Estimation of structured covariance matrices and multiple window spectrum analysis

A close relationship between low rank modeling and multiple window spectrum estimation is demonstrated by using maximum likelihood estimates of structured covariance matrices. The power in a narrow spectral band is estimated by estimating the variances in a low rank signal plus noise covariance model. This model is swept through the entire frequency band to obtain an estimate of power as a function of frequency. The resulting spectrum estimates are given by weighted combinations of eigenspectra. Each eigenspectrum results from projecting the data onto an orthogonal component of the signal subspace and squaring. The multiple window spectrum estimates of Thomson (1982) correspond to a particular choice for the low rank signal model. The low rank modeling and structured covariance matrix framework is also used to derive the maximum likelihood estimate for the center frequency of a signal in noise. This estimate is also obtained from a weighted combination of eigenspectra