基于角增量和角速率的旋转矢量算法的等效性

推导了基于角增量和角速率的两种旋转矢量算法（RVA）及其计算误差，并从理论上分析、比较了两种RVA及其圆锥补偿误差（CCE）；在不考虑传感器误差情况下，对两种算法的CCE进行了基于典型圆锥运动的仿真。结果表明，两种RVA的CCE由采样频率和圆锥运动频率的比值定量确定：当比值大于1〖KG*9〗000时，相同子样数的两种算法的CCE相等；两种RVA具有圆锥误差补偿效应的范围为该比值介于3和1〖KG*9〗000之间。在该有效范围内，CCE随比值的减小而单调增大，并且相同子样数的两种算法的CCE随着子样数的增大而趋于相等；当比值小于等于3时，两种算法的圆锥误差补偿效应同样减弱。从而得出两种算法的圆锥误差补偿效应的近似等效性。对于捷联惯组的设计、RVA的选择及其在惯组高动态环境下的应用具有一定指导作用。

Equivalence Analysis of Rotation Vector Algorithms Based on AngleIncrement and Angular Velocity

The rotation vector algorithms(RVA) based on angular increment and angular velocity as well as their calculation errors are deduced in the frequency domain. Both RVAs and their coning compensation errors (CCE) are analyzed and compared in theory. When the sensors’ errors are ignored, CCEs of the two algorithms based on typical coning motion are simulated. It is showed that CCE of two RVAs is determined quantitatively by the ratio of sampling frequency to coning motion frequency in the same way: when the ratio is greater than 1〖KG*9〗000, CCEs of the two RVAs that have the same amount of sub sample are equal; the effective scope that RVA has the function of coning error compensation is that the ratio is greater than 3 and less than 1〖KG*9〗000. Within this scope, CCE increases monotonously with the decrease of the ratio, and the CCEs of two RVAs that have the same amounts of sub samples tends to be equal with the increase of the amount of sub samples; when the ratio is less than or equal to 3, the function of coning error compensation of the two RVAs weakens equally. Thus it can be concluded that the function of coning error compensation of the two RVAs is approximately equivalent, which has certain instructive significance for the design of SINS and the seletcion of RVA as well as the application of SINS in highly dynamic environments.