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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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