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Improved Minimum Entropy Filtering for Continuous Nonlinear Non-Gaussian Systems Using a Generalized Density Evolution Equation

机译：基于广义密度演化方程的连续非线性非高斯系统的改进最小熵滤波

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This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE) criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF) of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF).
机译：基于改进的最小误差熵（MEE）准则，研究了多元连续非线性非高斯系统的滤波问题。用一组具有非高斯系统噪声和测量噪声的非线性连续方程来描述该系统。利用最近开发的广义密度演化方程来公式化估计误差的联合概率密度函数（PDF）。结合估计误差的熵和均方误差，构造了一种新的性能指标，以确保估计误差不仅具有较小的不确定性，而且接近零。根据共轭梯度法，然后通过最小化改进的最小误差熵准则来获得最佳滤波器增益矩阵。另外，提出条件以保证估计误差动态在均方意义上是指数有界的。最后，比较仿真结果表明，所提出的MEE滤波器优于非线性无味卡尔曼滤波器（UKF）。

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