Spatial smoothing for localized correlated sources – Its effect on different localization methods in the nearfield

The spatial smoothing (SS) technique has been proved to be effective in decorrelating coherent signals by restoring the rank of the signal covariance matrix R. Averaging the covariance matrices of subarrays of the original array, is a technique which increases the rank of the smoothed matrix RSS. Algorithms like MUSIC or Capon, which rely on the use of the signal covariance matrix R and fail in the case of correlated sources, can be applied to scenarios with correlated sources after spatial smoothing. However, SS is most practically applied to uniformly spaced arrays or to arrays which have a translational symmetry. In addition the formulation is strictly applicable only to such farfield conditions, where the incoming waves are plane waves and the steering vectors to the sources of the different subarrays are identical. These conditions are not fulfilled in the nearfield. Spatial smoothing is now applied with an acoustic camera in the nearfield and it is shown that up to some limits this technique is applicable. Effects/limitations are studied using simulation and measurements with several Beamforming algorithms (MUSIC, Capon and Orthogonal Beamforming) are carried out. The results demonstrate the benefits of SS even in the nearfield up to some limits, which are given through the distance of the different subarrays in comparison to the spatial resolution of the Beamforming algorithm. Especially at lower frequencies SS in connection with MUSIC- or Capon-Beamforming give better resolution in comparison to D + S Beamforming.