基于希尔伯特-黄变换的超宽带信号检测方法

摘要

基于超宽带信号检测中希尔伯特-黄变换经验模态分解的边界问题，研究分析了基于非等间隔灰色模型预测极值点的解决方法。针对该方法在某些极值分布情况时个别极值点检测不到的问题，提出了时序残差修正的非等间隔灰色模型解决新方法。通过理论推导，证明了该新方法的有效性，在此基础上，对实际超宽带信号进行了结合新方法的希尔伯特-黄变换检测仿真。分析和仿真结果表明，改进的经验模态分解可以较为准确地重构出淹没在干扰或者噪声中的超宽带脉冲信号，明显改善了超宽带信号检测的准确度。通过与离散小波变换对比分析，体现出希尔伯特-黄变换更适合用于检测超宽带信号。%Based on end effects of Empirical Mode Decomposition(EMD)of Hilbert-Huang Transform(HHT)in detecting Ultra-Wideband(UWB)signal, the method of Non-equidistance Grey Model(NGM)mitigating end effects of EMD by predicting uncertain data is analyzed. In order to solve the problem that some extreme can hardly be detected in particular situation, modified NGM(1,1)model using Fourier series(TFNGM(1,1))at time domain to mitigate end effects of EMD is proposed. Proposed method with HHT is testified by theoretical derivation, and is used to detect UWB signal. Simulation results show the proposed method can accurately reconstruct UWB-IR signal with noise and interference, obviously improves the accuracy of UWB detection. Comparison with discrete wavelet transform demonstrates the proposed method is suitable to detect UWB signal.