通过加权弹性网络准则识别主导冲击响应
Leading Impulse Response Identification via the Weighted Elastic Net Criterion
AI总结：
本文提出通过加权弹性网络准则识别线性时不变离散时间动态系统冲击响应的低复杂度估计，证明在足够数据量下，冲击响应从某一时间索引开始几乎必然为零。
摘要：
本文研究了从受噪声干扰的输入输出数据中寻找线性时不变离散时间动态系统冲击响应低复杂度估计的问题。为此，我们引入了一个由标准预测误差成本的平均值加上加权l1正则化项构成的识别准则，该正则化项促进稀疏解。尽管此类准则通常能产生许多零解，但我们的识别问题中关键问题在于这些零的位置，因为合理的低阶模型应在冲击响应的尾部为零。本文的关键结果表明，在标准假设（如独立同分布输入和噪声序列及系统稳定性）下，所提出的准则得到的冲击响应估计在某一时间索引（称为主导阶）之后几乎必然为零，对于足够大的数据量。报告了数值实验以支持理论结果，并与其他先进方法进行了比较。
英文摘要：
This paper deals with the problem of finding a low-complexity estimate of the impulse response of a linear time-invariant discrete-time dynamic system from noise-corrupted input-output data. To this purpose, we introduce an identification criterion formed by the average (over the input perturbations) of a standard prediction error cost, plus a weighted l1 regularization term which promotes sparse solutions. While it is well known that such criteria do provide solutions with many zeros, a critical issue in our identification context is where these zeros are located, since sensible low-order models should be zero in the tail of the impulse response. The flavor of the key results in this paper is that, under quite standard assumptions (such as i.i.d. input and noise sequences and system stability), the estimate of the impulse response resulting from the proposed criterion is indeed identically zero from a certain time index (named the leading order) onwards, with arbitrarily high probability, for a sufficiently large data cardinality. Numerical experiments are reported that support the theoretical results, and comparisons are made with some other state-of-the-art methodologies.
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