Jian Chen

High spatiotemporal resolution surface deformation information offers the advantage of comprehensively, precisely, and rapidly revealing surface deformation characteristics, and is key data for early identification and dynamic warning of geological disasters such as landslides and ground subsidence. However, the vast majority of monitoring methods suffer from shortcomings such as low spatiotemporal resolution, and traditional feature tracking algorithms exhibit limited reliability in long-term, non-rigid deformation scenarios. To address these issues, a surface deformation tracking method based on Time-Series Multi-View Collaborative Tracking (TS-MVCT) was constructed. The TS-MVCT framework estimates the spatial positions of the initial point cloud after deformation by establishing 2D correspondences between temporally adjacent observations within consecutive short-term intervals, followed by reliability-weighted depth fusion for 3D position estimation. To validate the effectiveness of the constructed method, an indoor simulated surface deformation experiment was conducted. The experimental results demonstrate that, compared to the M3C2 algorithm, which primarily characterizes displacement along the local surface normal, TS-MVCT effectively reduces deformation underestimation and the loss of displacement components in different spatial directions, while enabling the estimation of 3D displacement vectors at a higher density than SIFT-FT. Quantitative validation under laboratory conditions indicates that the relative deviations of the retrieved 3D displacements—measured against manually annotated reference values—are generally within 2 mm. On markerless natural surfaces, the algorithm achieves PSR and reprojection-error values within a similar numerical range to those of artificial-target regions, indicating comparable internal matching and multi-view geometric consistency under the controlled experimental conditions. In summary, the TS-MVCT framework presents a viable non-contact approach for acquiring 3D surface deformation information, providing deformation data for future geological hazard monitoring.

To address the challenges of effectively removing noise from deformation monitoring data and the inadequacies of traditional indices in comprehensively evaluating denoising performance, the sample entropy combined with successive variational mode decomposition (SE-SVMD) method is devised, and the comprehensive evaluation approach accounting for inter-index correlations is proposed. SVMD is applied to extract modes and adaptively obtain optimal components, while SE is utilized to determine the effective modes. A comprehensive evaluation index is constructed based on degree of variation in indices, information content, and conflict and overlap characteristics. Finally, validated through simulated and measured data, SE-SVMD outperforms variational mode decomposition (VMD) and ensemble empirical mode decomposition (EEMD) in simulated signal denoising, reducing root mean square error (RMSE) by 0.072 mm and 0.1 mm, enhancing signal-to-noise ratio (SNR) by 1.48 dB and 1.44 dB, respectively, and achieving a correlation coefficient of 0.995. In the measured data from 142 IGS tracking stations, SE-SVMD exhibits a 12.34% and 17.80% reduction in RMSE and an increase in the mean SNR by 5.41% and 6.24% compared to VMD and EEMD.Employing the proposed comprehensive evaluation index, the mean results of the methods are 0.52, 0.60, and 0.37, validating the approach effectiveness in quantifying denoising performance.

Accurate prediction of slope displacement is an important prerequisite for building an effective geological hazard early warning system for disaster prevention and reduction. However, the inherent nonlinearity and time-varying characteristics of slope displacement evolution greatly affect the prediction accuracy. To improve the slope displacement prediction accuracy, a multi-modal data-driven Bayesian-optimized Convolutional Neural Network and Long Short-Term Memory (Bayes-CNN-LSTM) model was constructed. The performance of the model was evaluated using multi-modal monitoring data from the GuShan mine slope. Experimental results showed that the Bayes-CNN-LSTM model achieved an average coefficient of determination (R²) of 0.971, with a mean absolute error (MAE) of 0.444 mm and a root mean square error (RMSE) of 0.618 mm. Compared with the CNN-LSTM, LSTM, CNN, SVM, TCN, and Transformer models, the MAE of the constructed model was decreased by 25.1%, 31.3%, 32.3%, 24.1%, 24.7%, and 17.7%, respectively, and the RMSE decreased by 20.1%, 26.9%, 29.5%, 18.0%, 20.7%, and 12.4%, respectively. Furthermore, the proper integration of multi-modal data can effectively improve the prediction accuracy when extrapolating slope displacement. Based on rainfall and earth pressure data, the average MAE and RMSE of extrapolation (24-h) prediction using the constructed model were decreased by 30.2% and 24.6%, respectively. The model effectively improves the accuracy of slope displacement prediction and enhances the practicality of the slope safety monitoring system, providing valuable reference for slope safety monitoring.

