The partitioned eigenvector method for towed array shape estimation

The eigenvector method for estimating the positions of the receivers of an ocean-towed array is based on the eigendecomposition of the array signal correlation matrix to find the phase delays between the array receivers. Previous work has shown that for reasonable SNR, the bias and variance of the phase estimates is relatively independent of the number of receivers in the array. This suggests that the computational cost of the eigenvector method could be substantially improved by partitioning the array receivers into groups of smaller sub-arrays and then applying the eigenvector method to each sub-array. This paper introduces the interleaved partitioned eigenvector method, and shows that it significantly reduces the computational cost without adversely affecting the quality of the position estimates. Numerical examples substantiate the theoretical work of this paper and also demonstrate the improvement in beamforming when employing the shape estimation algorithm.