{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T05:36:25Z","timestamp":1768714585321,"version":"3.49.0"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T00:00:00Z","timestamp":1651536000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T00:00:00Z","timestamp":1651536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.62072074"],"award-info":[{"award-number":["No.62072074"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.62076054"],"award-info":[{"award-number":["No.62076054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.62027827"],"award-info":[{"award-number":["No.62027827"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.61902054"],"award-info":[{"award-number":["No.61902054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.62002047"],"award-info":[{"award-number":["No.62002047"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Frontier Science and Technology Innovation Projects of National Key R&D Program","award":["No.2019QY1405"],"award-info":[{"award-number":["No.2019QY1405"]}]},{"name":"the Sichuan Science and Technology Innovation Platform and Talent Plan","award":["No.2020JDJQ0020"],"award-info":[{"award-number":["No.2020JDJQ0020"]}]},{"name":"the Sichuan Science and Technology Support Plan","award":["No.2020YFSY0010"],"award-info":[{"award-number":["No.2020YFSY0010"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Nowadays, the increasingly complex and changeable marine environment makes the signals received by the underwater sensing equipment not only contain the weak signals radiated by underwater targets but also accompanied by marine solid background noise, which leads to the degradation and distortion of underwater acoustic signals and the decline of underwater communication quality. Under the severe influence of ocean noise, the underwater acoustic sensing and acquisition system will have the problems of high SNR ratio threshold, minimal sensing bandwidth, and unable to sense the signal with unknown frequency effectively. The L\u00e9vy noise model has been selected to describe the marine noise environment and explain its scientificity in this paper. A parameter estimation method for L\u00e9vy noise is proposed. Under the condition of characteristic index <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha =1.5$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b1<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1.5<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and noise intensity <jats:inline-formula><jats:alternatives><jats:tex-math>$$D=0.1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>D<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>0.1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of the L\u00e9vy noise model, the estimated mean values of parameters are 1.5026 and 1.1664. The estimated variances are 0.0034 and 0.0046, which proves the effectiveness and applicability of the estimation method. Then, an improved dual-coupled Duffing oscillator sensing system is proposed to sense the weak signals with unknown frequency under L\u00e9vy noise. Under the background of L\u00e9vy with characteristic index <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha =1.5$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b1<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1.5<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, deflection parameter <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta =0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b2<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and noise intensity <jats:inline-formula><jats:alternatives><jats:tex-math>$$D=0.1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>D<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>0.1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the