Skip to main content
Erschienen in:

16.07.2024

Method for DOA Estimation of Coprime Arrays Through Joint Auxiliary Arrays with Atomic Norm Minimization in the Presence of Gain-Phase Errors

verfasst von: Qiang Guo, Wenjie Zhao, Liangang Qi, Yani Wang, Kaliuzhnyi Mykola, Stepan Duplii

Erschienen in: Circuits, Systems, and Signal Processing | Ausgabe 10/2024

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Coprime arrays (CPA) are extensively applied to estimate the direction of arrival (DOA). Yet, the effectiveness of existing DOA estimation algorithms for coprime arrays is predicated on the precise calibration of the array. Gain-phase errors in the sensors, when present, are magnified by the co-array, greatly impacting the performance of DOA estimation algorithms. To address the issue, this paper proposes a joint DOA estimation algorithm combining auxiliary arrays with atomic norm minimization. Exploiting the sub-array decomposition feature of coprime array, gain-phase error estimation is accomplished with the addition of precisely calibrated auxiliary arrays. Besides, the estimated gain-phase errors are used to correct the covariance of the signals received by the array. By combining array interpolation, all virtual sensors are fully utilized, and the interpolated virtual received signals are reconstructed into a Toeplitz matrix. The covariance matrix of these signals is then refined using atomic norm minimization, preparing the data for the final DOA estimation performed by subspace algorithms. In addition, for comparative analysis, the Cramér–Rao bound has also been derived under the condition of gain-phase errors, providing a benchmark for the performance of the proposed algorithm.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

ATZelektronik

Die Fachzeitschrift ATZelektronik bietet für Entwickler und Entscheider in der Automobil- und Zulieferindustrie qualitativ hochwertige und fundierte Informationen aus dem gesamten Spektrum der Pkw- und Nutzfahrzeug-Elektronik. 

Lassen Sie sich jetzt unverbindlich 2 kostenlose Ausgabe zusenden.

ATZelectronics worldwide

ATZlectronics worldwide is up-to-speed on new trends and developments in automotive electronics on a scientific level with a high depth of information. 

Order your 30-days-trial for free and without any commitment.

