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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).
In order to detect weak signals from the chaotic background, the phase space reconstruction theory of complex nonlinear systems is analyzed and studied, and a prediction method based on generalized window function is proposed. The method is based on the generalized embedded window , The Lorenz system’s embedding dimension and time delay are determined by self-correlation function method, and the phase space reconstruction is realized. The error prediction model of Lorenz system is established by least squares support vector machine to detect weak target signals (transient and periodic signals). Simulation results show that the proposed method has small error and can effectively detect weak target signals from chaotic background noise and reduce the impact of noise on the target signal.Compared with the traditional method, , Which can effectively improve the prediction accuracy. When the SNR is -87.41 dB under chaotic noise, the RMSE of the SVM method decreases by nearly two orders of magnitude compared with the 0.049 (-54.60 dB) 0.000036123 (at -87.41 dB).