This paper presents a novel filter design for the single-output stochastic non-linear systems subjected to non-Gaussian noises and the proposed assumptions. Based on a state transformation, the unmeasurable states of the systems can be estimated where non-linear terms in the systems have been eliminated. It has been shown that the estimation error is linearly dynamical regarding to the presented vector-valued filter gain which can be optimised by minimising the entropy-based performance criterion. In addition, the convergence of the presented algorithm is analysed in mean-square sense and a numerical example is given to verify the effectiveness of the presented filtering algorithm. Meanwhile, the extended Kalman filter, unscented particle filter and minimum entropy filter are given for the comparisons of the filtering performance. Following the presented framework, some extensions of the presented filtering algorithm are discussed to indicate the flexibility of the filter design. The contribution of this paper can be summarised as establishing a novel minimum entropy filtering framework which consists of model transformation, entropy optimisation and convergence analysis.

中文翻译：

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使用状态变换对单输出非高斯随机系统进行最小熵滤波


本文针对受非高斯噪声影响的单输出随机非线性系统提出了一种新颖的滤波器设计以及所提出的假设。基于状态变换，可以在消除系统中的非线性项的情况下估计系统的不可测量状态。已经表明，估计误差对于所提出的矢量值滤波器增益是线性动态的，可以通过最小化基于熵的性能标准来优化该增益。此外，从均方意义上分析了该算法的收敛性，并给出了数值算例，验证了该滤波算法的有效性。同时给出了扩展卡尔曼滤波器、无味粒子滤波器和最小熵滤波器的滤波性能比较。按照所提出的框架，讨论了所提出的滤波算法的一些扩展，以表明滤波器设计的灵活性。本文的贡献可以概括为建立了一种新颖的最小熵过滤框架，该框架由模型转换、熵优化和收敛分析组成。