Abstract
Tracking low-elevation targets over an uneven surface is challenging because of the complicated and volatile multipath signals. Multipath signals cause the amplitude and phase distortion of direct signal, which degrades the performance and generates mismatch between existing classical multipath signal and actual model. Machine learning-based methods are data-driven, they do not rely on prior assumptions about array geometries, and are expected to adapt better to array imperfections. The amplitude comparison Direction-of-Arrival (DOA) algorithm performs a few calculations, has a simple system structure, and is widely used. In this paper, an efficient DOA estimation approach based on Sum/Difference pattern is merged with deep neural network. Fully learn the potential features of the direct signal from the echo signal. In order to integrate more phase features, the covariance matrix is applied to the amplitude comparison algorithm, it can accommodate multiple snapshot signals instead of a single pulse automatically. The outputs of the deep neural network are concatenated to reconstruct a covariance matrix for DOA estimation. Moreover, the superiority in computational complexity and generalization of proposed method are proved by simulation experiments compared with state-of-the-art physics-driven and data-driven methods. Field data sets acquired from a VHF array radar are carried out to verify the proposed method satisfies practicability in the severe multipath effect.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11045-022-00861-9/MediaObjects/11045_2022_861_Fig13_HTML.png)
Similar content being viewed by others
References
Bresler, Y., & Macovski, A. (1986). Exact maximum likelihood parameter estimation of superimposed exponential signals in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(5), 1081–1089. https://doi.org/10.1109/TASSP.1986.1164949.
Chen, B., Zhao, G., & Zhang, S. (2010). Altitude measurement based on beam split and frequency diversity in VHF radar. IEEE Transactions on Aerospace and Electronic Systems, 46(1), 3–13. https://doi.org/10.1109/TAES.2010.5417144.
Huang, Z. T., Liu, Z. M., Liu, J., & Zhou, Y. Y. (2010). Performance analysis of music for non-circular signals in the presence of mutual coupling. IET Radar Sonar and Navigation, 4(5), 703–711.
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 Transactions on Vehicular Technology, 67(9), 8549–8560. https://doi.org/10.1109/TVT.2018.2851783.
Krim, H., & Viberg, M. (1996). Two decades of array signal processing research: The parametric approach. IEEE Signal Processing Magazine, 13(4), 67–94. https://doi.org/10.1109/79.526899.
Li, J. (1992). Improved angular resolution for spatial smoothing techniques. IEEE Transactions on Signal Processing, 40(12), 3078–3081. https://doi.org/10.1109/78.175754.
Liu, Z., Zhang, C., & Yu, P. S. (2018). Direction-of-arrival estimation based on deep neural networks with robustness to array imperfections. IEEE Transactions on Antennas and Propagation, 66(12), 7315–7327. https://doi.org/10.1109/TAP.2018.2874430.
Moon, S.-H., Han, D.-S., Oh, H.-S., & Cho, M.-J. (2003). Monopulse angle estimation with constrained adaptive beamforming using simple mainlobe maintenance technique. In: IEEE Military Communications Conference, 2003. MILCOM 2003., vol. 2, pp. 1365–13692. https://doi.org/10.1109/MILCOM.2003.1290425
Nielsen, R. O. (2001). Accuracy of angle estimation with monopulse processing using two beams. IEEE Transactions on Aerospace and Electronic Systems, 37(4), 1419–1423. https://doi.org/10.1109/7.976976.
Pak, J., & Shin, J. W. (2019). Sound localization based on phase difference enhancement using deep neural networks. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 27(8), 1335–1345. https://doi.org/10.1109/TASLP.2019.2919378.
Randazzo, A., Abou-Khousa, M. A., Pastorino, M., & Zoughi, R. (2007). Direction of arrival estimation based on support vector regression: Experimental validation and comparison with music. IEEE Antennas and Wireless Propagation Letters, 6, 379–382. https://doi.org/10.1109/LAWP.2007.903491.
Schmidt, R. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3), 276–280. https://doi.org/10.1109/TAP.1986.1143830.
Sebt, M., Sheikhi, A., & Nayebi, M. (2010). Robust low-angle estimation by an array radar. IET Radar, Sonar and Navigation, 4(6), 780–790.
Sherman, S. M. (1971). Complex indicated angles applied to unresolved radar targets and multipath. IEEE Transactions on Aerospace and Electronic Systems AES, 7(1), 160–170. https://doi.org/10.1109/TAES.1971.310264.
Stoica, P., & Gershman, A. B. (1999). Maximum-likelihood DOA estimation by data-supported grid search. IEEE Signal Processing Letters, 6(10), 273–275. https://doi.org/10.1109/97.789608.
Takahashi, R., Inaba, T., Takahashi, T., & Tasaki, H. (2018). Digital monopulse beamforming for achieving the CRLB for angle accuracy. IEEE Transactions on Aerospace and Electronic Systems, 54(1), 315–323. https://doi.org/10.1109/TAES.2017.2756519.
Wang, R., Wen, B., & Huang, W. (2018). A support vector regression-based method for target direction of arrival estimation from HF radar data. IEEE Geoscience and Remote Sensing Letters, 15(5), 674–678. https://doi.org/10.1109/LGRS.2018.2807405.
White, W. D. (1974). Low-angle radar tracking in the presence of multipath. IEEE Transactions on Aerospace and Electronic Systems AES, 10(6), 835–852. https://doi.org/10.1109/TAES.1974.307892.
Wu, L., Liu, Z., & Huang, Z. (2019). Deep convolution network for direction of arrival estimation with sparse prior. IEEE Signal Processing Letters, 26(11), 1688–1692. https://doi.org/10.1109/LSP.2019.2945115.
**ang, H., Chen, B., Yang, M., & Li, C. (2019). Altitude measurement based on characteristics reversal by deep neural network for VHF radar. IET Radar, Sonar & Navigation, 13, 98–103.
**ang, 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 Transactions on Vehicular Technology, 69(5), 5068–5078. https://doi.org/10.1109/TVT.2020.2977894.
**ang, H., Chen, B., Yang, M., Xu, S., & Li, Z. (2021). Improved direction-of-arrival estimation method based on LSTM neural networks with robustness to array imperfections. Applied Intelligence, 51, 4420–4433.
**ang, 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.
Xu, Z., **ong, Z., Wu, J., & **ao, S. (2016). Symmetrical difference pattern monopulse for low-angle tracking with array radar. IEEE Transactions on Aerospace and Electronic Systems, 52(6), 2676–2684. https://doi.org/10.1109/TAES.2016.140436.
Zhang, Y., & Ye, Z. (2008). Efficient method of DOA estimation for uncorrelated and coherent signals. IEEE Antennas and Wireless Propagation Letters, 7, 799–802. https://doi.org/10.1109/LAWP.2008.2001420.
Ziskind, I., & Wax, M. (1988). Maximum likelihood localization of multiple sources by alternating projection. IEEE Transactions on Acoustics, Speech, and Signal Processing, 36(10), 1553–1560. https://doi.org/10.1109/29.7543.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 61971323), the Fundamental Research Funds for the Central Universities and the Innovation Fund of **dian University. The authors sincerely express their gratitude to anonymous reviewers and the editors for their helpful and constructive comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Xu, S., Chen, B. & **ang, H. A low computational complexity DOA estimation using sum/difference pattern based on DNN. Multidim Syst Sign Process 34, 205–225 (2023). https://doi.org/10.1007/s11045-022-00861-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-022-00861-9