Dynamic Relations in Sampled Processes
Dynamic Relations in Sampled Processes
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DOI：
10.1109/lcsys.2018.2859481
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发表时间：
2018-05
影响因子：
3
通讯作者：
T. Georgiou;A. Lindquist
中科院分区：
文献类型：
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作者：
T. Georgiou;A. Lindquist
可能存在于连续时间中的线性动力学关系，或者在某种自然采样率下，在降低的观测采样率下是不能直接辨别的。事实上，在降低的速率，向量时间序列的矩阵谱密度具有最大秩，从而不能用于确定其条目之间的潜在动态关系。这种迄今未公开的不准确来源似乎困扰着在假设的观测噪声中寻求补救的现成识别技术。在这封信中，我们解释了不同采样率下随机模型之间的确切关系，并展示了如何在数据允许的最佳时间尺度上构建随机模型。然后，我们指出，正确的数量的动力学依赖关系，只能通过考虑随机模型在这个最好的时间尺度，这在一般情况下是比观测采样率快。
Linear dynamical relations that may exist in continuous-time, or at some natural sampling rate, are not directly discernable at reduced observational sampling rates. Indeed, at reduced rates, matricial spectral densities of vectorial time series have maximal rank and thereby cannot be used to ascertain potential dynamic relations between their entries. This hitherto undeclared source of inaccuracies appears to plague off-the-shelf identification techniques seeking remedy in hypothetical observational noise. In this letter we explain the exact relation between stochastic models at different sampling rates and show how to construct stochastic models at the finest time scale that data allows. We then point out that the correct number of dynamical dependencies can only be ascertained by considering stochastic models at this finest time scale, which in general is faster than the observational sampling rate.