Skip to main content
SpringerLink
Log in

Improved direction-of-arrival estimation method based on LSTM neural networks with robustness to array imperfections

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Array imperfections severely degrade the performance of most physics-driven direction-of-arrival (DOA) methods. Deep learning-based methods do not rely on any assumptions, can learn the latent data features of a given dataset, and are expected to adapt better to array imperfections compared with existing physics-driven methods. Hence, an improved DOA estimation method based on long short-term memory (LSTM) neural networks for situations with array imperfections is proposed in this paper. Various analyses given by this paper demonstrate that the phase features are the key to DOA estimation. Considering the sequential characteristics of the moving target and the correlation of multi-frame data features, the LSTM neural networks are used to learn and enhance the phase features of sampled data. The DOA estimation accuracy and generalization capability are improved by mitigating the phase distortion using LSTM. Numerical simulations and statistical results show that the proposed method is satisfactory in terms of both the generalization capability and imperfection adaptability compared with state-of-the-art physics-driven and data-driven methods.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Johnson DH, Dan ED (1993) Array signal processing: concepts and techniques P T R. Prentice Hall

  2. Van Veen BD, Buckley KM (1988) Beamforming: a versatile approach to spatial filtering. IEEE ASSP Mag 5(2):4–24. https://doi.org/10.1109/53.665

    Article  Google Scholar 

  3. Litva J, Lo TK (1996) Digital beamforming in wireless communications. Artech House, Inc

  4. Li J, Stoica P (2006) Robust adaptive beamforming. Wiley Online Library

  5. Schmidt R (1986) Multiple emitter location and signal parameter estimation. IEEE Trans Antennas Propag 34(3):276–280. https://doi.org/10.1109/TAP.1986.1143830

    Article  Google Scholar 

  6. Roy R, Kailath T (1989) ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans Acous Speech Signal Process 37(7):984–995. https://doi.org/10.1109/29.32276

    Article  MATH  Google Scholar 

  7. Gonen E, Mendel JM (1999) Subspace-based direction finding methods. In: Madisetti VK, Williams DB (eds) The digital signal processing handbook, chapitre 62

  8. Liu Z, Zhou Y (2013) A unified framework and sparse Bayesian perspective for direction-of-arrival estimation in the presence of array imperfections. IEEE Trans Signal Process 61(15):3786–3798. https://doi.org/10.1109/TSP.2013.2262682

    Article  MathSciNet  MATH  Google Scholar 

  9. Carlin M, Rocca P, Oliveri G, Viani F, Massa A (2013) Directions-of-arrival estimation through Bayesian compressive sensing strategies. IEEE Trans Antennas Propag 61(7):3828–3838. https://doi.org/10.1109/TAP.2013.2256093

    Article  MathSciNet  MATH  Google Scholar 

  10. Yang Z, Xie L, Zhang C (2013) Off-grid direction of arrival estimation using sparse Bayesian inference. IEEE Trans Signal Process 61(1):38–43. https://doi.org/10.1109/TSP.2012.2222378

    Article  MathSciNet  MATH  Google Scholar 

  11. Malioutov D, Cetin M, Willsky AS (2005) A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans Signal Process 53(8):3010–3022. https://doi.org/10.1109/TSP.2005.850882

    Article  MathSciNet  MATH  Google Scholar 

  12. Ziskind I, Wax M (1988) Maximum likelihood localization of multiple sources by alternating projection. IEEE Trans Acous Speech Signal Process 36(10):1553–1560. https://doi.org/10.1109/29.7543

    Article  MATH  Google Scholar 

  13. Jaffer AG (1988) Maximum likelihood direction finding of stochastic sources: a separable solution. In: ICASSP-88., International conference on acoustics, speech, and signal processing. https://doi.org/10.1109/ICASSP.1988.197258, vol 5, pp 2893–2896

  14. Stoica P, Nehorai A (1988) Music, maximum likelihood and cramer-rao bound. In: ICASSP-88., International conference on acoustics, speech, and signal processing. https://doi.org/10.1109/ICASSP.1988.197097, vol 4, pp 2296–2299