sensing error rate of our system with unknown frequency is <jats:inline-formula><jats:alternatives><jats:tex-math>$$0.054\\%$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>0.054<\/mml:mn>\n                    <mml:mo>%<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the lowest sensing signal amplitude is <jats:inline-formula><jats:alternatives><jats:tex-math>$$A=0.010$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>A<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>0.010<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the lowest sensing SNR ratio is \u2212\u00a023.9254 dB, and the frequency of multi-frequency weak signals to be measured can be obtained. The estimation error of frequency sensing is <jats:inline-formula><jats:alternatives><jats:tex-math>$$0.33\\%$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>0.33<\/mml:mn>\n                    <mml:mo>%<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1186\/s13638-022-02120-8","type":"journal-article","created":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T11:21:54Z","timestamp":1651576914000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A practical underwater information sensing system based on intermittent chaos under the background of L\u00e9vy noise"],"prefix":"10.1186","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7568-5647","authenticated-orcid":false,"given":"Hanwen","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Zhen","family":"Qin","sequence":"additional","affiliation":[]},{"given":"Yichao","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Dajiang","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Ji","family":"Gen","sequence":"additional","affiliation":[]},{"given":"Hao","family":"Qin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,3]]},"reference":[{"key":"2120_CR1","unstructured":"D. Chen, Z. Zhao, X. Qin, Y. Luo, M. Cao, H. Xu, A. Liu, Magleak: a learning-based side-channel attack for password recognition with multiple sensors in IIoT environment. IEEE Trans. Ind. Inf. (2020)"},{"issue":"5","key":"2120_CR2","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1109\/MNET.2017.1600248","volume":"31","author":"N Zhang","year":"2017","unstructured":"N. Zhang, P. Yang, S. Zhang, D. Chen, W. Zhuang, B. Liang, X.S. Shen, Software defined networking enabled wireless network virtualization: challenges and solutions. IEEE Netw. 31(5), 42\u201349 (2017). https:\/\/doi.org\/10.1109\/MNET.2017.1600248","journal-title":"IEEE Netw."},{"issue":"1","key":"2120_CR3","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/MWC.2018.1700193","volume":"25","author":"N Zhang","year":"2018","unstructured":"N. Zhang, P. Yang, J. Ren, D. Chen, L. Yu, X. Shen, Synergy of big data and 5g wireless networks: opportunities, approaches, and challenges. IEEE Wirel. Commun. 25(1), 12\u201318 (2018). https:\/\/doi.org\/10.1109\/MWC.2018.1700193","journal-title":"IEEE Wirel. Commun."},{"key":"2120_CR4","doi-asserted-by":"crossref","unstructured":"H. Gao, C. Liu, A hybrid approach to trust node assessment and management for vanets cooperative data communication: historical interaction perspective. IEEE Intell. Transp. Syst. Trans. 1\u201310 (2021)","DOI":"10.1109\/TITS.2021.3129458"},{"issue":"3","key":"2120_CR5","doi-asserted-by":"publisher","first-page":"5520","DOI":"10.1109\/JIOT.2019.2903245","volume":"6","author":"L Ale","year":"2019","unstructured":"L. Ale, N. Zhang, H. Wu, D. Chen, T. Han, Online proactive caching in mobile edge computing using bidirectional deep recurrent neural network. IEEE Internet Things J. 6(3), 5520\u20135530 (2019)","journal-title":"IEEE Internet Things J."