This paper studies system identification of ARMA models with binary-valued observations. Compared with existing quantized identification of ARMA models, this problem is more challenging since the accessible information is much less. Different from the identification of FIR models with binary-valued observations, the prediction of original system output and the parameter both need to be estimated in ARMA models. We propose an online identification algorithm consisting of parameter estimation and prediction of original system output. The parameter estimation and the prediction of original output are strongly coupled but mutually reinforcing. By analyzing the two estimates at the same time instead of analyzing separately, we finally prove that the parameter estimate can converge to the true parameter with convergence rate $O(1/k)$ under certain conditions. Simulations are given to demonstrate the theoretical results.

本文研究了具有二值观测值的 ARMA 模型的系统识别。与现有的 ARMA 模型量化识别相比，这个问题更具挑战性，因为可访问的信息要少得多。与使用二值观测值的FIR模型的识别不同，ARMA模型需要对原始系统输出的预测和参数进行估计。我们提出了一种由参数估计和原始系统输出预测组成的在线识别算法。参数估计和原始输出的预测是强耦合但相辅相成的。通过同时分析两个估计而不是分别分析，我们最终证明参数估计可以以收敛速度收敛到真实参数$欧(\mathrm{1个}/k)$在某些条件下。给出了仿真来证明理论结果。