基于中心误差熵准则的非高斯系统滤波器设计

Filtering Design for Non-Gaussian Stochastic Systems Based on Central Error Entropy Criterion

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。

It is an effective way to use the stochastic distributed control theory to solve filtering problems for non-Gaussian systems.Minimum entropy filtering is one of the representative results.The state estimation method based on the minimum entropy criterion can fully characterize the randomness of the estimation error,which is more suitable than the mean-variance-criterion based states estimation method.However,there are some problems for the minimum entropy filtering theory,such as,owing to the shift-invariant of the entropy,only the randomness of the estimation error can be minimized while the magnitude may not be convergent to zero.In order to solve this problem,this paper presents a novel central error entropy criterion（CEEC）to investigate the filtering problem for linear non-Gaussian systems.Firstly,based on the minimum entropy criterion,the filtering design method is proposed by using the nonparametric estimation theory and stochastic gradient decent method.Moreover,the convergence of the estimation error system is analyzed.Then,a novel CEEC is formulated,which is the weighted sum of information potential and correntropy.Maximizing the information potential can minimize the randomness of estimation error globally;and maximizing the correntropy can fix the peak of the error probability density function（PDF）close to zero.Finally,a numerical example is given to show that the CEEC based filtering is superior to the MEE based filtering.