Improving GNSS-RTK multipath error extraction with an integrated CEEMDAN and STD-based PCA algorithm

To address the background noise interference in GNSS-RTK during prolonged structural monitoring, the integration of the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and the standard deviation (STD)-based principal component analysis (PCA) method (CEEMDAN-PCA-S) is proposed for de-noising. The CEEMDAN-PCA-S aims to de-noise the internal random noise by leveraging its white noise characteristics and subsequently extract the multipath error by leveraging its periodic repetition characteristics. The efficiency of CEEMDAN-PCA-S is verified with a simulation and a field experiment. The simulation results demonstrate that the STD-based PCA (PCA-S) could achieve superior amplitude consistency with the original signal compared to traditional PCA. Additionally, the correlation coefficients of the multipath error obtained with different algorithms are PCA-S (0.9243) < CEEMDAN (0.9582) < CEEMDAN-PCA-S (0.9945). Moreover, the residual error of CEEMDAN-PCA-S is minimal in terms of amplitude and root mean square error (RMSE), confirming its superior de-noising performance compared to CEEMDAN and PCA-S. The outcomes of a field experiment utilizing the GNSS-RTK indicate that the correlation coefficients between the multipath error extracted with CEEMDAN-PCA-S and the CEEMDAN residual errors are all above 0.94. The CEEMDAN-PCA-S decreases the RMSE of residual error to 0.1599 cm, marking a 79% reduction from the original signal. Moreover, both the amplitude and mean value are reduced by 83% and 16%. In conclusion, the proposed CEEMDAN-PCA-S could effectively remove white noise and subsequently extract the multipath error, enhancing the accuracy of GNSS-RTK for long-term structural monitoring and safety warnings.