Noise reduction of GNSS coordinate time series based on adaptive wavelet basis optimization and an improved threshold function

To address the insufficient noise suppression in global navigation satellite system (GNSS) coordinate time series, this paper proposes a denoising method based on adaptive optimal wavelet basis selection and the collaborative optimization of an improved threshold function (ITF). The method innovatively combines a dual optimization mechanism: on one hand, it adaptively selects the wavelet basis function and decomposition level through sparse quantification analysis, solving the compatibility issues of traditional methods; on the other hand, an ITF with two-parameter adjustable shape is proposed, which can flexibly control the shape of the threshold function, effectively improve the noise reduction accuracy and maintain the signal characteristics. In this paper, the noise reduction effects of hard threshold function, soft threshold function, Jing-yi threshold function and ITF are compared and analyzed through experiments. The simulation results show that the noise reduction effect of ITF is remarkable. After noise reduction, the signal-to-noise ratio is increased by 304.7%, and the root mean square error is reduced by 50.2%. For the measured GNSS coordinate time series, the noise reduction effect of ITF is still obvious. After noise reduction, the white noise is completely filtered out, and the amplitude and velocity uncertainty of flicker noise are significantly reduced. Among them, the decrease of velocity uncertainty in E, N and U directions reached 85.4%, 86.2% and 87.8%, respectively. The above experimental results show that the wavelet denoising method based on adaptive wavelet basis optimization and ITF shows good results in noise suppression and signal fidelity.