Extraction of periodic signals in Global Navigation Satellite System (GNSS) vertical coordinate time series using the adaptive ensemble empirical modal decomposition method

Empirical modal decomposition (EMD) is an efficient tool for extracting a signal from stationary or non-stationary time series and is enhanced in stability and robustness by ensemble empirical mode decomposition (EEMD). Adaptive EEMD further improves computational efficiency through adaptability in the white noise amplitude and set average number. However, its effectiveness in the periodic signal extraction in Global Navigation Satellite System (GNSS) coordinate time series regarding the inevitable missing data and offset issues has not been comprehensively validated. In order to thoroughly investigate their impacts, we simulated 5 years of daily time series data with different missing data percentages or a different number of offsets and conducted them 300 times for each simulation. The results show that high accuracy could reach the overall random missing rate below 15 % and avoid consecutive misses exceeding 30 d. Meanwhile, offsets should be corrected in advance regardless of their magnitudes. The analysis of the vertical components of 13 stations within the Australian Global Sea Level Observing System (GLOSS) monitoring network demonstrates the advantage of adaptive EEMD in revealing the time-varying characteristics of periodic signals. From the perspectives of correlation coefficients (CCs), root mean square error (RMSE), power spectral density indices ( kappa ) and signal-to-noise ratio (SNR), the means for adaptive EEMD are 0.36, 0.81, - 0.18 and 0.48, respectively, while for least squares (LS), they are 0.27, 0.86, - 0.50 and 0.23. Meanwhile, a significance test of the residuals further substantiates the effectiveness in periodic signal extraction, which shows that there is no annual signal remaining. Also, the longer the series, the higher the accuracy of the reasonable extracted periodic signal concluded via the significance test. Moreover, driving factors are more effectively facilitated by the time-varying periodic characteristics compared with the constant periodic signal derived by LS. Overall, the application of adaptive EEMD could achieve high accuracy in analyzing GNSS time series, but it should be based on properly dealing with missing data and offsets.