SINS初始对准QCDKF算法研究

摘要

根据载体姿态四元数描述特点及其计算优势,建立了捷联惯导系统大失准角情形初始对准乘性四元数误差模型.该模型构造姿态矩阵代价函数计算其最大特征值,求取对应特征向量作为预测四元数均值并选择具有单位范数的特征向量来满足预测四元数均值计算保范性和符号不变性要求；利用秉性四元数误差表示四元数Sigma点与预测均值四元数间距,进而计算四元数预测误差方差矩阵.结合中心差分滤波(CDKF)算法提出四元数CDKF算法(QCDKF),实现大角度失准角情形的SINS初始对准仿真研究,与EKF算法相比,QCDKF算法数值计算稳定性较好,姿态误差角和速度误差滤波精度得到明显改善和提高.%Considering the characteristics and computation superiority of quaternion representing body attitude movement, and aiming at the initial alignment procedure of strapdown inertial navigation system (SINS) with large initial misalignment angles,its multiplicative quaternion error model were developed. It proposes the new calculation method in which the attitude matrix cost function was constructed to calculate its maximum eigenvalues, and select the eigenvector which corresponds to the maximum eigenvalue as the predicted quaternion mean to guarantee its unit normalization and the sign invariability. The multiplicative quaternion error representing the distance between quaternion Sigma-points and the predicted quaternion mean calculates the quaternion prediction error variance matrix, which can effectively overcome the application limits for SPKF algorithms in quaternion filtering implementation. Combined with the central divided difference filtering (CDKF) algorithm, it proposes the new quaternion CDKF algorithm ( QCDKF) for quaternion filtering problems in the SINS'simulation experiments. The simulations results showed that, compared with EKF algorithm, the proposed algorithm can significantly improve the filtering precision of both attitude misalignment angles and velocity and have better stabilization in the numerical calculation.