传递对准误差模型及其QCDKF算法

QCDKF algorithm for a transfer alignment system by using multiplicative quaternion error model

基于乘性四元数计算量小、精度高、非奇异性和全姿态工作特点以及大角度传递对准系统设计要求,建立了可适用于任意失准角情形的传递对准系统速度姿态匹配乘性四元数误差模型;以乘性四元数描述的载体姿态矩阵为对象,构造姿态矩阵代价函数计算乘性四元数均值,使其满足四元数规范化要求,进而计算四元数误差方差矩阵;联合中心差分卡尔曼滤波(CDKF)算法,实现传递对准系统的四元数中心差分卡尔曼滤波(QCDKF)算法.仿真结果表明:该算法能够有效解决大失准角情形下惯导系统传递对准问题,数值计算稳定性较好,计算精度和对准时间都满足系统设计要求.

Based on the actual design requirements of transfer alignment system for large initial misalignment angle and the features of multiplicative quaternion which being little calculation burden, higher precision, non-singularity and all attitude working, it develops the velocity and attitude matching transfer alignment system error model with multiplicative quaternion which can be true to arbitrary magnitude misalignment angles. With the definition of multiplicative quaternion directly representing attitude matrix, it develops the method which, with the attitude matrix for the object, constructs its cost function and calculates the mean of multiplicative quaternion and its quaternion error variance matrix which can meet the normalization requirements of the quaternion mean. Jointing with the central divided difference Kalman filtering （CDKF） algorithm, the quaternion CDKF （QCDKF） algorithm of transfer alignment system for large initial misalignment angles is developed. The simulation results indicate that the QCDKF algorithm can effectively conduct transfer alignment of inertial navigation system with arbitrary magnitude misalignment angles, and have better numerical computation stability, and its calculation accuracy and alignment time meets design requirements.