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.

Due to the cuboid satellite body of BeiDou-3 satellites, the accuracy of their orbit showed a trend of systematic variation with the sun-satellite-earth angle (ε) using the Extend CODE Orbit Model (ECOM1). Therefore, an a priori cuboid box-wing model (named the cuboid model) is necessary to compensate ECOM1. Considering that the body-dimensions and optical properties of the BeiDou-3 satellites used to construct the box-wing model have not yet been fully released, the adjustable box-wing model (ABW) was used for precise orbit determination (POD). The a priori cuboid box-wing model was directly estimated by the precision radiation accelerations, obtained from ABW POD. When using ECOM1 model, for 14 < β < 40°, a linear systematic variation of D0 related to the elevation of the sun above the orbital plane (β-angle) with a slope of 0.048 nm/s²/°, was found for C30. After adding the cuboid model to assist ECOM1 (named Cuboid + ECOM1), the slope was reduced to 0.005 nm/s²/°, and for C20 satellite, the standard deviation (STD) of D0 was improved, from 1.28 to 0.85 nm/s² (34%). For satellite laser ranging (SLR) validation, when using the ECOM1 model, the systematic variation with the ε angle was about 14 cm for C20 and C30. After using the Cuboid + ECOM1 model, the variation was significantly reduced to about 5 cm. For C20 and C21, compared with the ECOM1 model, the root mean square (RMS) of the ECOM2 and Cuboid + ECOM1 model was improved by about 0.54 (10.3%) and 0.43 cm (8.7%). For C29 and C30, the RMS of ECOM2 and Cuboid + ECOM1 model was improved for about 0.7 (10.9%) and 1.6 cm (25.6%). Finally, the RMS of the SLR residuals of 4.37 to 4.88 cm was achieved for BeiDou-3 POD.

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.