Novel approach to rank determination of multichannel data covariance matrices

The rank selection problem of a multichannel data covariance matrix is addressed by the Bayesian methodology. A maximum a posteriori solution is derived, and a bootstrap technique for its implementation proposed. Our rule is tested on simulated sensor array data that represent random signals embedded in white Gaussian noise. The tests include comparisons with the popular AIC and MDL criteria. The results show that the Bayesian rule outperforms them, particularly for low signal-to-noise ratios and small direction-of-arrival separations.