On the convergence of the minimum variance spectral estimator in nonstationary noise

A simple proof of the convergence of the minimum variance (MV) spectral estimator to the point spectrum, as the order of the covariance matrix goes to infinity, is presented. This is done in the multichannel setting where the corrupting unknown noise process is allowed to be nonstationary. Also obtained are explicit bounds on the rate of convergence. The results suggest that the MV(n) spectrum is robust with respect to the type of contaminating noise. While the results are obtained in the multichannel random process setting, the same arguments hold in the random field setting