Conventional Global Navigation Satellite System (GNSS) time transfer algorithms typically model receiver clock offsets as white noise for estimation, neglecting the physical characteristics of atomic clocks, which consequently limits the performance of GNSS time transfer. To overcome this limitation, this study proposes an undifferenced GPS/Galileo combined Precise Point Positioning (PPP) time transfer model, incorporating both one-state (only clock offset parameter) and two-state (both clock offset and frequency offset parameters) refined clock models with clock instantaneous re-initialization (CIR) strategy at the day boundary epoch. Using observations from International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) stations equipped with external hydrogen masers, precise time transfer performance under refined clock models was evaluated based on undifferenced GPS/Galileo combined PPP float solutions and PPP ambiguity resolutions. Experimental results demonstrate that, compared to traditional models, the refined clock models improve time transfer accuracy and frequency stability by an average of 6.7% and 25.8%, respectively. The improvement is most significant for short term frequency stability, with a maximum enhancement exceeding 85%. As the averaging time increases, the improvement in long term frequency stability gradually diminishes. Notably, the two-state refined clock model slightly outperforms the one-state model in time transfer performance, with the two-state refined clock model improving short-, medium-, and long term frequency stability by 11.5%, 8.0%, and 0.2%, respectively, compared to the one-state refined clock model. These findings strongly advocate adopting the two-state refined clock model to optimize both time transfer precision and short term stability in high-accuracy applications.

The BDS-3 global navigation satellite system now supports five frequencies signals, enabling the construction of optimal combined observations characterized by long wavelength, ionosphere-reduced, and low noise. These features are advantageous for achieving real-time ambiguity resolution. In this contribution, the characteristics of optimal linear combinations for BDS-3 under various assumed error scenarios is analyzed in detail. Additionally, the performance of BDS-3 single-epoch multi-frequency carrier ambiguity resolution (MCAR) employing the geometry-based (GB) method is comprehensively evaluated, which encompasses triple-frequency (TCAR), quad-frequency (QCAR), and penta-frequency (PeCAR) ambiguities resolution. Utilizing measured data from BDS-3, the findings indicate that the ambiguity resolution rate of the B1C basic signal exceeds 95%, outperforming the B2a signal. Furthermore, when employing the GB-QCAR and GB-PeCAR, the positioning accuracy of the B1C signal under fixed solutions is essentially consistent with that of the GB-TCAR. Even with a satellite cutoff elevation angle of 30°, the B1C signal ambiguity resolution rate remains above 91%. In summary, the GB-MCAR method proves effective in obstructed environments, and an increase in the number of frequencies enhances the reliability of ambiguity resolution.

The detection and repair of Galileo multi-frequency (quad/pent-frequency) cycle slips are susceptible to the effects of multipath, pseudo-range noise, and high ionospheric disturbances. Taking into account the combination noise and ionospheric amplification factors, the optimal multi-frequency combination coefficients are selected for cycle slip detection. The approach addresses the issue from both the observational and computational levels, ensuring the accuracy and efficiency of cycle slip repair. On the observational level, the noise in pseudo-range observations is typically much higher than that in carrier phase observations. To mitigate the impact of pseudo-range observation noise and its associated multipath effects, the carrier smoothing pseudo-range method is considered, aiming to improve the accuracy of cycle slip repair. On the computational level, to avoid the extensive computational load caused by the LAMBDA algorithm’s space search, a dual constraint is applied to the Least Squares (LS) method using the L2-norm criterion and the non-negative solution criterion. The integer rounding of the parameter solution is then adopted as the fixed cycle slip solution. The experimental results are as follows: For quad-frequency cycle slip detection and repair (QCDR), one Geometry-Free and Ionosphere-Free (GFIF) combination [0, 1, −3, 2] and three phase Geometry-Free (GF) combinations [−1, 1, 0, 0], [0, −1, 1, 0], [0, −1, 0, 1] are selected. For pent-frequency cycle slip detection and repair (PCDR), one GFIF combination [0, −1, 2, 0, −1] and four GF combinations [0, 0, −1, −1, 2], [−1, 1, 0, 0, 0], [−1, 0, 0, 0, 1], [0, 1, −3, 0, 2] are chosen. Using the proposed algorithm, under regular conditions, the success rate for detecting quad/pent-frequency cycle slips is 100%, with repair success rates of 99.60% and 99.48%, respectively. In ionospheric environments with varying levels of disturbance, three monitoring stations are selected. The success rates for quad-frequency cycle slip repair are 99.96%, 99.05%, and 99.96%, while the success rates for pent-frequency cycle slip repair are 99.96%, 99.15%, and 99.94%.

