Abstract

We consider the anisotropy-based filtering problem for a linear discrete time-varying multiplicative noise system on a finite time horizon. A random disturbance with an inaccurately known distribution is fed to the system input. The uncertainty in the description of this distribution is characterized by a constraint on the anisotropic functional. The output of the original system is estimated using the selected filter of a certain type according to the principle of minimizing the performance indicator in the form of the anisotropic norm of the filtering error system. Based on the lemma on the boundedness of the anisotropic norm of the filtering error system, relations for the unknown filter matrices are derived. As special cases, we consider anisotropy-based filtering problems for a system with measurement dropouts as well as a similar problem for a system with a filter of a special type. A numerical example where the method is used to synthesize an anisotropy-based filter is given.

中文翻译：

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基于各向异性的线性离散时变系统滤波，在有限范围内具有乘性噪声

摘要

我们考虑有限时间范围内线性离散时变乘法噪声系统的基于各向异性的滤波问题。具有不准确已知分布的随机扰动被馈送到系统输入。这种分布描述中的不确定性的特点是对各向异性函数的约束。根据过滤误差系统的各向异性范数形式的性能指标最小化的原则，使用选定的某种类型的过滤器来估计原始系统的输出。基于滤波误差系统各向异性范数有界的引理，推导出未知滤波矩阵的关系。作为特殊情况，我们考虑具有测量丢失的系统的基于各向异性的过滤问题以及具有特殊类型过滤器的系统的类似问题。给出了使用该方法合成基于各向异性的滤波器的数值示例。