Identification for Multivariate ARMA Systems without SPR Condition

When the ELS algorithm is applied to identifying the multivariate ARMA system A(z)y_k = B(z)w_k, the SPR condition is usually required and the covariance matrix Rw of Wk is normally not estimated. In this paper the recursive algorithms are proposed for estimating coefficients of A(z), B(z), and the covariance matrix R_w, of w_k by recursively approximating the solution to the algebraic equation satisfied by the estimated parameters. The conditions imposed on the system are natural: stability of A(z), identifiability of the system, and iid for {w_k}-The restrictive strictly positive realness condition (SPR) is not required and the algorithm is easily computable.