  15. Miller MI, Fuhrmann DR (1990) Maximum-likelihood narrow-band direction finding and the em algorithm. IEEE Trans Acous Speech Signal Process 38(9):1560–1577. https://doi.org/10.1109/29.60075

    Article  MATH  Google Scholar 

  16. Krim H, Viberg M (1996) Two decades of array signal processing research: the parametric approach. IEEE Signal Process Mag 13(4):67–94. https://doi.org/10.1109/79.526899

    Article  Google Scholar 

  17. Allen B, Ghavami M (2005) Adaptive array systems: fundamentals and applications. John Wiley & Sons

  18. Viberg M, Swindlehurst AL (1994) Analysis of the combined effects of finite samples and model errors on array processing performance. IEEE Trans Signal Process 42(11):3073–3083. https://doi.org/10.1109/78.330367

    Article  Google Scholar 

  19. Liu ZM, Huang ZT, Zhou YY (2009) Bias analysis of MUSIC in the presence of mutual coupling. IET Signal Process 3(1):74–84. https://doi.org/10.1049/iet-spr:20070213

    Article  Google Scholar 

  20. Huang Z, Liu Z, Liu J, Zhou YY (2010) Performance analysis of MUSIC for non-circular signals in the presence of mutual coupling. IET Radar Sonar Navigation 4(5):703–711. https://doi.org/10.1049/iet-rsn.2009.0003

    Article  Google Scholar 

  21. Friedlander B, Weiss AJ (1991) Direction finding in the presence of mutual coupling. IEEE Trans Antennas Propag 39(3):273–284. https://doi.org/10.1109/8.76322

    Article  Google Scholar 

  22. Porat B, Friedlander B (1997) Accuracy requirements in off-line array calibration. IEEE Trans Aerosp Electron Syst 33(2):545–556. https://doi.org/10.1109/7.575894

    Article  Google Scholar 

  23. Lin M, Yang L (2006) Blind calibration and DOA estimation with uniform circular arrays in the presence of mutual coupling. IEEE Antennas Wireless Propag Lett 5:315–318. https://doi.org/10.1109/LAWP.2006.878898

    Article  Google Scholar 

  24. Flanagan BP, Bell KL (2001) Array self-calibration with large sensor position errors. Signal Process 81(10):2201–2214. https://doi.org/10.1016/S0165-1684(01)00121-9. http://www.sciencedirect.com/science/article/pii/S0165168401001219

    Article  Google Scholar 

  25. Ng BC, See CMS (1996) Sensor-array calibration using a maximum-likelihood approach. IEEE Trans Antennas Propag 44(6):827–835. https://doi.org/10.1109/8.509886

    Article  Google Scholar 

  26. Stavropoulos KV, Manikas A (2000) Array calibration in the presence of unknown sensor characteristics and mutual coupling. In: 2000 10th European signal processing conference, pp 1–4

  27. Huang K, Wu Y, Wang C, et al. (2020) A projective and discriminative dictionary learning for high-dimensional process monitoring with industrial applications. IEEE Trans Industr Inform, 1–1. https://doi.org/10.1109/TII.2020.2992728

  28. Wu X, Zhong M, Guo Y, et al. (2020) The assessment of small bowel motility with attentive deformable neural network. Inform Sci 508:22–32. https://doi.org/10.1016/j.ins.2019.08.059

    Article  Google Scholar 

  29. Xiang H, Chen B, Yang T, Liu D (2020) Phase enhancement model based on supervised convolutional neural network for coherent DOA estimation. Appl Intell 50:2411–2422. https://doi.org/10.1007/s10489-020-01678-4

    Article  Google Scholar 

  30. Liu Y, Zhou B, Han C, Guo T, Qin J (2020) A novel method based on deep learning for aligned fingerprints matching. Appl Intell 50:397–416. https://doi.org/10.1007/s10489-019-01530-4

    Article  Google Scholar 

  31. Kuang P, Ma T, Chen Z, Li F (2019) Image super-resolution with densely connected convolutional networks. Appl Intell 49:125–136. https://doi.org/10.1007/s10489-018-1234-y

