Asymptotic statistics for wavenumber estimation

The use of an array of sensors for determining the properties of propagating waves is of considerable importance in many applications. For example, in radar and sonar, an array of sensors is used to determine the spectral content and spatial coordinates of targets. In many situations estimates of the spectral and spatial parameters are based on the estimated cross-spectral matrix. In this paper we establish asymptotic distributional properties for wavenumber estimates using the asymptotic statistical properties of eigenvalues and eigenvectors of smoothed cross-spectral matrix estimates.