Recovering the poles of linear systems

The problem of identifying the poles of stochastic linear systems from stationary and nonstationary multivariable observations, when the order is possibly unknown, is considered. The order and the characteristic polynomial coefficients are estimated from the sample covariance function and the poles are solved from the estimated characteristic equation. For large samples, the estimates converge strongly to the true values. For finite samples, however, the statistical errors may produce spurious poles. The resolution of the order and the poles depends on the condition of the sample correlation matrix, which, in turn, depends on the true poles location.