    Article  Google Scholar 

  32. Noda K, Yamaguchi Y, Nakadai K, et al. (2015) Audio-visual speech recognition using deep learning. Appl Intell 42:722–737. https://doi.org/10.1007/s10489-014-0629-7

    Article  Google Scholar 

  33. Brklja B, Janev M, Obradovi R, et al. (2014) Sparse representation of precision matrices used in GMMs. Appl Intell 41:956–973. https://doi.org/10.1007/s10489-014-0581-6

    Article  Google Scholar 

  34. Pastorino M, Randazzo A (2005) A smart antenna system for direction of arrival estimation based on a support vector regression. IEEE Trans Antennas Propag 53(7):2161–2168. https://doi.org/10.1109/TAP.2005.850735

    Article  Google Scholar 

  35. Randazzo A, Abou-Khousa MA, Pastorino M, Zoughi R (2007) Direction of arrival estimation based on support vector regression: experimental validation and comparison with MUSIC. IEEE Antennas Wireless Propag Lett 6:379–382. https://doi.org/10.1109/LAWP.2007.903491

    Article  Google Scholar 

  36. Terabayashi K, Natsuaki R, Hirose A (2014) Ultrawideband direction-of-arrival estimation using complex-valued spatiotemporal neural networks. IEEE Transon Neural Netw Learn Syst 25(9):1727–1732. https://doi.org/10.1109/TNNLS.2014.2313869

    Article  Google Scholar 

  37. Gao Y, Hu D, Chen Y, Ma Y (2017) Gridless one-bit DOA estimation exploiting SVM approach. IEEE Commun Lett 21(10):2210–2213. https://doi.org/10.1109/LCOMM.2017.2723359

    Article  Google Scholar 

  38. nleren MF, Yaldiz E (2016) Direction of arrival estimation by using artificial neural networks. In: 2016 European modelling symposium (EMS). https://doi.org/10.1109/EMS.2016.049, pp 242–245

  39. Southall HL, Simmers JA, O’Donnell TH (1995) Direction finding in phased arrays with a neural network beamformer. IEEE Trans Antennas Propag 43(12):1369–1374. https://doi.org/10.1109/8.475924

    Article  Google Scholar 

  40. El Zooghby AH, Christodoulou CG, Georgiopoulos M (2000) A neural network-based smart antenna for multiple source tracking. IEEE Trans Antennas Propag 48(5):768–776. https://doi.org/10.1109/8.855496

    Article  Google Scholar 

  41. Huang H, Yang J, Huang H, Song Y, Gui G (2018) Deep learning for super-resolution channel estimation and DOA estimation based massive MIMO system. IEEE Trans Veh Technol 67(9):8549–8560. https://doi.org/10.1109/TVT.2018.2851783

    Article  Google Scholar 

  42. Wu L, Huang Z (2019) Coherent SVR learning for wideband direction-of-arrival estimation. IEEE Signal Process Lett 26(4):642–646. https://doi.org/10.1109/LSP.2019.2901641

    Article  MathSciNet  Google Scholar 

  43. Xiang H, Chen B, Yang M, Li C (2019) Altitude measurement based on characteristics reversal by deep neural network for VHF radar. IET Radar Sonar Navig 13(1):98–103. https://doi.org/10.1049/iet-rsn.2018.5121

    Article  Google Scholar 

  44. Xiang H, Chen B, Xu H (2019) Spatial distribution feature learning for DOA estimation in multi-path environment. In: 2019 IEEE International conference on computational electromagnetics (ICCEM). https://doi.org/10.1109/COMPEM.2019.8778948, pp 1–4

  45. Xiang H, Chen B, Yang M, Yang T, Liu D (2019) A novel phase enhancement method for low-angle estimation based on supervised DNN learning. IEEE Access 7:82329–82336. https://doi.org/10.1109/ACCESS.2019.2924156

    Article  Google Scholar 

  46. Agatonovi M, Stankovi Z, Milovanovi B, Donov N (2011) DOA estimation using radial basis function neural networks as uniform circular antenna array signal processor. In: 2011 10th International conference on telecommunication in modern satellite cable and broadcasting services (TELSIKS). https://doi.org/10.1109/TELSKS.2011.6143173, vol 2, pp 544–547

