摘要
针对载体捷联惯性导航系统(SINS)姿态确定中乘性四元数扩展卡尔曼滤波在大初始失准角情形下收敛速度慢及计算精度较低的问题,提出了捷联惯导与星敏感器组合系统姿态估计模型的单位四元数二阶中心差分算法.在推导系统姿态四元数非线性误差模型及其变量计算基础上,利用拉格朗日代价函数法计算四元数加权均值和四元数状态向量,以及非四元数向量分离策略计算估计均值及其方差矩阵,实施中心差分最优姿态估计计算达到提高算法计算精度和降低系统计算量的目的.仿真验证表明:在载体大初始失准角情形下,该算法相比于乘性扩展卡尔曼算法和四元数无迹卡尔曼算法,滤波精度得到提高,算法收敛速度相比于乘性扩展卡尔曼算法有所改善.
A unit quaternion second-order central divided Kalman filtering algorithm was proposed to solve the slow convergence rate and low computational accuracy problems of carriers attitude determination multiplicative quaternion extended Kalman filter algorithm in the strapdown inertial navigation system（SINS）with large initial attitude angle error.The unit quaternion nonlinear attitude estimation model was derived for strapdown inertial navigation system combined with observation equation and observational data of high accuracy charge coupled device（CCD）star sensor,addressing to the unit quaternion weighting sum normalization problem.The Lagrange cost function was derived to compute the predicted average unit quaternion by minimized the cost function,and at the same time the quaternion central divided difference Kalman filter algorithm separating the quaternion state vector and non-quaternion vector to calculate their predicted average values and error covariance matrix to achieve the goals that the algorithm could improve computational efficiency and numerical stability.The simulation results indicate that the proposed quaternion central divided Kalman filter algorithm,compared with traditional multiplicative quaternion extended Kalman filter and quaternion unscented Kalman filter,provides higher estimation precision with faster convergence rate and better numerical stability,and the numerical computation time is improved compared to multiplicative quaternion extended Kal-man filter algorithm.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2014年第9期19-23,48,共6页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(U1204603)
郑州轻工业学院博士基金资助项目(2011BSJJ00048)
关键词
惯性导航系统
姿态估计
拉格朗日算子
电荷耦合器件星敏感器
单位四元数
中心差分卡尔曼滤波
inertial navigation system
attitude estimation
Lagrange multipliers
charge coupled de-vice（CCD）star sensor
unit quaternion
central divided Kalman filter（CDKF）
