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为了从混沌背景中检测微弱信号,研究分析了复杂非线性系统的相空间重构理论,提出了一种基于广义窗函数的最小二乘支持向量机的预测法. 该方法以广义嵌入窗为基础,利用自关联函数法确定Lorenz系统的嵌入维数和时间延迟, 实现相空间重构,结合最小二乘支持向量机建立Lorenz系统的误差预测模型, 检测微弱目标信号(瞬态和周期信号).仿真实验表明,该方法的预测模型具有较小的误差, 能够有效地从混沌背景噪声中检测出微弱目标信号,减小噪声对目标信号的影响. 与传统方法相比,在降低检测门限的同时,能够有效地提高预测的精度, 在混沌噪声下信噪比为-87.41 dB的情况下,相对于传统支持向量机方法所得的均方根误差0.049(-54.60 dB时)降低近两个数量级至0.000036123(-87.41 dB时).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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[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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