Currently, the four major Global Navigation Satellite Systems (GNSS) are capable of supporting multi-frequency signals, and Real-time (RT) State Space Representation (SSR) correction products have been enriched and improved. Multi-GNSS, multi-frequency observations and multiple satellite RT SSR correction products present new opportunities to implement precise RT time transfer. This study extends the traditional post-processing dual-frequency undifferenced (UD) Precise Point Positioning (PPP) time transfer to RT multi-frequency scenarios, establishes models for dual-frequency, triple-frequency, quad-frequency and penta-frequency multi-GNSS PPP time transfer, and evaluates the product availability, orbit accuracy and clock offset accuracy of RT SSR products from BKG, CNE, DLR, ESA, GFZ, GMV, WHU, and IGS. A multi-frequency and multi-GNSS RT PPP time transfer experiment was conducted by selecting data from four stations, BRUX, PTBB, ONSA and SPT0, with precise atomic clocks mounted for one week. The accuracy of various SSR products in RT PPP time transfer was compared, and the performance of BDS/Galileo combination dual-frequency to penta-frequency RT UD PPP time transfer was evaluated. The experimental results show that the standard deviation and frequency stability difference of RT PPP time transfer among each SSR product is relatively small, especially after combining multi-systems. The frequency stability tends to be entirely consistent. In general, the WHU, GFZ, GMV, and WHU SSR products offer notable advantages in terms of accuracy and frequency stability for GPS, GLONASS, Galileo, and BDS RT PPP time transfer, respectively. Multi-GNSS and multi-frequency signals have both enhanced RT PPP time transfer performance, with a particularly noticeable improvement in terms of accuracy and short-term frequency stability. The effect of multi-GNSS on RT PPP time transfer is more pronounced than that of multi-frequency alone. Considering the higher costs associated with multi-frequency GNSS receivers, prioritizing multi-GNSS for RT PPP time transfer is recommended.

In recent years, the quantity of visible satellites has increased significantly due to multiple satellite systems that leaped forward. The BeiDou Navigation Satellite System (BDS) and Galileo satellite navigation system (Galileo) broadcast triple-frequency signals and above to users, thus enhancing the reliability, continuity, and availability of the single-epoch real-time kinematic (RTK) positioning. In this study, an improved single-epoch multifrequency multisystem RTK method is successfully developed for the medium-long baseline. First, the Galileo and BDS extra-wide-lane (EWL) ambiguities are fixed at a high success rate, and the Galileo and BDS wide-lane (WL) ambiguity is achieved via the transformation process. Second, the fixed WL ambiguities of Galileo and BDS are exploited to elevate the fixed rate of GPS WL ambiguity. Third, the parametric strategies for ionospheric delay are carried out to upregulate the narrow-lane (NL) ambiguity-fixed rate of GPS. Further, the real-time data are adopted for verifying the feasibility of the method developed in this study. The experimental results demonstrate the optimal carrier-to-noise density ratio (C/N0) of full operational capability (FOC) E5a/E5b at all frequencies, followed by IIR-M L1, and IIR-A/B L2 exhibits the worst performance. Generally, the multipath combination (MPC) of Galileo signals shows root mean square (RMS) values within 0.4 m, ordered as follows: . For the BDS-2, the B3 signal exhibits optimal performance, while the B1 signal is the worst. The RMS of MPC errors of L1 signals is smaller than the L2 signals for the GPS. Furthermore, under the 50 km baseline, the GPS NL ambiguity-fixed rate using the ionosphere-free (IF) combination reaches only 47.74% at the ratio threshold of 2. Finally, compared to the ionosphere-free combination method, the GPS NL ambiguity-fixed rate is increased by 45.52% with the presented method. The proposed approach broadens the future application of deformation monitoring in medium-long baseline scenarios.

