角速率输入下两种姿态描述模型的讨论

The Discussion of the Two Navigation Attitude Algorithm Models under Angular Rate Input

由于捷联惯导中四元数模型会产生系数矩阵条件数不为1和弱的刚性问题导致求解发生错误,这时采用双欧模型描述会有更好的效果。双欧法利用正、反欧拉方程间精华区倒挂关系进行分区交替运算,把精华区扩展到全域,不仅根除了奇异性,而且计算误差小,误差没有增长趋势。文中从科学计算的角度,较为充分地分析了两种姿态描述模型的特点与不足,并做了圆锥运动环境下相关的数字仿真进行了验证,发现双欧法优于四元数模型。

In the strapdown navigation system, the application of the quaternion differential equation will cause the problem that the conditional number not to be 1 and weak rigidity. However, dual Euler method performs better in some special environment. The dual Euler method separates the essential area from overall calculating area and alternate calculation on the inverse relationship of essence area between the ordinary and reversed Euler equations. The essential are- a is expanded to the whole area. Not only the singularity is overcome completely, but also calculating mistakes are less than others and the tendency of the magnitude is not increasing. It shows that the two kinds of methods are featured with both advantages and disadvantages. Moreover, numerical simulation is used for verification under conical motion, and it is found that the dual Euler method is better than the quaternion model.