基于分段量化测量的简约系统辨识
Parsimonious System Identification from Fragmented Quantized Measurements
摘要：
量化是将输入信号从无限连续集合映射到具有有限数量元素的可数集合的过程。它是一个非线性的不可逆过程，这使得传统的系统辨识方法不再适用。在这项工作中，我们提出了一种方法，简约的线性时不变系统辨识时，只有量化的意见，从嘈杂的数据，是可用的。更正式地说，给定的先验信息的系统，由一个紧凑的集包含系统的极点，和量化的实现，我们的算法的目的是在识别最低阶系统，是兼容的可用信息。拟议的方法还考虑到现有数据可能会支离破碎。我们提出的算法依赖于ADMM方法来解决一个$\ell_{p},(0<p<1),$准范数目标问题。数值结果突出的性能相比，所提出的方法的$\ell_{1}$最小化的诱导解的稀疏性。
英文摘要：
Quantization is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system identification no longer applicable. In this work, we propose a method for parsimonious linear time invariant system identification when only quantized observations, discerned from noisy data, are available. More formally, given a priori information on the system, represented by a compact set containing the poles of the system, and quantized realizations, our algorithm aims at identifying the least order system that is compatible with the available information. The proposed approach takes also into account that the available data can be subject to fragmentation. Our proposed algorithm relies on an ADMM approach to solve a $\ell_{p},(0<p<1),$ quasi-norm objective problem. Numerical results highlight the performance of the proposed approach when compared to the $\ell_{1}$ minimization in terms of the sparsity of the induced solution.
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