},{"issue":"3","key":"2120_CR6","doi-asserted-by":"publisher","first-page":"1504","DOI":"10.1109\/JIOT.2020.3012452","volume":"8","author":"Y Ding","year":"2020","unstructured":"Y. Ding, G. Wu, D. Chen, N. Zhang, L. Gong, M. Cao, Z. Qin, DeepEDN: a deep-learning-based image encryption and decryption network for internet of medical things. IEEE Internet Things J. 8(3), 1504\u20131518 (2020)","journal-title":"IEEE Internet Things J."},{"issue":"9","key":"2120_CR7","doi-asserted-by":"publisher","first-page":"6153","DOI":"10.1109\/TII.2020.3039500","volume":"17","author":"Y Yin","year":"2021","unstructured":"Y. Yin, Q. Huang, H. Gao, Y. Xu, Personalized APIs recommendation with cognitive knowledge mining for industrial systems. IEEE Trans. Ind. Inf. 17(9), 6153\u20136161 (2021)","journal-title":"IEEE Trans. Ind. Inf."},{"key":"2120_CR8","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1016\/j.future.2021.07.004","volume":"125","author":"Y Xu","year":"2021","unstructured":"Y. Xu, Y. Wu, H. Gao, S. Song, Y. Yin, X. Xiao, Collaborative APIs recommendation for artificial intelligence of things with information fusion. Future Gener. Comput. Syst. 125, 471\u2013479 (2021)","journal-title":"Future Gener. Comput. Syst."},{"issue":"2","key":"2120_CR9","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1109\/TGCN.2021.3067374","volume":"5","author":"Y Huang","year":"2021","unstructured":"Y. Huang, H. Xu, H. Gao, X. Ma, W. Hussain, SSUR: an approach to optimizing virtual machine allocation strategy based on user requirements for cloud data center. IEEE Trans. Green Commun. Netw. 5(2), 670\u2013681 (2021)","journal-title":"IEEE Trans. Green Commun. Netw."},{"issue":"4","key":"2120_CR10","doi-asserted-by":"publisher","first-page":"4002","DOI":"10.1109\/TNSM.2021.3125395","volume":"18","author":"X Ma","year":"2021","unstructured":"X. Ma, H. Xu, H. Gao, M. Bian, Real-time multiple-workflow scheduling in cloud environments. IEEE Trans. Netw. Serv. Manag. (TNSM) 18(4), 4002\u20134018 (2021)","journal-title":"IEEE Trans. Netw. Serv. Manag. (TNSM)"},{"key":"2120_CR11","doi-asserted-by":"crossref","unstructured":"H. Peyvandi, M. Farrokhrooz, H. Roufarshbaf, S.-J. Park, Sonar systems and underwater signal processing: classic and modern approaches. SONAR Syst. 173\u2013206 (2011)","DOI":"10.5772\/17505"},{"key":"2120_CR12","doi-asserted-by":"crossref","unstructured":"S. Ma, H. Wang, X. Shen, H. Dong, Stochastic resonance for underwater vlf weak signal detection under l\u00e9vy noise background. In: 2017 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), pp. 1\u20135 (2017). IEEE","DOI":"10.1109\/ICSPCC.2017.8242466"},{"key":"2120_CR13","volume-title":"Sonar Technology","author":"T Tian","year":"2006","unstructured":"T. Tian, G. Liu, D. Sun, Sonar Technology (Harbin Engineering University Press, Harbin, 2006)"},{"key":"2120_CR14","unstructured":"X. Liu, Y. Qin, Modem marine power vs state marine strategy. J. Soc. Sci. 73\u201379 (2004)"},{"issue":"9","key":"2120_CR15","doi-asserted-by":"publisher","first-page":"1597","DOI":"10.1049\/iet-rsn.2018.5540","volume":"13","author":"YL He","year":"2019","unstructured":"Y.L. He, Y. Wang, N. Zou, Parametric GLRT for multichannel adaptive signal detection in space-time correlated compound-gaussian disturbance. IET Radar Sonar Navig. 13(9), 1597\u20131608 (2019)","journal-title":"IET Radar Sonar Navig."