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To extract weak signal from the chaotic background, in this paper we analyze the theory of state space reconstruction of complicated nonlinear system, and put forward an estimation method utilizing the least-squares support vector machine (LS-SVM) based on a generalized window function. In the algorithm the generalized embedded window is taken as a foundation and the correlation function method is used to determine the embedded dimension and time delay of Lorenz system and so the state space reconstruction is realized and by combining the error forecasting model in which the LS-SVM is used to estimate the errors, the detection of the weak target signal, such as transient and periodic signal, is achieved. It is illustrated in the simulation experiments that the model proposed can detect the weak signals effectively from a chaotic background and reduce the influence of noise on the target signals, which possesses minor forecasting error. Compared with those conventional methods, this method has a remarkable advantage in reducing detection threshold and improving the accuracy of prediction. When the signal-to-noise ratio is -87.41 dB in the chaotic noise background, the new method can reduce the root mean square error nearly two orders of magnitude, reach 0.000036123, while the traditional SVM can only reach 0.049 under the condition of -54.60 dB.
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Keywords:
- embedding dimension /
- generalized window /
- state space reconstruction /
- least-squares support vector machine
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[2] Li X Q, Deng Z D 2009 ICBME 2008. Proceedings 23 390
[3] Wang H P, Wang L M, Wan C L 2010 Ship Electronic Engineering 30 167 (in Chinese) [王红萍, 王黎明, 万程亮 2010 舰船电子工程 30 167]
[4] Kao J W, Berber S M, Kecman V 2010 16th Asia-Pacific Conference on Communications (APCC) 215
[5] Lampropoulos G A, Leung H 2000 IEEE International Radar Conference 404
[6] Wang Y N, Liu L J, Zhou B W, Zhang H 2010 Chin. J. Sci. Instrum. 31 410 (in Chinese) [王耀南, 刘良江, 周博文, 张辉 2010 仪器仪表学报 31 410]
[7] Takens F 1981 Lecture Notes in Mathematics 898 366
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[9] Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[10] Kim H S, Eykholt R, Sales J D 1999 Physica D 127 4850
[11] Kugiumtzis D 1996 Physica D 95 1328
[12] Harikrishnan K P, Misra R, Ambika G, Kembhavib A K 2006 Physica D: Nonlinear Phenomena 215 137
[13] Lu Z B, Cai Z M, Jiang K Y 2007 J. Sys. Simul. 19 2528 (in Chinese) [陆振波, 蔡志明, 姜可宇 2007 系统仿真学报 19 2528]
[14] Kenshi S, Yuko N, Shinichi A 2008 Chaos, Solitons and Fractacls 38 1274
[15] Diogo C S, Ricardo S, Romis A 2011 Digital Signal Processing 21 417
[16] Kurian A P, Leung H 2009 IEEE Trans. Cir. Sys.-I: Regular Papers 56 820
[17] Cui W Z, Zhu C C, Bao W X, Liu J H 2004 Acta Phys. Sin. 53 3303 (in Chinese) [崔万照, 朱长纯, 保文星, 刘君华 2004 53 3303]
[18] Li Y, Xu K, Yang B J, Yuan Y, Wu Y 2008 Acta Phys. Sin. 57 3353 (in Chinese) [李月, 徐凯, 杨宝俊, 袁野, 吴宁 2008 57 3353]
