On Robust Beamforming for Distorted Towed Linear Array Using Product Theorem


To solve the beamforming performance degradation problem of the towed linear array caused by the shape distortion, we propose a robust beamforming way for distorted towed linear array. The proposed method basically uses the segmented processing, which can be divided into 3 steps. Firstly, towed linear array is divided into sub-arrays. Then, the weights of sub-arrays are obtained and outputs of beamforming of sub-arrays are obtained. In the end, according to the principle of the product theorem, the correlation calculations are performed on the output of the sub-array. Due to the adoption of sub-array correlation calculations, the proposed method can upgrade beamforming performance. Compared with the traditional distortion array processing method, the proposed method can improve the local signal-to-interference plus noise ratio (SINR) by about 2–3 dB. Simulation and sea trial data verify the effectiveness of the proposed method.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


  1. 1.

    Liu, Q., Li, L., Huizhi, C.A.I.: The array signal simulator design of passive towed sonar. Tech. Acoust. 28(4), 463–466 (2009). https://doi.org/10.3969/j.issn1000-3630.2009.04.005

    Article  Google Scholar 

  2. 2.

    Wang, S., Wang, X., Pang, Y.: Research on precise array shape estimation system based on Doppler shift and stochastic resonance technique. Tech. Acoust. 37(3), 222–226 (2018). https://doi.org/10.16300/j.cnki.1000-3630.2018.03.005

    Article  Google Scholar 

  3. 3.

    Liu, G., Wang, S., Yu, X.: A robust beamforming technique for flexible arrays. Appl. Acoust. 30(1), 26–30 (2011)

    Google Scholar 

  4. 4.

    Felisberto, P., Jesus, S.M.: Towed array beamforming during ship’s maneuvering. IEE Proc. Radar Sonar Navig. 143(3), 210–215 (1996)

    Article  Google Scholar 

  5. 5.

    Bo, L., Zhang, X., Xiong, J.: Robust capon beamforming for towed array sonar during maneuvering. J. Electr. Inf. Technol. 40(10), 2423–2429 (2018). https://doi.org/10.11999/jeit180022

    Article  Google Scholar 

  6. 6.

    Howard, B.E., Sych, J.M.: Calculation of the shape of towed underwater acoustic array. IEEE J. Ocean. Eng. 17(2), 193–203 (1992). https://doi.org/10.1109/48.126976

    Article  Google Scholar 

  7. 7.

    Wang, S.: Effect of array shape distortion on 3D detection performance of towed line array and compensation technique. Telecommun. Eng 58(2), 145–151 (2018). https://doi.org/10.3969/j.issn.1001-893x.2018.02.005

    Article  Google Scholar 

  8. 8.

    Rao W.: Investigation of the method of towed array shape estimation. [Master dissertation]. National University of Defense Technology, (2007)

  9. 9.

    Wang Y.: The research for array shape estimation of towed linear array sonar. [Master dissertation]. Harbin Engineering University (2017)

  10. 10.

    Teng, Y., Zeng, S.: A shape estimation algorithm of deformed towed array in passive sonar. J. Unmanned Undersea Syst. 26(5), 309–503 (2018). https://doi.org/10.11993/j.issn.2096-3920.2018.05.020

    Article  Google Scholar 

  11. 11.

    Ferguson, B.G., Gray, D.A., Riley, J.L.: Comparison of sharpness and eigenvector methods for towed array shape estimation. J. Acoust. Soc. Am. 91(3), 1565–1570 (1992). https://doi.org/10.1121/1.402437

    Article  Google Scholar 

  12. 12.

    Lai, Z.: Method for array shape-estimation based on heading sensor data. Ship Sci. Technol. 42(1), 172–174 (2020)

    Google Scholar 

  13. 13.

    Dong Y.: Study on single towed line array shape estimation and port/starboard rapid discrimination. [Master dissertation]. Harbin Engineering University (2013)

  14. 14.

    Smith, J.J., Leung, Y.H., Cantoni, A.: The CramerRao lower bound for towed array shape estimation with a single source. IEEE Trans. Signal Process. 44(4), 1033–1036 (1996). https://doi.org/10.1109/78.492565

    Article  Google Scholar 

  15. 15.

    Du, X.X., Cui, H., Zhang, Z.D.: A numerical method for analyzing the influence of underwater vehicle flowfieldon dynamic behavior of towed sonar cable array. Ocean Eng. 175, 163–175 (2019)

    Article  Google Scholar 

  16. 16.

    Paidoussis, M.P.: Dynamics of flexible slenders cylinder in axial flow Part I. Theory. J. Fluid Mech. 26(4), 717–736 (1996)

    MathSciNet  Article  Google Scholar 

  17. 17.

    Gray, D.A., Anderson, B.D.O., Bitmead, R.R.: Towed array shape estimation using Kalmanfilters-Theoretical models. IEEE J. Ocean. Eng. 18(4), 543–556 (1993)

    Article  Google Scholar 

  18. 18.

    Riley, J.L., Gray, D.A.: Towed array shape estimation using Kalman filters-Experimental Investigation. IEEE J. Ocean. Eng. 18(4), 572–581 (1993)

    Article  Google Scholar 

  19. 19.

    Lu, F., Milios, E., Stergiopoulos, S., et al.: New towed-array shape-estimation scheme for real-time sonar systems. IEEE J Ocean. Eng. 28(3), 552–563 (2003)

    Article  Google Scholar 

  20. 20.

    Dong Y.F.: Study on single towed line array shape estimation and port/starboard rapid discrimination. [Master dissertation]. Harbin Engineering University (2013)

  21. 21.

    Ll, Q.H.: On the problem of ehoiees of operatioual mode for towed line arrav with distorted shape. Acta Acust. 16(1), 31–36 (1991)

    Google Scholar 

  22. 22.

    Zhou, F.H.: Hydroacoustic Transducer and Array. National Defense Industry Press, Beijing (1984)

    Google Scholar 

Download references


This work was supported by the National Natural Science Foundation of China (Grant No. 51679247).

Author information



Corresponding author

Correspondence to Gaoxiang Xing.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lu, D., Xing, G., Luo, T. et al. On Robust Beamforming for Distorted Towed Linear Array Using Product Theorem. Acoust Aust (2020). https://doi.org/10.1007/s40857-020-00189-z

Download citation


  • Linear array
  • Array shape distortion
  • Sub-array
  • Product theorem
  • Secondary beamforming