Noise reduction of GNSS vertical coordinate time series using ICEEMDAN-TCN

Nonlinear and non-stationary noise is a major cause of instability in GNSS coordinate time series velocity estimation. Effectively reducing noise in the time series is crucial to improving the accuracy of velocity estimation accuracy. To effectively remove noise from time series, this paper proposes a combined denoising model, ICEEMDAN-TCN, which integrates improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), multiscale permutation entropy (MPE), and temporal convolutional network (TCN). The study selects vertical coordinate time series from 394 stations across Chinese mainland for experimental verification and compares the results with ICEEMDAN, wavelet domain denoising (WD) and ICEEMDAN-WD methods. The results show that, whether using the unified optimal noise model or the evaluated optimal noise model for velocity estimation before and after denoising, ICEEMDAN-TCN outperforms ICEEMDAN, WD, and ICEEMDAN-WD in noise suppression, with an average suppression rate exceeding 90%. When the optimal noise model is used, both WD and ICEEMDAN-WD suppress noise but also increase velocity uncertainty, indicating over-denoising. In contrast, the proposed ICEEMDAN-TCN does not exhibit such issues.