To suppress the random drift error of a gyroscope signal, this paper proposes a novel denoising method, which is based on processing the intrinsic mode functions (IMFs) obtained by empirical mode decomposition (EMD). Considering that a gyroscope signal contains colored noise in addition to Gaussian white noise, fractal Gaussian noise (FGN) was introduced to quantify the noise in the gyroscope data. The proposed denoising method combines the FGN energy model and the modified method of Hausdorff distance (HD) to adaptively divide the IMFs into three categories (pure noise, pure information, and mixed components of noise and information). Then, the information IMFs and the mixed components after thresholding were selected to give the optimal signal reconstruction. Static and dynamic signal tests of the fiber optic gyroscope (FOG) were carried out to illustrate the performance of the proposed method, and compared with other traditional EMD denoising methods, such as the Euclidean norm measure method (EMD- $l_2$ -norm) and the sliding average filtering method (EMD-SA). The results of the analysis of both the static and dynamic signal tests indicate the effectiveness of the proposed method.

Conventional wavelet transform (WT) filters have less effect on de-noising and correction of a north-seeking gyroscope sensor exposed to vibration, since the optimal wavelet decomposed level for de-noising is difficult to determine. To solve this problem, this paper proposes an optimized WT filter which is suited to the magnetic levitation gyroscope (GAT). The proposed method was tested on an equivalent mock-up network of the tunnels associated with the Hong Kong‒Zhuhai‒Macau Bridge. The gyro-observed signals exposed to vibration were collected in our experiment, and the empirical values of the optimal wavelet decomposed levels (from 6 to 10) for observed signals were constrained and validated by the high-precision Global Navigation Satellite System (GNSS) network. The result shows that the lateral breakthrough error of the tunnel was reduced from 12.1 to 3.8 mm with a ratio of 68.7%, which suggests that the method is able to correct the abnormal signal of a north-seeking gyroscope sensor exposed to vibration.

The southeastern Tibetan Plateau (SETP), which hosts the most extensive marine glaciers on the Tibetan Plateau (TP), exhibits enhanced sensitivity to climatic fluctuations. Under global warming, persistent glacier mass depletion within the SETP poses a risk to water resource security and sustainability in adjacent nations and regions. This study deployed a high-precision ICESat-2 satellite altimetry technique to evaluate SETP glacier thickness changes from 2018 to 2022. Our results show that the average change rate in glacier thickness in the SETP is −0.91 ± 0.18 m/yr, and the corresponding glacier mass change is −7.61 ± 1.52 Gt/yr. In the SETP, the glacier mass loss obtained via ICESat-2 data is larger than the mass change in total land water storage observed by the Gravity Recovery and Climate Experiment follow-on satellite (GRACE-FO), −5.13 ± 2.55 Gt/yr, which underscores the changes occurring in other land water components, including snow (−0.44 ± 0.09 Gt/yr), lakes (−0.06 ± 0.02 Gt/yr), soil moisture (1.88 ± 1.83 Gt/yr), and groundwater (1.45 ± 0.70 Gt/yr), with a closure error of −0.35 Gt/yr. This demonstrates that this dramatic glacier mass loss is the main reason for the decrease in total land water storage in the SETP. Generally, there are decreasing trends in solid water storage (glacier and snow) against stable or increasing trends in liquid water storage (lakes, soil moisture, and groundwater) in the SETP. This persistent decrease in solid water is linked to the enhanced melting induced by rising temperatures. Given the decreasing trend in summer precipitation, the surge in liquid water in the SETP should be principally ascribed to the increased melting of solid water.

The signal measured by the maglev gyro sensor is sensitive to the influence of the instantaneous disturbance torque caused by the instantaneous strong wind or the ground vibration, which reduced the north-seeking accuracy of the instrument. To address this issue, we proposed a novel method combining the heuristic segmentation algorithm (HSA) and the two-sample Kolmogorov-Smirnov (KS) test (named HSA-KS method) to process the gyro signals and improve the north-seeking accuracy of the gyro. There were two key steps in the HSA-KS method: (i) all the potential change points were automatically and accurately detected by HSA, and (ii) the jumps in the signal caused by the instantaneous disturbance torque were quickly located and eliminated by the two-sample KS test. The effectiveness of our method was verified through a field experiment on a high-precision global positioning system (GPS) baseline at the 5th sub-tunnel of the Qinling water conveyance tunnel of the Hanjiang-to-Weihe River Diversion Project in Shaanxi Province, China. Our results from the autocorrelograms indicated that the jumps in the gyro signals can be automatically and accurately eliminated by the HSA-KS method. After processing, the absolute difference between the gyro and high-precision GPS north azimuths was enhanced by 53.5%, which was superior to the optimized wavelet transform and the optimized Hilbert-Huang transform.

The maglev gyroscope torque feedback orientation measurement system, equipped with abundant sampling data and high directional accuracy, plays a crucial role in underground engineering construction. However, when subjected to external instantaneous vibration interference, the gyroscope rotor signal frequently exhibits abnormal jumps, leading to significant errors in azimuth measurement results. To solve this problem, we propose a novel noise reduction algorithm that integrates Moving Average Filtering with Autoregressive Integrated Moving Average (MAF-ARIMA), based on the noise characteristics of the rotor jump signal. This algorithm initially adaptively decomposes the rotor signal, subsequently extracting the effective components of the north-seeking torque with precision and applying MAF processing to effectively filter out noise interference. Furthermore, we utilize the stable sampling trend data of the rotor signal as sample data, employing the ARIMA model to accurately predict the missing abnormal jump trend data, thereby ensuring the completeness and coherence of the rotor signal trend information. Experimental results demonstrate that, compared to the original rotor signal, the reconstructed signal processed by the MAF-ARIMA algorithm exhibits an average reduction of 70.58% in standard deviation and an average decrease of 47.31% in the absolute error of azimuth measurement results. These findings fully underscore the high efficiency and stability of the MAF-ARIMA algorithm in processing gyroscope rotor jump signals.

To eliminate the noise interference caused by continuous external environmental disturbances on the rotor signals of a maglev gyroscope, this study proposes a noise reduction method that integrates an adaptive particle swarm optimization variational modal decomposition algorithm with a strategy for error compensation of the trend term in reconstructed signals, significantly improving the azimuth measurement accuracy of the gyroscope torque sensor. The optimal parameters for the variational modal decomposition algorithm were determined using the adaptive particle swarm optimization algorithm, allowing for the accurate decomposition of noisy rotor signals. Additionally, using multi-scale permutation entropy as a criterion for discriminant, the signal components were filtered and summed to obtain the denoised reconstructed signal. Furthermore, an empirical mode decomposition algorithm was employed to extract the trend term of the reconstructed signal, which was then used to compensate for the errors in the reconstructed signal, achieving significant noise reduction. On-site experiments were conducted on the high-precision GNSS baseline of the Xianyang Yuan Tunnel in the second phase of the project to divert water from the Han River to the Wei River, where this method was applied to process and analyze multiple sets of rotor signals. The experimental results show that this method effectively suppresses continuous external environmental interference, reducing the average standard deviation of the compensated signals by 46.10% and the average measurement error of the north azimuth by 45.63%. Its noise reduction performance surpasses that of the other four algorithms.