- 长安大学地质工程与测绘学院, 西安市雁塔路126号, 710064
摘要: 为了精确剔除GNSS （global navigation satellite system）坐标时间序列中的噪声，本文提出一种联合遗传算法（genetic algorithm，GA）和变分模态分解（variational mode decomposition，VMD）的降噪方法GA-VMD。该方法首先利用GA优化VMD参数，然后引入多尺度排列熵（multiscale permutation entropy，MPE）作为噪声分量的筛选标准，最后将剩余分量重构得到降噪后的信号。本文通过仿真信号和实测数据的降噪实例，并与小波降噪（wavelet denoising，WD）、经验模态分解（empirical mode decomposition，EMD）等方法对比，分析GA-VMD的降噪效果。实验结果表明：对于仿真信号而言，GA-VMD方法相较于WD、EMD方法，信噪比分别提高了5.18dB和2.91dB，互相关系数分别提高了0.05和0.02；对于实测数据而言，GA-VMD方法对测站的速度不确定度和闪烁噪声的平均改正率分别为79.89%和84.46%，优于其他两种方法。以上分析表明GA-VMD方法能够有效减少GNSS坐标时序的噪声，提高其精度。
A Denoising Method for GNSS Time Series Based on GAVMD and Multi-Scale Permutation Entropy
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Abstract: Objectives: Global navigation satellite system (GNSS) coordinate time series provide important data support for the study of crustal movement and deformation, and plate tectonics. Due to the noise caused by various external factors, the GNSS coordinate time series cannot reflect the real motion information of the station well. To effectively reduce the noise in the GNSS time series, we adopted a noise-reduction method, GA-VMD, combining genetic algorithm (GA) and variational mode decomposition (VMD). Methods: Firstly, the genetic algorithm was used to optimize VMD parameters, and the envelope entropy of the input signal was used as the fitness function of the genetic algorithm to find the optimal VMD parameter combination suitable for the signal. According to the optimized parameters, the signal was decomposed by VMD to obtain A series of modal components. Then we calculated the multi-scale permutation entropy (MPE) of each component and then regarded the MPE as the criterion of the noise component. Finally, according to the MPE, the noise components were identified and removed, and the remaining components were reconstructed to obtain the noise-reduced signal. In this paper, the noise reduction effect of GA-VMD was analyzed through the example of noise reduction of analog signal and observation data, and compared with wavelet denoising (WD) and empirical mode decomposition (EMD) methods. Results: The results show that:(1) the noise reduction results from the analog signals show that WD and EMD have the incomplete and excessive troubles on the noise reduction, respectively. However, GA-VMD can effectively eliminate noise and retain effective signals. From the evaluation index, compared with WD and EMD, the signal-to-noise ratio were increased by 5.18dB and 2.91dB, the correlation coefficient by 0.05 and 0.02, respectively, when using GA-VMD. (2) For the complex observation, we used the noise and velocity uncertainty as accuracy indicators to evaluate the noise reduction effects of the three methods. The results show that WD can only extract a part of the white noise, while EMD and GA-VMD can completely remove the white noise. GA-VMD can reduce the flicker noise to the range of 0 to 6 mm·a-0.25. For the velocity uncertainty, the average gain rates of GA-VMD relative to the WD and EMD is 69% and 15.33%, respectively. GA-VMD has an average correction rate of 79.89% and 84.46% for the velocity uncertainty and flicker noise of GNSS coordinate time series. Conclusion: Therefore, GA-VMD is the most effective one among the three noise reduction methods, which can effectively reduce the noise in the GNSS time series and improve its accuracy. However, in this paper, we only discussed the effect of GA on VMD parameter optimization without comparing it with other method. Hence, it will be the key for studying the advantages and shortcomings of those optimization algorithms in the selection of VMD, and improving the accuracy on the GNSS time series in the future.