基于最优滤波器的强混沌背景中谐波信号检测方法研究

Harmonic signal detection method from strong chaotic background based on optimal filter

强混沌背景中的微弱谐波信号检测有重要的工程研究意义.目前的检测方法主要是基于Takens理论的混沌相空间重构方法,然而这些方法往往对信干噪比要求高,且对高斯白噪声敏感等.本文注意到混沌信号的二阶统计特性是不变的,根据这个特点提出了一种基于最优滤波器的强混沌背景中的微弱谐波信号检测方法.该方法首先构建一个数据矩阵,在频域上对每个频率通道分别检测谐波信号,从而将信号检测问题转化为最优化问题,然后利用最优化理论设计滤波器,使待检测频率通道的信号增益保持不变,而尽量抑制其他频率通道的信号,最后通过判断每一频率通道的输出信干噪比来检测谐波信号.与传统方法相比,本文方法有如下优点:1)可以检测更低信干噪比下的微弱谐波信号;2)可检测的信号幅度范围更大;3)抗白噪声性能更强.仿真结果证明了本文方法的有效性.

It is of great significance to study the weak harmonic signal detection from strong chaotic background. Current detection methods mainly use the chaotic phase space reconstruction method based on Takens theory, among which the neural network method has attracted the most attention. However, these methods require high signal-to-interference- plus-noise ratio （SINR） and are sensitive to Gaussian white noise, etc. Noticing the fact that the second-order statistical properties of chaotic signals are stationary, we propose a harmonic signal detection method from strong chaotic background based on optimal filter. We first construct a data matrix, whose rows are the detection signal and reference signals. The reference signals only contain chaotic interference. Then we calculate the one-dimensional fast Fourier transformation of the data matrix to make each column of the matrix form a frequency channel. The harmonic signal can be detected by searching each frequency channel in the frequency domain, thus the signal detection problem is converted into an optimization problem. Further~ we use the optimization theory to design a filter such that it can maintain the gain of the signal from the current frequency channel and suppress signals from other frequency channels as far as possible. Finally, the harmonic signal can be obtained by calculating the output SINR of each frequency channel. In order to reduce the calculation, we can further design a local region optimal filter. We choose part of frequency channels to constitute a local area, thus the dimension of the chaotic interference covariance matrix is greatly reduced. Theoretically speaking, the more the number of auxiliary frequency channels, the better the detection results are. However, in the practical application, choosing two channels on the left and right side of current channel each can obtain a very good detection effect. After obtaining the chaotic interference covariance matrix, we can further achieve the output SINR of each frequency channel. Compared with the traditional methods, the proposed method has the following advantages： 1） it can detect a weak harmonic signal under lower SINR; 2） it can detect a greater range of signal amplitude; 3） it is robust against white Gaussian noise. The simulation results with taking Lorenz system as the strong chaotic background show that the proposed method still has a very good detection effect when SINR = -81.03 dB, and the stronger the harmonic signal, the better the detection effect is, while the neural network method can work under the condition of SINR higher than -67.03 dB; the proposed method still can correctly detect the target signal in the case that the SNR is as low as -20 dB, but the neural network method has a poor detection effect under the same condition.