In this paper, the problem of identifying Multiple-Input-Single-Output (MISO) systems with fractional models from noisy input-output available data is studied. The proposed idea is to use Higher-Order-Statistics (HOS), like fourth-order cumulants (foc), instead of noisy measurements. Thus, a fractional fourth-order cumulants based-simplified and refined instrumental variable algorithm (frac-foc-sriv) is first developed. Assuming that all differentiation orders are known a priori, it consists in estimating the linear coefficients of all Single-Input-Single-Output (SISO) sub-models composing the MISO model. Then, the frac-foc-sriv algorithm is combined with a nonlinear optimization technique to estimate all the parameters: coefficients and orders. The performances of the developed algorithms are analyzed using numerical examples. Thanks to fourth-order cumulants, which are insensitive to Gaussian noise, and the iterative strategy of the instrumental variable algorithm, the parameters estimation is consistent.

在本文中，研究了从噪声输入输出可用数据中识别具有分数模型的多输入单输出（MISO）系统的问题。提出的想法是使用高阶统计量 (HOS)，如四阶累积量 (foc)，而不是噪声测量。因此，首先开发了一种基于分数四阶累积量的简化和细化工具变量算法（frac-foc-sriv）。假设所有微分阶数都是先验已知的，则其包括估计构成MISO模型的所有单输入单输出(SISO)子模型的线性系数。然后，将 frac-foc-sriv 算法与非线性优化技术相结合来估计所有参数：系数和阶数。使用数值示例分析了所开发算法的性能。由于四阶累积量对高斯噪声不敏感，以及工具变量算法的迭代策略，参数估计是一致的。