[19] Xing H Y, Xu W 2007 Acta Phys. Sin. 56 3773 (in Chinese) [行鸿彦, 徐伟 2007 56 3773]
[20] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 143 (in Chinese) [行鸿彦, 金天力 2010 59 143]
[21] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2005 54 550]
[22] Xiu C B, Liu X D, Zhang Y H 2003 Trans. Beijing Institute Technol. 23 219 (in Chinese) [修春波, 刘向东, 张宇河 2003 北京理工大学学报 23 219]
[23] Xu J, Long K P, Rournier P D, Taha A K, Charge P 2010 Chin. Phys. Lett. 27 080506
[24] Yang S Q, Jia C Y 2002 Acta Phys. Sin. 51 2454 (in Chinese) [杨绍清, 贾传荧 2002 51 2454]
[25] Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 010509 (in Chinese) [王梦蛟, 曾以成, 陈光辉, 贺娟 2011 60 010509]
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[1] Dai S Q, Deng X J, Duan Z P 2001 Advances in Mechanics 31 323 (in Chinese) [戴世强, 邓学姜, 段祝平 2001 力学进展 31 323324]
[2] Li X Q, Deng Z D 2009 ICBME 2008. Proceedings 23 390
[3] Wang H P, Wang L M, Wan C L 2010 Ship Electronic Engineering 30 167 (in Chinese) [王红萍, 王黎明, 万程亮 2010 舰船电子工程 30 167]
[4] Kao J W, Berber S M, Kecman V 2010 16th Asia-Pacific Conference on Communications (APCC) 215
[5] Lampropoulos G A, Leung H 2000 IEEE International Radar Conference 404
[6] Wang Y N, Liu L J, Zhou B W, Zhang H 2010 Chin. J. Sci. Instrum. 31 410 (in Chinese) [王耀南, 刘良江, 周博文, 张辉 2010 仪器仪表学报 31 410]
[7] Takens F 1981 Lecture Notes in Mathematics 898 366
[8] Zhang S Q, Jia J, Gao M, Han S 2010 Acta Phys. Sin. 59 1576 (in Chinese) [张淑清, 贾健, 高敏, 韩叙 2010 59 1576]
[9] Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[10] Kim H S, Eykholt R, Sales J D 1999 Physica D 127 4850
[11] Kugiumtzis D 1996 Physica D 95 1328
[12] Harikrishnan K P, Misra R, Ambika G, Kembhavib A K 2006 Physica D: Nonlinear Phenomena 215 137
[13] Lu Z B, Cai Z M, Jiang K Y 2007 J. Sys. Simul. 19 2528 (in Chinese) [陆振波, 蔡志明, 姜可宇 2007 系统仿真学报 19 2528]
[14] Kenshi S, Yuko N, Shinichi A 2008 Chaos, Solitons and Fractacls 38 1274
[15] Diogo C S, Ricardo S, Romis A 2011 Digital Signal Processing 21 417
[16] Kurian A P, Leung H 2009 IEEE Trans. Cir. Sys.-I: Regular Papers 56 820
[17] Cui W Z, Zhu C C, Bao W X, Liu J H 2004 Acta Phys. Sin. 53 3303 (in Chinese) [崔万照, 朱长纯, 保文星, 刘君华 2004 53 3303]
[18] Li Y, Xu K, Yang B J, Yuan Y, Wu Y 2008 Acta Phys. Sin. 57 3353 (in Chinese) [李月, 徐凯, 杨宝俊, 袁野, 吴宁 2008 57 3353]
[19] Xing H Y, Xu W 2007 Acta Phys. Sin. 56 3773 (in Chinese) [行鸿彦, 徐伟 2007 56 3773]
[20] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 143 (in Chinese) [行鸿彦, 金天力 2010 59 143]
[21] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2005 54 550]
[22] Xiu C B, Liu X D, Zhang Y H 2003 Trans. Beijing Institute Technol. 23 219 (in Chinese) [修春波, 刘向东, 张宇河 2003 北京理工大学学报 23 219]
[23] Xu J, Long K P, Rournier P D, Taha A K, Charge P 2010 Chin. Phys. Lett. 27 080506
[24] Yang S Q, Jia C Y 2002 Acta Phys. Sin. 51 2454 (in Chinese) [杨绍清, 贾传荧 2002 51 2454]
[25] Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 010509 (in Chinese) [王梦蛟, 曾以成, 陈光辉, 贺娟 2011 60 010509]
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