The identification problem in case of data with missing values is challenging and currently not fully understood. For example, there are no general nonconservative identifiability results, nor provably correct data efficient methods. In this paper, we consider a special case of periodically missing output samples, where all but one output sample per period may be missing. The novel idea is to use a lifting operation that converts the original problem with missing data into an equivalent standard identification problem. The key step is the inverse transformation from the lifted to the original system, which requires computation of a matrix root. The well-posedness of the inverse transformation depends on the eigenvalues of the system. Under an assumption on the eigenvalues, which is not verifiable from the data, and a persistency of excitation-type assumption on the data, the method based on lifting recovers the data-generating system.

中文翻译：

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从具有周期性缺失输出样本的数据中进行识别


数据缺失值的识别问题具有挑战性，目前尚未完全理解。例如，没有通用的非保守可识别性结果，也没有可证明正确的数据有效方法。在本文中，我们考虑周期性丢失输出样本的特殊情况，其中每个周期除了一个输出样本之外的所有输出样本都可能丢失。新颖的想法是使用提升操作将丢失数据的原始问题转换为等效的标准识别问题。关键步骤是从提升系统到原始系统的逆变换，这需要计算矩阵根。逆变换的适定性取决于系统的特征值。在对特征值的假设（无法从数据中验证）和对数据的激励型假设的持续性下，基于提升的方法恢复了数据生成系统。