This paper considers the identification problem of the ARMA system followed by a binary sensor, in which the internal variables are corrupted by additive ARMA noises. Recursive estimates for the parameters of the linear system and for the threshold of the binary sensor are given by the stochastic approximation algorithms with expanding truncations (SAAWET). Under reasonable conditions, all the estimates are proved to be convergent to the true values with probability one. The almost surely convergence rates are also investigated. A simulation example is included to justify the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.