This article studies singular systems with uncertain parameters by using a direct method which is called the first restricted equivalent transformation (FRET). The stochastic uncertain parameters we studied in the article, which are more general and challenging, are different from the two existing types: time‐invariant parameters and time‐varying parameters. We propose an optimal filtering algorithm to filter out artifacts, such as noise, from the uncertain parameter by using the projection theorem and the FRET. The proposed algorithm guarantees optimum in the sense of linear minimum mean‐square error. Simulation results verify the proposed algorithm.

中文翻译：

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具有随机不确定参数的奇异系统的最优状态估计

本文通过使用称为第一受限等效变换（FRET）的直接方法研究具有不确定参数的奇异系统。我们在本文中研究的随机不确定性参数更为笼统且更具挑战性，它与两种现有类型不同：时不变参数和时变参数。我们提出了一种最佳的滤波算法，可以通过使用投影定理和FRET从不确定参数中滤除诸如噪声之类的伪影。所提出的算法在线性最小均方误差的意义上保证了最优。仿真结果验证了该算法的有效性。