Blind multivariable ARMA subspace identification

In this paper, we study the deterministic blind identification of multiple channel state-space models having a common unknown input using measured output signals that are perturbed by additive white noise sequences. Different from traditional blind identification problems, the considered system is an autoregressive system rather than an FIR system; hence, the concerned identification problem is more challenging but possibly having a wider scope of application. Two blind identification methods are presented for multi-channel autoregressive systems. A cross-relation identification method is developed by exploiting the mutual references among different channels. It requires at least three channel systems with square and stably invertible transfer matrices. Moreover, a general subspace identification method is developed for which two channel systems are sufficient for the blind identification; however, it requires the additive noises to have identical variances and the transfer matrices having no transmission zeros. Finally, numerical simulations are carried out to demonstrate the performance of the proposed identification algorithms.