IDENTIFICATION OF RANK-ONE RATIONAL SPECTRAL DENSITIES FROM NOISY OBSERVATIONS - A STOCHASTIC-REALIZATION APPROACH

Let S be a q x q spectral density matrix which is the sum of a rational rank one spectral density S-1 and of a constant positive definite matrix Q. The identification problem of S-1 and Q from S is addressed. The conditions under which S-1 and Q are identifiable are first derived. Then, an identification method is proposed. It is based on a parametrization of the external stochastic realizations of S whose innovation sequence has a prescribed dimension.