The eigenvector method for estimating the positions of the receivers of a towed array is based on an eigendecomposition of the cross-spectral density matrix of the receiver outputs. The method assumes a signal scenario consisting of a single plane wave source in the presence of independent noise. This paper derives expressions for the bias and variance of the position estimates and shows that for acceptable performance, the array needs to be relatively linear and the source direction away from endfire. It also shows that the bias and variance is relatively independent of the number of receivers in the array. This observation led to the partitioned eigenvector method introduced in this paper. It is shown that the partitioning approach substantially reduces the computational cost of the array shape estimation algorithm without adversely affecting the quality of the position estimates. The theoretical work is substantiated with numerical simulations and compared to the Cramer-Rao lower bound (CRLB). Further-numerical simulations demonstrate the robustness of the technique against spatially correlated noise and an interference source.
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