Three‐dimensional matched‐field processing with an eigenvalue method

Abstract

An eigenvalue method for three‐dimensional matched‐field processing with a vertical array has been developed for localization of multiple sources in range and depth (bearing can also be determined with the method if the environment is asymmetric). The method involves applying the Bartlett beamformer to the eigenvectors of the cross‐spectral density matrix. This approach appears to be more effective than the standard eigenvalue approach involving beamforming on a linear combination of several eigenvectors. Eigenvalue beamforming methods are based on the orthogonal targets approximation [R. F. Gragg, NRL Rep. 9143, Naval Research Laboratory, Washington, DC (1989)]. The spatial correlation over a horizontal array of two sources is small provided the sources are sufficiently separated in bearing. On the other hand, the spatial correlation over a vertical array of two point sources may be relatively large for some source locations (i.e., the Bartlett matched‐field processor for a vertical array has relatively large sidelobes). However, simulations suggest that this effect does not seriously degrade the eigenvalue processing method for vertical arrays. Source motion will further enhance this processing method.