obvious advantages in accuracy under the conditions of high dynamic and large motor motions. The complex and dynamic test conditions including conical motion and rowing motion are set up. Under ideal conditions and actual conditions, the simulation tests are carried out respectively. The test results verify the significant advantages of the dual quaternion algorithm in overall performance.