Feng Tengfei, Shen Yunzhong, Wang Fengwei
College of Surveying and Geo-Informatics, Tongji University, 1239 Siping Road, Shanghai 200092, China.
Sensors (Basel). 2021 Feb 24;21(5):1569. doi: 10.3390/s21051569.
Independent component analysis (ICA) is one of the most effective approaches in extracting independent signals from a global navigation satellite system (GNSS) regional station network. However, ICA requires the involved time series to be complete, thereby the missing data of incomplete time series should be interpolated beforehand. In this contribution, a modified ICA is proposed, by which the missing data are first recovered based on the reversible property between the original time series and decomposed principal components, then the complete time series are further processed with FastICA. To evaluate the performance of the modified ICA for extracting independent components, 24 regional GNSS network stations located in North China from 2011 to 2019 were selected. After the trend, annual and semiannual terms were removed from the GNSS time series, the first two independent components captured 17.42, 18.44 and 17.38% of the total energy for the North, East and Up coordinate components, more than those derived by the iterative ICA that accounted for 16.21%, 17.72% and 16.93%, respectively. Therefore, modified ICA can extract more independent signals than iterative ICA. Subsequently, selecting the 7 stations with less missing data from the network, we repeatedly process the time series after randomly deleting parts of the data and compute the root mean square error (RMSE) from the differences of reconstructed signals before and after deleting data. All RMSEs of modified ICA are smaller than those of iterative ICA, indicating that modified ICA can extract more exact signals than iterative ICA.
独立成分分析（ICA）是从全球导航卫星系统（GNSS）区域站网中提取独立信号的最有效方法之一。然而，ICA要求所涉及的时间序列是完整的，因此不完整时间序列中的缺失数据应预先进行插值。在本研究中，提出了一种改进的ICA方法，该方法首先基于原始时间序列与分解后的主成分之间的可逆特性恢复缺失数据，然后使用快速独立成分分析（FastICA）对完整的时间序列进行进一步处理。为了评估改进的ICA提取独立成分的性能，选取了2011年至2019年位于中国北方的24个区域GNSS网络站点。从GNSS时间序列中去除趋势项、年项和半年项后，前两个独立成分分别捕获了北向、东向和天向坐标分量总能量的17.42%、18.44%和17.38%，比迭代ICA分别捕获的16.21%、17.72%和16.93%更多。因此，改进的ICA比迭代ICA能提取更多的独立信号。随后，从网络中选取缺失数据较少的7个站点，在随机删除部分数据后对时间序列进行重复处理，并根据删除数据前后重建信号的差异计算均方根误差（RMSE）。改进的ICA的所有RMSE均小于迭代ICA的RMSE，表明改进的ICA比迭代ICA能提取更精确的信号。
