一种基于相关系数矩阵分解的非线性滤波方法  

A nonlinear filter method based on correlated coefficient matrix decomposition

作　　者：丛源材[1] 戴洪德[1] 周绍磊[1] 

机构地区：[1]海军航空工程学院控制工程系,山东烟台264001

出　　处：《华中科技大学学报（自然科学版）》2014年第1期124-128,共5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(61004002);航空基金资助项目(20110184)

摘　　要：介绍了基于统计线性回归的确定采样型滤波器结构,回归点选取的差异是这一类滤波器的本质区别,针对确定性采样型滤波器在选取回归点过程中为获得协方差矩阵的平方根矩阵所采用的矩阵分解问题,通过对协方差矩阵的分析,提出将协方差矩阵分解为标准差对角矩阵和相关系数矩阵,采用对相关系数矩阵进行奇异值分解的方法来获得协方差矩阵的平方根矩阵,从而得到一种新的回归点选取方法.该方法消除了状态向量中量纲的影响,获得了更准确的回归点,从而可以提高滤波精度.最后,采用两个典型的非线性模型对新的非线性滤波方法进行了验证,通过仿真验证了该滤波方法的有效性.The structure of deterministic sampling filter was introduced from statistical linear regres-sion.The internal difference between the deterministic sampling filters was the sampling points used in the filter.Considering the problem that it needed matrix decomposition while choosing sampling points,the covariance matrix was decomposed into diagonal matrix of normal deviation and correlated coefficient matrix,which eliminated the dimension effect of the state.Then through an implementa-tion of singular value decomposition to correlated coefficient matrix,a set of more accurate recursive points could be obtained which improved the filtering precision.Finally,the effectiveness of the new filter was validated through the simulation of two typical nonlinear models.

关 键 词：非线性滤波 统计线性回归 奇异值分解 相关系数矩阵 确定性采样 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]