优化EWT-NLM的自适应GNSS高程时间序列降噪方法

提出一种引入样本熵（SE）优化的经验小波变换（EWT）结合非局部均值（NLM）滤波的组合自适应降噪方法。该方法使用SE确定全部经验模态分量中低频有效信号界限，叠加其余中高频分量后进行NLM滤波处理，之后重构滤波信号与有效信号为最终降噪信号，从而达到滤除高频噪声的目的。模拟数据与实测数据的实验结果表明，优化的EWT-NLM方法整体优于EMD、EWT方法，RMSE分别降低13.41%/10.63%（实测数据/模拟数据）、7.13%/5.78%，信噪比分别提升22.03%/22.54%、9.72%/7.42%。

Optimized EWT-NLM Adaptive GNSS Vertical Time Series Noise Reduction Method

We propose a combinational adaptive noise reduction method combining empirical wavelet transform (EWT) and non-local mean (NLM) filtering with sample entropy (SE) optimization . This method uses SE to determine the low-frequency effective signal limit of all empirical modal components, superimposes the remaining medium and high-frequency components, and performs NLM filtering. Finally, the filtered signal and the effective signal are reconstructed as the final noise reduction signal to filter high-frequency noise. Using simulated data and measured data for experimental research, the results show that the optimized EWT-NLM method is overall better than the EMD and EWT methods. The RMSE decreases by 13.41%/10.63%(measured data/simulated data), 7.13%/5.78%, and the signal-to-noise ratio increases by 22.03%/22.54%, 9.72%/7.42%.