一种基于Chebyshev正交多项式的卡尔曼滤波器  

A Kalman Filter Based on the Chebyshev Orthogonal Polynomial

作　　者：靳宗信[1] 樊红娟 

机构地区：[1]黄河科技学院信息工程学院,郑州450063 [2]河南省经济技术学校电教中心,郑州450044

出　　处：《西南大学学报（自然科学版）》2015年第8期138-143,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金(61101232);郑州市嵌入式系统应用技术重点实验室(121PYFZX177);郑州市科技局科技发展计划(20140661)

摘　　要：针对卡尔曼滤波器滤波非线性系统做了改进,提出了一种基于Chebyshev正交多项式的卡尔曼滤波器.非线性系统经Chebyshev正交多项式分解后,再利用标准卡尔曼算法求解,理论上可以无限逼近此系统,使其达到理想精度.为了验证算法的有效性,本文对此作了理论推导,并将算法应用于混沌系统,实验中传输信号与理想信号之间的误差由白噪声产生,仿真结果表明,其性能优于Unscented卡尔曼滤波器.The Kalman filter for nonlinear system is improved, and a Kalman filter based on the Chebyshev orthogonal polynomial is proposed in this paper. Using the Kalman filter for solving nonlinear systems after they are decomposed by the Chebyshev orthogonal polynomial can, theoretically, achieve infinite approximation and arbitrary precision. In order to verify the effectiveness of the algorithm, theoretical derivation is made in this paper, and the algorithm is applied to chaotic system. The error between the transmitted signal and the ideal signal is generated by the white noise in the experiment. The simulation results show that the performance of the algorithm presented in this paper is superior to that of the unscented Kalman filter.

关 键 词：Chebyshev正交多项式 卡尔曼滤波 UNSCENTED卡尔曼滤波 混沌信号 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]