Weitere Produktempfehlungen anzeigen
Literatur
1.
Zurück zum Zitat S.H. Cao, Z.F. Ye, D.Y. Xu et al., A hadamard product based method for doa estimation and gain-phase error calibration. IEEE Trans. Aerosp. Electron. Syst. 49(2), 1224–1233 (2013)CrossRef S.H. Cao, Z.F. Ye, D.Y. Xu et al., A hadamard product based method for doa estimation and gain-phase error calibration. IEEE Trans. Aerosp. Electron. Syst. 49(2), 1224–1233 (2013)CrossRef
2.
Zurück zum Zitat H. Chen, H.G. Lin, W. Liu, Q. Wang, Q. Shen, G. Wang, Augmented multi-subarray dilated nested array with enhanced degrees of freedom and reduced mutual coupling. IEEE Trans. Signal Process. 72, 1387–1399 (2024)MathSciNetCrossRef H. Chen, H.G. Lin, W. Liu, Q. Wang, Q. Shen, G. Wang, Augmented multi-subarray dilated nested array with enhanced degrees of freedom and reduced mutual coupling. IEEE Trans. Signal Process. 72, 1387–1399 (2024)MathSciNetCrossRef
3.
Zurück zum Zitat P. Chen, Z.M. Chen, Z.X. Cao, X.B. Wang, A new atomic norm for DOA estimation with gain-phase errors. IEEE Trans. Signal Process. 68, 4293–4306 (2020)MathSciNetCrossRef P. Chen, Z.M. Chen, Z.X. Cao, X.B. Wang, A new atomic norm for DOA estimation with gain-phase errors. IEEE Trans. Signal Process. 68, 4293–4306 (2020)MathSciNetCrossRef
4.
Zurück zum Zitat B. Friedlander, A sensitivity analysis of the MUSIC algorithm. IEEE Trans. Acoust. Speech Signal Process. 38(10), 1740–1751 (1990)CrossRef B. Friedlander, A sensitivity analysis of the MUSIC algorithm. IEEE Trans. Acoust. Speech Signal Process. 38(10), 1740–1751 (1990)CrossRef
5.
Zurück zum Zitat B. Friedlander, On the sensitivity of covariance based direction finding to gain and phase perturbations. ICASSP, IEEE Int. Conf. Acoust. Speech Signal Process. Proc. 4, 445–448 (1992) B. Friedlander, On the sensitivity of covariance based direction finding to gain and phase perturbations. ICASSP, IEEE Int. Conf. Acoust. Speech Signal Process. Proc. 4, 445–448 (1992)
6.
Zurück zum Zitat M.C. Fu, Z. Zheng, K. Zhang, W.Q. Wang, Coarray interpolation for direction finding and polarization estimation using coprime EMVS array via atomic norm minimization. IEEE Trans. Veh. Technol. 72(8), 10162–10172 (2023)CrossRef M.C. Fu, Z. Zheng, K. Zhang, W.Q. Wang, Coarray interpolation for direction finding and polarization estimation using coprime EMVS array via atomic norm minimization. IEEE Trans. Veh. Technol. 72(8), 10162–10172 (2023)CrossRef
7.
Zurück zum Zitat Y.D. Guo, X.W. Hu, W.K. Feng, J. Gong, Low-complexity 2D DOA estimation and self-calibration for uniform rectangle array with gain-phase error. Remote Sens. 14(13), 3010 (2022)CrossRef Y.D. Guo, X.W. Hu, W.K. Feng, J. Gong, Low-complexity 2D DOA estimation and self-calibration for uniform rectangle array with gain-phase error. Remote Sens. 14(13), 3010 (2022)CrossRef
8.
Zurück zum Zitat B. Hu, X.Y. Shen, M. Jiang, K.H. Zhao, Off-grid DOA estimation based on compressed sensing on multipath environment. Int. J. Antennas Propag. 2023, 9315869 (2023)CrossRef B. Hu, X.Y. Shen, M. Jiang, K.H. Zhao, Off-grid DOA estimation based on compressed sensing on multipath environment. Int. J. Antennas Propag. 2023, 9315869 (2023)CrossRef
9.
Zurück zum Zitat B. Hu, X.C. Wu, X. Zhang, Q. Yang, W.B. Deng, DOA estimation based on compressed sensing with gain/phase uncertainties. IET Radar Sonar Navig. 12(11), 1346–1352 (2018)CrossRef B. Hu, X.C. Wu, X. Zhang, Q. Yang, W.B. Deng, DOA estimation based on compressed sensing with gain/phase uncertainties. IET Radar Sonar Navig. 12(11), 1346–1352 (2018)CrossRef
10.
Zurück zum Zitat J.X. Kou, M. Li, C.L. Jiang, Robust direction-of-arrival estimation for coprime array in the presence of miscalibrated sensors. IEEE Access 8, 27152–27162 (2020)CrossRef J.X. Kou, M. Li, C.L. Jiang, Robust direction-of-arrival estimation for coprime array in the presence of miscalibrated sensors. IEEE Access 8, 27152–27162 (2020)CrossRef
11.
