一种改进WVSSA算法的GNSS时间序列降噪方法

A noise reduction method for GNSS time series based on improved WVSSA algorithm

针对变分模态分解(VMD)中不适合的模态分解数和惩罚因子易出现过度分解与分解不足等现象的问题,提出一种改进VMD和利用复合指标改进奇异谱分析(SSA)的鲸鱼变分模态奇异谱分析(WVSSA)方法:采用WOA算法确定VMD分解的最佳参数组合进行VMD分解和重构;并用基于复合评价指标改进的SSA方法进行二次降噪;最后利用10个基准站与仿真信号分解降噪以验证方法的有效性。周期信号与噪声信号降噪分析结果表明,WVSSA方法与经验模态分解(EMD)、集合经验模态分解(EEMD)相比,均方根误差降低0.6222、0.6053mm,信噪比增加1.0349、1.0298dB,相关性增加0.0645、0.0625;全球卫星导航系统(GNSS)时序降噪分析结果表明,WVSSA方法均方根误差比EMD、EEMD平均降低0.9156、0.8271 mm,信噪比平均增加2.7606、2.4727 dB,相关性平均增加0.1754、0.1531。WVSSA方法在时间序列识别和去除噪声上更为有效。

Aiming at the problem that it is liable to excessive decomposition and insufficient decomposition for unsuitable modal decomposition numbers and penalty factors in variational mode decomposition(VMD),the paper proposed a method of whale optimization algorithm variable modal decomposition singular spectrum analysis(WVSSA)to improve VMD and use composite index to improve singular spectrum analysis(SSA):WOA algorithm was used to determine the best parameter combination of VMD decomposition for VMD decomposition and reconstruction;and the improved SSA method based on composite evaluation index was used to carry out secondary noise reduction;finally,10 reference stations and simulated signals were used to decompose and reduce noise to verify the effectiveness of the method.Results of periodic signal and noise signal denoising analysis showed that compared with empirical mod e decomposition(EMD)and ensemble empirical mode decomposition(EEMD),the root-mean-square error of WVSSA method would be reduced by 0.6222 and 0.6053 mm,the signalto-noise ratio(SNR)would be increased by 1.0349 and 1.0298 dB,and the correlation would be increased by 0.0645 and 0.0625;meanwhile,results of global navigation satellite system(GNSS)sequential noise reduction analysis showed that the root-meansquare error of WVSSA method would be lower than that of EMD and EEMD by 0.9156 and 0.8271 mm on average,the SNR would be increased by 2.7606 and 2.4727 dB on average,and the correlation would be increased by 0.1754 and 0.1531 on average.In general,WVSSA method could be more effective in time series identification and noise removal.