  47. Wu L, Liu Z, Huang Z (2019) Deep convolution network for direction of arrival estimation with sparse prior. IEEE Signal Process Lett 26(11):1688–1692

    Article  Google Scholar 

  48. Elbir AM (2020) DeepMUSIC: multiple signal classification via deep learning. IEEE Sensors Lett 4(4):1–4

    Article  Google Scholar 

  49. Liu Z, Zhang C, Yu PS (2018) Direction-of-arrival estimation based on deep neural networks with robustness to array imperfections. IEEE Trans Antennas Propag 66(12):7315–7327

    Article  Google Scholar 

  50. Wang Y, Wang J, Zhang W, Yang J, Gui G (2020) Deep learning-based cooperative automatic modulation classification method for MIMO systems. IEEE Trans Veh Technol, 4575–4579. https://doi.org/10.1109/TVT.2020.2976942

  51. Wu X, Zhong M, Guo Y et al (2020) Non-ferrous metals price forecasting based on variational mode decomposition and LSTM network. Knowl-Based Syst 188:105006. https://doi.org/10.1016/j.knosys.2019.105006

    Article  Google Scholar 

  52. Milan A, Rezatofighi SH, Dick A, Reid I, Schindler K (2017) Online multi-target tracking using recurrent neural networks. In: Thirty-First AAAI conference on artificial intelligence

  53. Ondruska P, Posner I (2016) Deep tracking: seeing beyond seeing using recurrent neural networks. In: Thirtieth AAAI conference on artificial intelligence

  54. Yang T, Chan AB (2017) Recurrent filter learning for visual tracking. In: 2017 IEEE International conference on computer vision workshops (ICCVW). https://doi.org/10.1109/ICCVW.2017.235, pp 2010–2019

  55. Gao C, Yan J, Zhou S, Chen B, Liu H (2019) Long short-term memory-based recurrent neural networks for nonlinear target tracking. Signal Process 164:67–73. https://doi.org/10.1016/j.sigpro.2019.05.027

    Article  Google Scholar 

  56. Gao C, Yan J, Zhou S, Varshney PK, Liu H (2019) Long short-term memory-based deep recurrent neural networks for target tracking. Inform Sci 502:279–296. https://doi.org/10.1016/j.ins.2019.06.039

    Article  Google Scholar 

  57. Tang Y, Lu Y (2014) Multi-resolution composite array for digital beamforming with high angular-resolution. IEEE Trans Antennas Propag 62(8):4377–4380. https://doi.org/10.1109/TAP.2014.2323427

    Article  Google Scholar 

  58. Xiang H, Chen B, Yang T, Liu D (2020) Improved de-multipath neural network models with self-paced feature-to-feature learning for doa estimation in multipath environment. IEEE Trans Veh Technol 69 (5):5068–5078

    Article  Google Scholar 

  59. Werbos PJ (1990) Backpropagation through time: what it does and how to do it. Proc IEEE 78 (10):1550–1560. https://doi.org/10.1109/5.58337

    Article  Google Scholar 

  60. Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. arXiv:1412.6980

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61571344, No. 61971323), Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University. The authors sincerely express their gratitude to anonymous reviewers and editors for their helpful and constructive comments and suggestions.

Author information

Authors and Affiliations

  1. National Laboratory of Radar Signal Processing, Xidian University, Xi’an, 710071, China

    Houhong Xiang, Baixiao Chen, Minglei Yang & Saiqin Xu

  2. Air and Missile Defense College, Air Force Engineering University, Xi’an, 710051, China

    Zhengjie Li

Authors
  1. Houhong Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baixiao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Minglei Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Saiqin Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhengjie Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baixiao Chen.

Ethics declarations

Conflict of interests

The authors declared that they have no conflicts of interest.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiang, H., Chen, B., Yang, M. et al. Improved direction-of-arrival estimation method based on LSTM neural networks with robustness to array imperfections. Appl Intell 51, 4420–4433 (2021). https://doi.org/10.1007/s10489-020-02124-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-020-02124-1

Keywords

Search

Navigation