基于毕卡迭代的捷联姿态更新精确数值解法

An Accurate Numerical Solution for Strapdown Attitude Algorithm Based on Picard Iteration

针对捷联惯导在大角度机动等场合下姿态精确求解问题,论文根据四元数微分方程的毕卡级数解法,提出一种新的求解姿态更新的数值算法。新算法利用角增量建立角速度多项式拟合,再根据多项式四元数的乘法特点将其变换为多项式的卷积运算,求得更新四元数的幂级数解。新算法在推导过程中未做任何近似和假设,不存在原理性误差。在大幅值圆锥运动和大角度机动环境下,新算法与传统算法进行了对比仿真试验,校验了新算法具有明显的精度优势。

For strapdown attitude updating algorithm, in order to reach a high accuracy under a high attitude maneuver,a new numerical attitude algorithm is proposed based on the Picard series solution for the attitude quaternion differential equation. In this new algorithm,the angular velocity polynomial fit is obtained for the gyro angular increment,and the product of the polynomial quaternion is converted into the convolution operation of the angular velocity polynomial coefficients,then the Picard series solution is well settled. There exists no approximation or hypothesis in this deduction,which means the new algorithm is analytically accurate. Finally,under the large amplitude cone motion and high maneuver environment,some comparison tests both using the traditional algorithm and the new presented algorithm are carried out,and the results show the significant accuracy improvement in the new algorithm.