In order to suppress the strong clutter component and separate the effective fretting component from narrow-band radar echo, a method based on complex variational mode decomposition (CVMD) is proposed in this paper. The CVMD is extended from variational mode decomposition (VMD), which is a recently introduced technique for adaptive signal decomposition, limited to only dealing with the real signal. Thus, the VMD is extended from the real domain to the complex domain firstly. Then, the optimal effective order of singular value is obtained by singular value decomposition (SVD) to solve the problem of under-decomposition or over-decomposition caused by unreasonable choice of decomposition layer, it is more accurate than detrended fluctuation analysis (DFA) and empirical mode decomposition (EMD). Finally, the strongly correlated modes and weakly correlated modes are judged by calculating the Mahalanobis distance between the band-limited intrinsic mode functions (BLIMFs) and the original signal, which is more robust than the correlation judgment methods such as computing cross-correlation, Euclidean distance, Bhattachryya distance and Hausdorff distance. After the weak correlation modes are eliminated, the signal is reconstructed locally, and the separation of the micro-motion signal is realized. The experimental results show that the proposed method can filter out the strong clutter component and the fuselage component from radar echo more effectively than the local mean decomposition (LMD), empirical mode decomposition and moving target indicator (MTI) filter.

中文翻译：

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微动信号处理应用的自适应复变分模式分解

为了抑制强杂波分量并将有效的微动分量与窄带雷达回波分开，提出了一种基于复变分模分解的方法。CVMD是从变异模式分解（VMD）扩展而来的，该模型是最近引入的用于自适应信号分解的技术，仅限于处理真实信号。因此，VMD首先从实域扩展到复杂域。然后，通过奇异值分解（SVD）获得奇异值的最佳有效阶数，以解决因分解层选择不合理而导致的分解不足或分解过度的问题，比去趋势波动分析（DFA）更准确，并且经验模式分解（EMD）。最后，通过计算带限本征函数（BLIMF）与原始信号之间的Mahalanobis距离，可以判断强相关模式和弱相关模式，这比相关判断方法（如计算互相关，欧几里得距离， Bhattachryya距离和Hausdorff距离。消除了弱相关模式后，对信号进行局部重构，实现了微动信号的分离。实验结果表明，与局部均值分解，经验模态分解和运动目标指示（MTI）滤波器相比，该方法能够更有效地从雷达回波中滤除强杂波分量和机身分量。