Dyadic wavelet transform and signal extraction of GNSS coordinate time series with missing data

The GNSS position time series are often analyzed by using traditional dyadic wavelet transform, which requires that the time series must be complete. However, missing data inevitably occur in the GNSS position time series due to a variety of causes. In order to extract signals from the incomplete position time series, a modified dyadic wavelet transform algorithm is developed and the corresponding formulas are derived in this paper based on the principle that missing data can be reproduced by its wavelet coefficients. The equivalence between new algorithm and zero-padding algorithm is proved, which indicates that the zero-padding algorithm is essentially a least squares minimum norm solution. Finally, the real position time series of 27 based stations from Crustal Movement Observation Network of China (CMONOC) and simulated data are adopted to verify the validation of the new algorithm, the results show that the difference between the signals extracted by new algorithm and interpolation algorithm is small, with the differences of mean medium errors of 27 base stations are only 2.01%(North), 0.54%(East), 1.26%(Up) and the mean ratios of variance for difference of two signals to the variance for two signals are only 1.16%(North), 0.54%(East), 1.62%(Up). © 2020, Surveying and Mapping Press. All right reserved.