To obtain a higher accuracy for the real-time Zenith Tropospheric Delay (ZTD), a refined tropospheric delay correction model was constructed by combining the tropospheric delay correction model based on meteorological parameters and the GPT3 model. The meteorological parameters provided by the Global Geodetic Observing System (GGOS) Atmosphere and the zenith tropospheric delay data provided by Centre for Orbit Determination in Europe (CODE) were used as references, and the accuracy and spatial–temporal characteristics of the proposed model were compared and studied. The results show the following: (1) Compared with the UNB3m, GPT and GPT2w models, the accuracy and stability of the GPT3 model were significantly improved, especially the estimation accuracy of temperature, the deviation (Bias) of the estimated temperature was reduced by 90.60%, 32.44% and 0.30%, and the root mean square error (RMS) was reduced by 42.40%, 11.02% and 0.11%, respectively. (2) At different latitudes, the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models had great differences in accuracy and applicability. In the middle and high latitudes, the Biases of the GPT3 + Saastamoinen model and the GPT3 + Hopfield model were within 0.60 cm, and the RMS values were within 4 cm; the Bias of the UNB3m model was within 2 cm, and the RMS was within 5 cm; in low latitudes, the accuracy and stability of the GPT3 + Saastamoinen model were better than those of the GPT3 + Hopfield and UNB3m models; compared with the GPT3 + Hopfield model, the Bias was reduced by 22.56%, and the RMS was reduced by 5.67%. At different heights, the RMS values of the GPT3 + Saastamoinen model and GPT3 + Hopfield model were better than that of the UNB3m model. When the height was less than 500 m, the Biases of the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models were 3.46 cm, 3.59 cm and 4.54 cm, respectively. At more than 500 m, the Biases of the three models were within 4 cm. In different seasons, the Bias of the ZTD estimated by the UNB3m model had obvious global seasonal variation. The GPT3 + Saastamoinen model and the GPT3 + Hopfield model were more stable, and the values were within 5 cm. The research results can provide a useful reference for the ZTD correction accuracy and applicability of GNSS navigation and positioning at different latitudes, at different heights and in different seasons.

The global navigation satellite system (GNSS), as a high-time resolution and high-precision measurement technology, has been widely used in the field of deformation monitoring. Owing to the influence of uncontrollable factors, there are inevitably some abnormal data in the GNSS monitoring series. Thus, it is necessary to detect and identify abnormal data in the GNSS monitoring series to improve the accuracy and reliability of the deformation disaster law analysis and warning. Many methods can be used to detect abnormal data, among which the statistical process control theory, represented by the cumulative sum (CUSUM), is widely used. CUSUM usually constructs statistics and determines control limits based on the threshold criteria of the average run length (ARL) and then uses the control limits to identify abnormal data in CUSUM statistics. However, different degrees of the ‘trailing’ phenomenon exist in the interval of abnormal data identified by the algorithm, leading to a higher false alarm rate. Therefore, we propose an improved CUSUM method that uses breaks for additive season and trend (BFAST) instead of ARL-based control limits to identify abnormal data in CUSUM statistics to improve the accuracy of identification. The improved CUSUM method is used to detect abnormal data in the GNSS coordinate series. The results show that compared with CUSUM, the improved CUSUM method shows stronger robustness, more accurate detection of abnormal data, and a significantly lower false alarm rate.