Error in direction estimation caused by an anisotropie noise field based on a typical vector sound intensity array

It has been an acceptable conclusion that the vector sound intensity array can estimate the direction of sound sources in high precision in an isotropic noise field, but the error in anisotropic noise field has not been systematically studied yet. The error in doa estimation caused by an anisotropic noise field is analyzed in detail here by taking the ocean surface noise field introduced by cron and Sherman for an example. Firstly, we analyze the spatial-correlation functions and spatial cross-spectral functions of the surface noise field and proposed a numerical simulation method of the surface noise field; then formulations of the deviation and variance of each three sound intensity components and cross-covariance functions between the different orthogonal components are obtained. Based on these functions and formulations we deduce the analytical expressions of the error in doa estimation of sound sources in the surface noise field; finally computer simulations for doa estimation based on a typical six-sensor vector sound intensity error are conducted by using the surface noise data produced by the numerical simulation method. The theoretical analysis and computer simulation results show that an anisotropic noise field originating at the surface has little influence on the directional accuracy based on the vector intensity array.