Towed Array Shape Estimation Based on Single or Double Near-Field Calibrating Sources

Towed array shape estimation is a crucial step for most array processing algorithms, since the position uncertainty of hydrophone elements seriously degrades the algorithm performance. Different from conventional methods using far-field calibrating sources, this paper introduces two kinds of towed array shape estimation methods, the single near-field source-dependent method (S-NFSDM) and the double near-field source-dependent method (D-NFSDM), respectively. Under the assumption that the frequency and direction of calibrating sources are known, the proposed methods can obtain the position of every hydrophone element based on eigenvector technique and the geometric relationship between the calibrating sources and hydrophone elements. In S-NFSDM, the shape of each segment between adjacent array elements is assumed to be straight, which ensures a low computational load and high real-time capability. But in this way, S-NFSDM can only estimate the distortion of uniform linear arrays. To address this, the D-NFSDM is proposed to eliminate the linear constraint of adjacent elements in S-NFSDM. Not only can it ensure the estimation accuracy of element positions, but also estimate distorted non-uniform linear arrays. The Cramer–Rao lower bounds of the proposed S-NFSDM and D-NFSDM are derived in this paper. Numerical simulations demonstrate that the S-NFSDM and D-NFSDM have better estimation performance than the classical method and strong robustness for different array shapes. Moreover, the estimation accuracy of Multiple Signal Classification algorithm can be improved obviously through the proposed methods in the direction of arrival estimation.