Using the non-causal nature of a fractional-order singular (FOS) model, this paper deals with the modification of an estimation algorithm developed by Nosrati and Shafiee, and demonstrates how the derived estimation procedure can be adjusted by additional information related to the future dynamics. The procedure adopts the maximum likelihood (ML) method leading to a 3-block fractional singular Kalman filter (FSKF). In addition to some conditions on existence and uniqueness of solutions for discrete-time linear stochastic FOS models, the estimability analyses are given and an optimal filter is presented. Finally, the performance of the derived filter is verified and validated via numerical simulation on a three machine infinite bus system.

中文翻译：

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随机分数奇异模型的最大似然估计


本文利用分数阶奇异 (FOS) 模型的非因果性质，对 Nosrati 和 Shafiee 开发的估计算法进行修改，并演示如何通过与未来相关的附加信息来调整派生的估计过程动力学。该过程采用最大似然 (ML) 方法，产生 3 块分数奇异卡尔曼滤波器 (FSKF)。除了离散时间线性随机 FOS 模型解的存在性和唯一性的一些条件之外，还给出了可估计性分析并提出了最优滤波器。最后，通过三机无限总线系统上的数值模拟来验证和验证所推导的滤波器的性能。