Reconstruction of gappy GPS coordinate time series using empirical orthogonal functions

Data gaps are an unfortunate aspect of Global Positioning System (GPS) time series and that can (a) slow down the maximum likelihood estimation for stochastic noise modeling and (b) hamper signal processing algorithms that require evenly spaced data. Simply filling the data gaps by linear interpolation does not significantly bias the velocity estimates in the least squares analysis, whereas it may be less suitable for periodic term estimates for vertical GPS observations especially those that are sampled with wide gaps. We use iterative empirical orthogonal function-based (EOF-based) method to recover the gappy GPS coordinate time series and discuss their effects on periodic term estimates. Ordinary least squares estimation-based (LSE-based) interpolation (including trend, annual, and semiannual terms) is performed for comparison. We demonstrate our method with synthetic examples, as well as real daily coordinate time series of 10 GPS sites with more than 14 years of data. The optimal window size and number of dominant EOFs are determined using crossvalidation. We find that EOF-based interpolation may bias amplitude estimates in the up component owing to the artificial signals introduced in the EOFs reconstruction. After skipping the “noisy” EOFs and including only EOFs that we are particularly interested, the bias becomes smaller. Moreover, EOF-based interpolation outperforms LSE interpolation in the wavelet analysis of GPS time series particularly for situations with wide gaps. Offsets are also found to be essentially nuisance parameters that must be removed prior to applying interpolation.