New stochastic realization algorithms for identification of ARMA models

Autoregressive moving-average (ARMA) models are of great interest in speech processing. This paper presents new stochastic realization algorithms for identification of such models, by use of a special canonical filter form in the state space, directly and simply connected with ARMA models. We take advantage of certain matrix properties to develop algorithms, which eliminate a matrix inversion, using either the autoeorrelation function of the signal , or the autocorrelation function of a pseudo-innovation sequence , or a cross-correlation function between and . We also present a new algorithm for optimal joint state and parameter estimation in the important case of autoregressive (AR) models. Results obtained with all these algorithms are given for simulated examples.