Statistics of the phase delays between array receivers estimated from the eigendecomposition of the signal correlation matrix

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. This paper derives the mean, variance and covariance of the phase delays when the correlation matrix is estimated from receiver data. It is shown that the variance of the relative phase delays is inversely proportional to the number of snapshots and SNR but relatively independent of the size of the correlation matrix. The theoretical derivations are supported by numerical simulations.>