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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.
A Kalman filter based on the Chebyshev orthogonal polynomial is proposed to improve the Kalman filter nonlinear system. After the nonlinear system is decomposed by the Chebyshev orthogonal polynomial and then solved by the standard Kalman algorithm, it is theoretically possible In order to verify the validity of the algorithm, this paper makes a theoretical derivation and applies the algorithm to the chaotic system. The error between the transmitted signal and the ideal signal in the experiment is generated by the white noise, Simulation results show that its performance is better than Unscented Kalman filter.