Circuits, Systems, and Signal Processing

, Volume 38, Issue 1, pp 153–172 | Cite as

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

  • Chunyue Li
  • Jiajia JiangEmail author
  • Fajie Duan
  • Xianquan Wang
  • Ling Ma
  • Lingran Bu
  • Zhongbo Sun


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.


Array shape estimation Near-field calibrating source CRLB DOA estimation 



This work was supported in part by the TianJin Natural Science Foundations of China under Grant No. 17JCQNJC01100, National Natural Science Foundations of China under Grant Nos. 61501319, 51775377, 61505140, National Key Research and Development Plan (2017YFF0204800), Young Elite Scientists Sponsorship Program By Cast of China under Grant No. 2016QNRC001, Open Project (MOMST2015-7) of Key Laboratory of Micro-Opto-Electro Mechanical System Technology, Tianjin University, Ministry of Education, Photoelectric Information and Instrument–Engineering Research Center of Beijing Open Project No. GD2015007.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Lab of Precision Measuring Technology and InstrumentsTianjin UniversityTianjinChina

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