},{"key":"2120_CR16","unstructured":"M. Chitre, Underwater acoustic communications in warm shallow waters channels. Ph.D. thesis, National University of Singapore (2006)"},{"key":"2120_CR17","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.dsp.2019.04.009","volume":"92","author":"SB Babarsad","year":"2019","unstructured":"S.B. Babarsad, S.M. Saberali, M. Majidi, Analytic performance investigation of signal level estimator based on empirical characteristic function in impulsive noise. Digit. Signal Process 92, 20\u201325 (2019)","journal-title":"Digit. Signal Process"},{"issue":"12","key":"2120_CR18","doi-asserted-by":"publisher","first-page":"5651","DOI":"10.1007\/s00034-019-01135-9","volume":"38","author":"JJ Jeong","year":"2019","unstructured":"J.J. Jeong, S. Kim, Robust adaptive filter algorithms against impulsive noise. Circuits. Syst. Signal Process 38(12), 5651\u20135664 (2019)","journal-title":"Circuits. Syst. Signal Process"},{"issue":"12","key":"2120_CR19","doi-asserted-by":"publisher","first-page":"2145","DOI":"10.1049\/iet-rsn.2019.0223","volume":"13","author":"M Hajiabadi","year":"2019","unstructured":"M. Hajiabadi, H. Radmanesh, M. Samkan, Robust adaptive beamforming in impulsive noise environments. IET Radar Sonar Navig. 13(12), 2145\u20132150 (2019)","journal-title":"IET Radar Sonar Navig."},{"key":"2120_CR20","doi-asserted-by":"crossref","unstructured":"A. Korakas, J.M. Hovem, Comparison of modeling approaches to low-frequency noise propagation in the ocean. In: 2013 MTS\/IEEE OCEANS-Bergen, pp. 1\u20137 (2013). IEEE","DOI":"10.1109\/OCEANS-Bergen.2013.6608079"},{"issue":"5","key":"2120_CR21","doi-asserted-by":"publisher","first-page":"2586","DOI":"10.1121\/1.4796132","volume":"133","author":"JH Haxel","year":"2013","unstructured":"J.H. Haxel, R.P. Dziak, H. Matsumoto, Observations of shallow water marine ambient sound: the low frequency underwater soundscape of the central oregon coast. J. Acoust. Soc. Am. 133(5), 2586\u20132596 (2013)","journal-title":"J. Acoust. Soc. Am."},{"issue":"3","key":"2120_CR22","doi-asserted-by":"publisher","first-page":"1824","DOI":"10.1121\/1.5126520","volume":"146","author":"M Siderius","year":"2019","unstructured":"M. Siderius, J. Gebbie, Environmental information content of ocean ambient noise. J. Acoust. Soc. Am. 146(3), 1824\u20131833 (2019)","journal-title":"J. Acoust. Soc. Am."},{"issue":"2","key":"2120_CR23","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1121\/1.1461915","volume":"3","author":"RK Andrew","year":"2002","unstructured":"R.K. Andrew, B.M. Howe, J.A. Mercer, M.A. Dzieciuch, Ocean ambient sound: comparing the 1960s with the 1990s for a receiver off the California coast. Acoust. Res. Lett. Online 3(2), 65\u201370 (2002)","journal-title":"Acoust. Res. Lett. Online"},{"key":"2120_CR24","unstructured":"S.A. Albeverio, Y.G. Kondratiev, L. Streit, How to generalize white noise analysis to non-Gaussian measures. Dyn. Complex Irregular Syst., 120\u2013130 (1993)"},{"issue":"3","key":"2120_CR25","first-page":"28","volume":"3","author":"Y Kondratiev","year":"1997","unstructured":"Y. Kondratiev, J.L. Silva, L. Streit, Generalized appell systems. Methods Funct. Anal. Topol. 3(3), 28\u201361 (1997)","journal-title":"Methods Funct. Anal. Topol."},{"issue":"1","key":"2120_CR26","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1142\/S0219025798000089","volume":"1","author":"YG Kondratiev","year":"1998","unstructured":"Y.G. Kondratiev, J.L. da Silva, L. Streit, Analysis on Poisson and gamma spaces. Infinice Dimens. Anal. Quantum Probab. Relat. Top. 1(1), 91\u2013117 (1998)","journal-title":"Infinice Dimens. Anal. Quantum Probab. Relat. Top."},{"key":"2120_CR27","doi-asserted-by":"crossref","unstructured":"T. Hida, White noise analysis and its applications. In: Proceedings of the International Mathematical Conference, pp. 43\u201348 (1982)","DOI":"10.1016\/S0304-0208(08)70413-4"},{"issue":"6","key":"2120_CR28","doi-asserted-by":"publisher","first-page":"1815","DOI":"10.3390\/s18061815","volume":"18","author":"J Jiang","year":"2018","unstructured":"J. Jiang, K. Wang, C. Zhang, M. Chen, H. Zheng, R. Albarracin, Sparse method for directional estimation using denoised four-order cumulants vector. Sensors 18(6), 1815 (2018)","journal-title":"Sensors"},{"issue":"7","key":"2120_CR29","doi-asserted-by":"publisher","first-page":"2403","DOI":"10.2298\/FIL2107403Y","volume":"35","author":"M Yanga","year":"2021","unstructured":"M. Yanga, Fractional stochastic differential equations driven by levy noise. Filomat 35(7), 2403\u20132424 (2021)","journal-title":"Filomat"},{"issue":"5","key":"2120_CR30","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1007\/s10463-019-00726-2","volume":"72","author":"S Beltaief","year":"2020","unstructured":"S. Beltaief, O. Chernoyarov, S. Pergamenchtchikov, Model selection for the robust efficient signal processing observed with small levy noise. Ann. Inst. Stat. Math. 72(5), 1205\u20131235 (2020)","journal-title":"Ann. Inst. Stat. Math."},{"issue":"1","key":"2120_CR31","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1109\/TVT.2020.3044994","volume":"70","author":"J Wang","year":"2020","unstructured":"J. Wang, J. Li, S. Yan, W. Shi, X. Yang, Y. Guo, T.A. Gulliver, A novel underwater acoustic signal denoising algorithm for gaussian\/non-gaussian impulsive noise. IEEE Trans. Veh. Technol. 70(1), 429\u2013445 (2020)","journal-title":"IEEE Trans. Veh. Technol."},{"key":"2120_CR32","volume-title":"Engineering Analysis and Application of Wavelet Transform","author":"SY Fu","year":"1999","unstructured":"S.Y. Fu, Engineering Analysis and Application of Wavelet Transform (Science Press, Beijing, 1999)"},{"key":"2120_CR33","doi-asserted-by":"crossref","unstructured":"Z. Qiao, Y.L., N. Li, Applications of stochastic resonance to machinery fault detection: a review and tutorial. Mech. Syst. Signal Process. 122, 502\u2013536 (2019)","DOI":"10.1016\/j.ymssp.2018.12.032"},{"issue":"6","key":"2120_CR34","first-page":"1175","volume":"50","author":"SQ Li","year":"2017","unstructured":"S.Q. Li, X.Z. Wu, Application of ale based on FTF algorithm in ship-radiated noise detection. Commun. Technol. 50(6), 1175\u20131180 (2017)","journal-title":"Commun. Technol."},{"issue":"1","key":"2120_CR35","first-page":"18","volume":"32","author":"SU Qing-wen","year":"2019","unstructured":"S.U. Qing-wen, Z. Jin-feng, Weak signal detection based on coupled chaotic oscillator. Shijiazhuang Tiedao Univ. 32(1), 18\u201323 (2019)","journal-title":"Shijiazhuang Tiedao Univ."},{"key":"2120_CR36","doi-asserted-by":"crossref","unstructured":"W.Y.F.H. Shao-Ping, J. Guo-Bin, Study on partial discharge signal detection by coupled duffing oscillators. Acta Phys. Sin. 62(13) (2013)","DOI":"10.7498\/aps.62.130505"},{"issue":"12","key":"2120_CR37","first-page":"1645","volume":"37","author":"N Li","year":"2016","unstructured":"N. Li, X. Li, C. Liu, Detection method of a short-time duffing oscillator array with variable amplitude coefficients. J. Harbin Eng. Univ. 37(12), 1645\u20131652 (2016)","journal-title":"J. Harbin Eng. Univ."},{"issue":"1","key":"2120_CR38","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s11595-005-1161-8","volume":"33","author":"S Zhou","year":"2009","unstructured":"S. Zhou, C. Lin, Application of chaos theory for weak signal of ship detecting. J. Wuhan Univ. Technol. 33(1), 161\u2013164 (2009)","journal-title":"J. Wuhan Univ. Technol."},{"issue":"06","key":"2120_CR39","first-page":"1175","volume":"50","author":"S Li","year":"2017","unstructured":"S. Li, X. Wu, Application of ale based on FTF algorithm in ship-radiated noise detection. Commun. Technol. 50(06), 1175\u20131180 (2017)","journal-title":"Commun. Technol."},{"key":"2120_CR40","first-page":"17","volume":"1","author":"Q Sun","year":"2012","unstructured":"Q. Sun, J. Zhang, Weak signal detection based on improved chaotic oscillator system with dual coupling. Comput. Mod. 1, 17\u201321 (2012)","journal-title":"Comput. Mod."},{"key":"2120_CR41","doi-asserted-by":"crossref","unstructured":"G. Li, Y. Hou, H. Yang, A new duffing detection method for underwater weak target signal. Alex. Eng. J.