Zurück zum Zitat J.X. Kou, M. Li, C.L. Jiang, A robust DOA estimator based on compressive sensing for coprime array in the presence of miscalibrated sensors. Sensors (Switzerland) 19(16), 3538 (2019)CrossRef J.X. Kou, M. Li, C.L. Jiang, A robust DOA estimator based on compressive sensing for coprime array in the presence of miscalibrated sensors. Sensors (Switzerland) 19(16), 3538 (2019)CrossRef
12.
Zurück zum Zitat B. Liao, G.S. Liao, Method for array gain and phase uncertainties calibration based on ISM and ESPRIT. J. Syst. Eng. Electron. 20(2), 223–228 (2009) B. Liao, G.S. Liao, Method for array gain and phase uncertainties calibration based on ISM and ESPRIT. J. Syst. Eng. Electron. 20(2), 223–228 (2009)
13.
Zurück zum Zitat C.L. Liu, P.P. Vaidyanathan, Super nested arrays: linear sparse arrays with reduced mutual coupling—part I: fundamentals. IEEE Trans. Signal Process. 64(15), 3997–4012 (2016)MathSciNetCrossRef C.L. Liu, P.P. Vaidyanathan, Super nested arrays: linear sparse arrays with reduced mutual coupling—part I: fundamentals. IEEE Trans. Signal Process. 64(15), 3997–4012 (2016)MathSciNetCrossRef
14.
Zurück zum Zitat C.L. Liu, P.P. Vaidyanathan, Remarks on the spatial smoothing step in coarray MUSIC. IEEE Signal Process. Lett. 22(9), 1438–1442 (2015)CrossRef C.L. Liu, P.P. Vaidyanathan, Remarks on the spatial smoothing step in coarray MUSIC. IEEE Signal Process. Lett. 22(9), 1438–1442 (2015)CrossRef
15.
Zurück zum Zitat C.L. Liu, P. P. Vaidyanathan, P. Pal, Coprime coarray interpolation for DOA estimation via nuclear norm minimization, in Proceedings—IEEE International Symposium on Circuits and Systems, 2016-July, pp. 2639–2642 (2016) C.L. Liu, P. P. Vaidyanathan, P. Pal, Coprime coarray interpolation for DOA estimation via nuclear norm minimization, in Proceedings—IEEE International Symposium on Circuits and Systems, 2016-July, pp. 2639–2642 (2016)
16.
Zurück zum Zitat Y.X. Li, Y.J. Chi, Off-the-grid line spectrum denoising and estimation with multiple measurement vectors. IEEE Trans. Signal Process. 64(5), 1257–1269 (2016)MathSciNetCrossRef Y.X. Li, Y.J. Chi, Off-the-grid line spectrum denoising and estimation with multiple measurement vectors. IEEE Trans. Signal Process. 64(5), 1257–1269 (2016)MathSciNetCrossRef
17.
Zurück zum Zitat F. Li, R.J. Vaccaro, Sensitivity analysis of DOA estimation algorithms to sensor errors. IEEE Trans. Aerosp. Electron. Syst. 28(3), 708–717 (1992)CrossRef F. Li, R.J. Vaccaro, Sensitivity analysis of DOA estimation algorithms to sensor errors. IEEE Trans. Aerosp. Electron. Syst. 28(3), 708–717 (1992)CrossRef
18.
Zurück zum Zitat C. Liu, X. Tang, Z. Zhang, A new gain-phase error pre-calibration method for uniform linear arrays. Sensors 23(5), 2544 (2023)CrossRef C. Liu, X. Tang, Z. Zhang, A new gain-phase error pre-calibration method for uniform linear arrays. Sensors 23(5), 2544 (2023)CrossRef
19.
Zurück zum Zitat A.F. Liu, G.S. Liao, C. Zeng, Z.W. Yang, Q. Xu, An eigenstructure method for estimating doa and sensor gain-phase errors. IEEE Trans. Signal Process. 59(12), 5944–5956 (2011)MathSciNetCrossRef A.F. Liu, G.S. Liao, C. Zeng, Z.W. Yang, Q. Xu, An eigenstructure method for estimating doa and sensor gain-phase errors. IEEE Trans. Signal Process. 59(12), 5944–5956 (2011)MathSciNetCrossRef
20.
Zurück zum Zitat C. F. Mecklenbräuker, P. Gerstoft, E. Ollila, Y. Park. Robust and Sparse M-Estimation of DOA. arXiv. (2023) C. F. Mecklenbräuker, P. Gerstoft, E. Ollila, Y. Park. Robust and Sparse M-Estimation of DOA. arXiv. (2023)
21.
Zurück zum Zitat P. Pal, P. P. Vaidyanathan, Coprime sampling and the music algorithm. 2011 Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2011 - Proceedings, 289-294 (2011) P. Pal, P. P. Vaidyanathan, Coprime sampling and the music algorithm. 2011 Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2011 - Proceedings, 289-294 (2011)
22.
Zurück zum Zitat P. Pal, P.P. Vaidyanathan, Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 58(8), 4167–4181 (2010)MathSciNetCrossRef P. Pal, P.P. Vaidyanathan, Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 58(8), 4167–4181 (2010)MathSciNetCrossRef
23.
