A new metric for multivariate spectral estimation leading to lowest complexity spectra

A new multivariate spectral estimation technique is proposed. It is based on a constrained spectrum approximation problem, where the distance between spectra is derived from the relative entropy rate between stationary Gaussian processes. This approach may be viewed as an extension of the high-resolution estimator called THREE introduced by Byrnes, Georgiou and Lindquist in 2000. The corresponding solution features a complexity upper bound which is equal to the one featured by THREE in the scalar case thereby improving on the one so far available in the multichannel framework. The solution is computed by means of a globally convergent, matricial Newton-type algorithm. Comparative simulation indicates that this new technique outperforms PEM and N4SID in the case of short data records.