基于中心误差熵准则的非高斯系统滤波器设计
发布时间：2019-03-18 19:44
【摘要】：针对现存的最小熵滤波理论由于熵具有平移不变性,基于最小熵准则的滤波方法只能保证估计误差的随机性尽可能小,而不能保证其收敛到零的问题,基于中心误差熵准则研究了一类线性非高斯系统的滤波器设计问题。首先在最小熵准则的框架下采用非参数估计理论和梯度下降法给出了滤波增益矩阵的设计方法,并对滤波误差系统的均方稳定性进行了分析。接着针对最小熵准则的不足,提出了新的中心误差熵准则,它是由信息势和互熵的加权求和构成的,最大化信息势以实现估计误差随机性的全局最小化,最大化互熵可以将误差概率密度函数的峰值固定到零,从而实现滤波误差尽可能小。最后采用数值算例分别针对最小熵滤波和最大中心误差熵滤波进行仿真,结果表明基于中心误差熵准则的滤波算法具有更好的性能。
[Abstract]:In view of the fact that the existing minimum entropy filtering theory has translation invariance, the filtering method based on the minimum entropy criterion can only ensure that the randomness of the estimation error is as small as possible, but it cannot ensure its convergence to zero. Based on the central error entropy criterion, the problem of filter design for a class of linear non-Gaussian systems is studied. In the framework of minimum entropy criterion, the design method of filter gain matrix is given by using non-parametric estimation theory and gradient descent method, and the mean square stability of filtering error system is analyzed. Then a new central error entropy criterion is proposed, which is composed of the weighted sum of information potential and mutual entropy, and maximizes the information potential to realize the global minimization of the randomness of estimation error. The maximum mutual entropy can fix the peak value of the error probability density function to zero, so that the filtering error can be as small as possible. Finally, numerical examples are used to simulate the minimum entropy filter and the maximum central error entropy filter respectively. The results show that the filtering algorithm based on the central error entropy criterion has better performance.
【作者单位】： 太原理工大学信息工程学院;
【基金】：国家自然科学基金(61503271) 山西省自然科学基金(20140210022-7)
【分类号】：TN713
本文编号：2443176
[Abstract]:In view of the fact that the existing minimum entropy filtering theory has translation invariance, the filtering method based on the minimum entropy criterion can only ensure that the randomness of the estimation error is as small as possible, but it cannot ensure its convergence to zero. Based on the central error entropy criterion, the problem of filter design for a class of linear non-Gaussian systems is studied. In the framework of minimum entropy criterion, the design method of filter gain matrix is given by using non-parametric estimation theory and gradient descent method, and the mean square stability of filtering error system is analyzed. Then a new central error entropy criterion is proposed, which is composed of the weighted sum of information potential and mutual entropy, and maximizes the information potential to realize the global minimization of the randomness of estimation error. The maximum mutual entropy can fix the peak value of the error probability density function to zero, so that the filtering error can be as small as possible. Finally, numerical examples are used to simulate the minimum entropy filter and the maximum central error entropy filter respectively. The results show that the filtering algorithm based on the central error entropy criterion has better performance.
【作者单位】： 太原理工大学信息工程学院;
【基金】：国家自然科学基金(61503271) 山西省自然科学基金(20140210022-7)
【分类号】：TN713
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