Zurück zum Zitat J. Pierre, M. Kaveh, Experimental performance of calibration and direction-finding algorithms. Proc. ICASSP IEEE Int. Conf. Acoust. Speech Signal Process. 2, 1365–1368 (1991) J. Pierre, M. Kaveh, Experimental performance of calibration and direction-finding algorithms. Proc. ICASSP IEEE Int. Conf. Acoust. Speech Signal Process. 2, 1365–1368 (1991)
24.
Zurück zum Zitat S. Qin, Y.D. Zhang, M.G. Amin, Generalized coprime array configurations for direction-of-arrival estimation. IEEE Trans. Signal Process. 63(6), 1377–1390 (2015)MathSciNetCrossRef S. Qin, Y.D. Zhang, M.G. Amin, Generalized coprime array configurations for direction-of-arrival estimation. IEEE Trans. Signal Process. 63(6), 1377–1390 (2015)MathSciNetCrossRef
25.
Zurück zum Zitat H. Qiao, P. Pal. Unified analysis of co-array interpolation for direction-of-arrival estimation. ICASSP, in IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, pp. 3056–3060 (2017) H. Qiao, P. Pal. Unified analysis of co-array interpolation for direction-of-arrival estimation. ICASSP, in IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, pp. 3056–3060 (2017)
26.
Zurück zum Zitat P. Stoica, A. Nehorai, MUSIC, maximum likelihood, and Cramer-Rao bound: further results and comparisons. IEEE Trans. Acoust. Speech Signal Process. 38(12), 2140–2150 (1990)CrossRef P. Stoica, A. Nehorai, MUSIC, maximum likelihood, and Cramer-Rao bound: further results and comparisons. IEEE Trans. Acoust. Speech Signal Process. 38(12), 2140–2150 (1990)CrossRef
27.
Zurück zum Zitat Z.G. Shi, C.W. Zhou, Y.J. Gu, N.A. Goodman, F. Qu, Source estimation using coprime array: a sparse reconstruction perspective. IEEE Sens. J. 17(3), 755–765 (2017)CrossRef Z.G. Shi, C.W. Zhou, Y.J. Gu, N.A. Goodman, F. Qu, Source estimation using coprime array: a sparse reconstruction perspective. IEEE Sens. J. 17(3), 755–765 (2017)CrossRef
28.
Zurück zum Zitat F.G. Sun, B. Gao, L.Z. Chen, P. Lan, A low-complexity ESPRIT-based DOA estimation method for co-prime linear arrays. Sensors (Switzerland) 16(9), 1367 (2016)CrossRef F.G. Sun, B. Gao, L.Z. Chen, P. Lan, A low-complexity ESPRIT-based DOA estimation method for co-prime linear arrays. Sensors (Switzerland) 16(9), 1367 (2016)CrossRef
29.
Zurück zum Zitat B. Sun, DOA estimation method for coprime array under gain and phase error. Syst. Eng. Electron. 43(12), 3488–3494 (2021). (in chinese) B. Sun, DOA estimation method for coprime array under gain and phase error. Syst. Eng. Electron. 43(12), 3488–3494 (2021). (in chinese)
30.
Zurück zum Zitat Z. Tan, Y.C. Eldar, A. Nehorai, Direction of arrival estimation using co-prime arrays: a super resolution viewpoint. IEEE Trans. Signal Process. 62(21), 5565–5576 (2014)MathSciNetCrossRef Z. Tan, Y.C. Eldar, A. Nehorai, Direction of arrival estimation using co-prime arrays: a super resolution viewpoint. IEEE Trans. Signal Process. 62(21), 5565–5576 (2014)MathSciNetCrossRef
31.
Zurück zum Zitat P.P. Vaidyanathan, P. Pal, Sparse sensing with co-pprime samplers and arrays. IEEE Trans. Signal Process. 59(2), 573–586 (2011)MathSciNetCrossRef P.P. Vaidyanathan, P. Pal, Sparse sensing with co-pprime samplers and arrays. IEEE Trans. Signal Process. 59(2), 573–586 (2011)MathSciNetCrossRef
32.
Zurück zum Zitat M.Z. Wang, A. Nehorai, Coarrays, MUSIC, and the Cramér-Rao Bound. IEEE Trans. Signal Process. 65(4), 933–946 (2017)MathSciNetCrossRef M.Z. Wang, A. Nehorai, Coarrays, MUSIC, and the Cramér-Rao Bound. IEEE Trans. Signal Process. 65(4), 933–946 (2017)MathSciNetCrossRef
33.
Zurück zum Zitat M.Z. Wang, Z. Zhang, A. Nehorai, Performance analysis of coarray-based MUSIC in the presence of sensor location errors. IEEE Trans. Signal Process. 66(12), 3074–3085 (2018)MathSciNetCrossRef M.Z. Wang, Z. Zhang, A. Nehorai, Performance analysis of coarray-based MUSIC in the presence of sensor location errors. IEEE Trans. Signal Process. 66(12), 3074–3085 (2018)MathSciNetCrossRef
34.