(2021)","DOI":"10.1016\/j.aej.2021.08.016"},{"issue":"8","key":"2120_CR42","doi-asserted-by":"publisher","first-page":"6664","DOI":"10.1109\/JIOT.2020.2984532","volume":"7","author":"S Jing","year":"2020","unstructured":"S. Jing, J. Hall, Y.R. Zheng, C. Xiao, Signal detection for underwater IoT devices with long and sparse channels. IEEE Internet Things J. 7(8), 6664\u20136675 (2020)","journal-title":"IEEE Internet Things J."},{"issue":"5","key":"2120_CR43","doi-asserted-by":"publisher","first-page":"05020001","DOI":"10.1061\/(ASCE)EM.1943-7889.0001764","volume":"146","author":"GM Moatimid","year":"2020","unstructured":"G.M. Moatimid, Stability analysis of a parametric duffing oscillator. J. Eng. Mech. 146(5), 05020001 (2020)","journal-title":"J. Eng. Mech."},{"issue":"6","key":"2120_CR44","doi-asserted-by":"publisher","first-page":"993","DOI":"10.15388\/namc.2021.26.24419","volume":"26","author":"M Liu","year":"2021","unstructured":"M. Liu, J. Chen, H. Jiang, Z. Yu, C. Hu, B. Lu, Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy. Nonlinear Anal. Model. Control 26(6), 993\u20131011 (2021)","journal-title":"Nonlinear Anal. Model. Control"},{"key":"2120_CR45","doi-asserted-by":"crossref","unstructured":"Z. Brze\u017aniak, W. Liu, J. Zhu, The stochastic strichartz estimates and stochastic nonlinear Schr\u00f6dinger equations driven by levy noise. J. Funct. Anal. 281(4) (2021)","DOI":"10.1016\/j.jfa.2021.109021"},{"issue":"11","key":"2120_CR46","doi-asserted-by":"publisher","first-page":"1450085","DOI":"10.1142\/S0217984914500857","volume":"28","author":"W Xu","year":"2014","unstructured":"W. Xu, M. Hao, X. Gu, G. Yang, Stochastic resonance induced by levy noise in a tumor growth model with periodic treatment. Mod. Phys. Lett. B 28(11), 1450085 (2014)","journal-title":"Mod. Phys. Lett. B"},{"key":"2120_CR47","doi-asserted-by":"crossref","unstructured":"L. Deng, X. Zhao, B. Yin, A method of extracting underwater acoustic beaconing signal. In: 2021 OES China Ocean Acoustics (COA), pp. 744\u2013747 (2021). IEEE","DOI":"10.1109\/COA50123.2021.9519864"},{"key":"2120_CR48","unstructured":"G. Li, K. Zhao, H. Yang, A new method for detecting line spectrum of ship-radiated noise based on a new double duffing oscillator differential system (2020)"},{"issue":"12","key":"2120_CR49","doi-asserted-by":"publisher","first-page":"2884","DOI":"10.1109\/78.476432","volume":"43","author":"X Ma","year":"1995","unstructured":"X. Ma, C.L. Nikias, Parameter estimation and blind channel identification in impulsive signal environments. IEEE Trans. Signal Process. 43(12), 2884\u20132897 (1995)","journal-title":"IEEE Trans. Signal Process."},{"key":"2120_CR50","doi-asserted-by":"crossref","unstructured":"X. Gu, J. Lou, K. Liu, P. Hu, Underwater detection signal based on LM-BP neural network algorithm. J. Phys. Conf. Ser. 1533 (2020)","DOI":"10.1088\/1742-6596\/1533\/3\/032035"}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-022-02120-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13638-022-02120-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-022-02120-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T11:26:26Z","timestamp":1651577186000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/s13638-022-02120-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,3]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["2120"],"URL":"https:\/\/doi.org\/10.1186\/s13638-022-02120-8","relation":{},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,3]]},"assertion":[{"value":"7 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors have agreed and given their consent for submission of this paper to Euraship Journal of Wireless Communication.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"41"}}