GNSS technology is a crucial tool for mining subsidence monitoring. However, it faces challenges from external environmental interference, resulting in a noisy time series. The zenith-direction noise, in particular, significantly impacts the measurement results. We introduce a novel noise reduction method, PSOGWO-ICEEMDAN-WT, combining a hybrid gray wolf particle swarm optimization algorithm with an enhanced adaptive noise-complete set empirical modal decomposition and wavelet thresholding. We first use the PSOGWO algorithm to determine the optimal white noise weights and the number of noise additions for ICEEMDAN. Then, we apply PSOGWO-ICEEMDAN decomposition to the GNSS zenith direction time series data, yielding a series of intrinsic modal functions (IMFs). We then employ multiscale alignment entropy as an evaluation metric and set thresholds to segregate the IMFs into noise-containing components. The IMFs are divided into noise-containing and pure IMF components. We apply wavelet thresholding to reduce noise in the former. Finally, we combine these noise-reduced components with the pure IMFs to obtain the cleaned data. We conducted experiments using both simulated signals and measured data from an automated monitoring station in a mining area. The results confirm that our method effectively removes noise from GNSS zenith direction time-series data, providing reliable data for subsequent workings settlement analysis.