Optimal Nonuniform Sampling for System Identification on Sparsely Sampled Data*

In this paper, the problem of optimal Nonuniform sampling (NUS) is addressed for the purpose of sparsely sampled data system identification. Given a set of uniformly sampled data, its spectral information is available in the range limited by Nyquist rate, and results in alias out of the range. This cannot meet the “informative enough” condition, which is one indispensable prerequisite for system identifiability. Nevertheless, deliberate NUS pattern with certain random distributions can keep the alias-free feature of sampled signals and recover wider spectrum of the original signal, so that the identifiability is still guaranteed. In the case that no ideal alias-free signal is available, a criterion of alias suppression is founded and the optimal sampling is proposed to give an effective estimation of such systems with sparse samples. Simulation results shows the practicality and effectiveness of the proposed optimal sampling method, and how the identified model accuracy is affected by NUS.