This study aims to determine how to deal with the identification from input and output data of switched linear systems (SLSs) with Box and Jenkins models. The identification difficulties of this system are that there exist unknown switched signal, unknown middle variables, and colored noise terms in the identification process. To address these issues, the proposed identification method proceeds in two stages, including the estimation of the switched signal of SLSs and the identification of the parameters of all subsystems. First, the Gaussian mixture model is established to represent the distribution of the input and output data of SLSs. Then, the posterior probability is calculated by the expectation-maximization (EM) algorithm and the naive Bayes classifier, and the switched signal is estimated according to the maximum probability criterion. Next, the auxiliary model based multi-innovation generalized extended least square (AM-MI-GELS) algorithm is used to estimate the parameters of all subsystems. Finally, the effectiveness of the proposed method is verified through the simulation example.

中文翻译：

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基于期望最大化和贝叶斯算法的切换线性系统识别

本研究旨在确定如何使用 Box 和 Jenkins 模型处理切换线性系统 (SLS) 的输入和输出数据的识别。该系统的识别难点在于识别过程中存在未知的切换信号、未知的中间变量和有色噪声项。为了解决这些问题，所提出的识别方法分两个阶段进行，包括 SLS 切换信号的估计和所有子系统参数的识别。首先，建立高斯混合模型来表示SLSs输入输出数据的分布。然后，通过期望最大化（EM）算法和朴素贝叶斯分类器计算后验概率，并根据最大概率准则估计切换信号。接下来，使用基于辅助模型的多创新广义扩展最小二乘（AM-MI-GELS）算法估计所有子系统的参数。最后通过仿真算例验证了所提方法的有效性。