Zurück zum Zitat Y.Z. Yang, J.H. Wang, W.J. Cui, B. Ba, Coherent direction of arrival estimation based on low-rank matrix recovery utilising L\(<\)inf\(>\)2\(<\)/inf\(>\)-norm with moving coprime arrays. IET Radar Sonar Navig. 17(11), 1646–1653 (2023)CrossRef Y.Z. Yang, J.H. Wang, W.J. Cui, B. Ba, Coherent direction of arrival estimation based on low-rank matrix recovery utilising L\(<\)inf\(>\)2\(<\)/inf\(>\)-norm with moving coprime arrays. IET Radar Sonar Navig. 17(11), 1646–1653 (2023)CrossRef
35.
Zurück zum Zitat S.K. Yadav, N.V. George, Fast direction-of-arrival estimation via coarray interpolation based on truncated nuclear norm regularization. IEEE Trans. Circuits Syst. II Express Briefs 68(4), 1522–1526 (2021) S.K. Yadav, N.V. George, Fast direction-of-arrival estimation via coarray interpolation based on truncated nuclear norm regularization. IEEE Trans. Circuits Syst. II Express Briefs 68(4), 1522–1526 (2021)
37.
Zurück zum Zitat L.M. Zhao, H.Q. Liu, Y. Li, Y. Zhou, DOA estimation under sensor gain and phase uncertainties, in Proceedings of 2015 International Conference on Estimation, Detection and Information Fusion, ICEDIF 2015, pp. 209–213 (2015) L.M. Zhao, H.Q. Liu, Y. Li, Y. Zhou, DOA estimation under sensor gain and phase uncertainties, in Proceedings of 2015 International Conference on Estimation, Detection and Information Fusion, ICEDIF 2015, pp. 209–213 (2015)
38.
Zurück zum Zitat Z. Zheng, W.Q. Wang, Y.Y. Kong, Y.D. Zhang, MISC array: a new sparse array design achieving increased degrees of freedom and reduced mutual coupling effect. IEEE Trans. Signal Process. 67(7), 1728–1741 (2019)MathSciNetCrossRef Z. Zheng, W.Q. Wang, Y.Y. Kong, Y.D. Zhang, MISC array: a new sparse array design achieving increased degrees of freedom and reduced mutual coupling effect. IEEE Trans. Signal Process. 67(7), 1728–1741 (2019)MathSciNetCrossRef
39.
Zurück zum Zitat Z. Zheng, Y.X. Huang, W.Q. Wang, H.C. So, Direction-of-arrival estimation of coherent signals via coprime array interpolation. IEEE Signal Process. Lett. 27, 585–589 (2020)CrossRef Z. Zheng, Y.X. Huang, W.Q. Wang, H.C. So, Direction-of-arrival estimation of coherent signals via coprime array interpolation. IEEE Signal Process. Lett. 27, 585–589 (2020)CrossRef
40.
Zurück zum Zitat C.W. Zhou, J.F. Zhou, Direction-of-arrival estimation with coarray ESPRIT for coprime array. Sensors (Switzerland) 17(8), 1779 (2017)CrossRef C.W. Zhou, J.F. Zhou, Direction-of-arrival estimation with coarray ESPRIT for coprime array. Sensors (Switzerland) 17(8), 1779 (2017)CrossRef
41.
Zurück zum Zitat C.W. Zhou, Z.G. Shi, Y.J. Gu, N. A. Goodman, Doa estimation by covariance matrix sparse reconstruction of coprime array. ICASSP, in IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 2015-August, pp. 2369–2373 (2015) C.W. Zhou, Z.G. Shi, Y.J. Gu, N. A. Goodman, Doa estimation by covariance matrix sparse reconstruction of coprime array. ICASSP, in IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 2015-August, pp. 2369–2373 (2015)
42.
Zurück zum Zitat C.W. Zhou, Y.J. Gu, X. Fan, Z.G. Shi, G.Q. Mao, Y.D. Zhang, Direction-of-arrival estimation for coprime array via virtual array interpolation. IEEE Trans. Signal Process. 66(22), 5956–5971 (2018)MathSciNetCrossRef C.W. Zhou, Y.J. Gu, X. Fan, Z.G. Shi, G.Q. Mao, Y.D. Zhang, Direction-of-arrival estimation for coprime array via virtual array interpolation. IEEE Trans. Signal Process. 66(22), 5956–5971 (2018)MathSciNetCrossRef
43.
Zurück zum Zitat X. Zhang, Z. Zheng, W.Q. Wang, H.C. So, DOA estimation of coherent sources using coprime array via atomic norm minimization. IEEE Signal Process. Lett. 29, 1312–1316 (2022)CrossRef X. Zhang, Z. Zheng, W.Q. Wang, H.C. So, DOA estimation of coherent sources using coprime array via atomic norm minimization. IEEE Signal Process. Lett. 29, 1312–1316 (2022)CrossRef
Metadaten
Titel
Method for DOA Estimation of Coprime Arrays Through Joint Auxiliary Arrays with Atomic Norm Minimization in the Presence of Gain-Phase Errors
verfasst von
Qiang Guo
Wenjie Zhao
Liangang Qi
Yani Wang
Kaliuzhnyi Mykola
Stepan Duplii
Publikationsdatum
16.07.2024
Verlag
Springer US
Erschienen in
Circuits, Systems, and Signal Processing / Ausgabe 10/2024
Print ISSN: 0278-081X
Elektronische ISSN: 1531-5878
DOI
https://doi.org/10.1007/s00034-024-02746-7