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The accuracy of InSAR in monitoring mining surface subsidence is always a matter of concern for surveyors. Taking a mining area in Shandong Province, China, as the study area, D-InSAR and SBAS-InSAR were used to obtain the cumulative subsidence of a mining area over a multi-period, which was compared with the mining progress of working faces. Then dividing the mining area into regions with different magnitudes of subsidence according to the actual mining situation, the D-InSAR-, SBAS-InSAR- and leveling-monitored results of different subsidence magnitudes were compared and the Pearson correlation coefficients between them were calculated. The results show that InSAR can accurately detect the location, range, spatial change trend, and basin edge information of the mining subsidence. However, InSAR has insufficient capability to detect the subsidence center, having high displacement rates, and its monitored results are quite different from those of leveling. To solve this problem, the distance from each leveling point to the subsidence center was calculated according to the layout of the rock movement observation line. Besides, the InSAR-monitored error at each leveling point was also calculated. Then, according to the internal relationship between these distances and corresponding InSAR-monitored errors, a correction model of InSAR-monitored results was established. Using this relationship to correct the InSAR-monitored results, results consistent with the actual situation were obtained. This method effectively makes up for the deficiency of InSAR in monitoring the subsidence center of a mining area.

SBAS-InSAR technology has been widely researched and applied in the large-scale monitoring of mining areas, but due to the influence of spatial and temporal discorrelation, atmospheric delay and noise on the deformation results, as well as the requirements on image quantity, quality and spatial continuity, the SBAS-InSAR technology inferior to the levelling monitoring results in terms of measurement accuracy and reliability. Taking the Yuncheng coal mine as the research area, and after using SBAS InSAR to monitor the subsidence, the levelling monitoring data was used as the constraint to construct the subsidence error surface by polynomial surface fitting, and then the SBAS-InSAR subsidence monitoring results were be corrected. The experimental results show that the settlement difference is better than ±50mm/a, which effectively improves the overall accuracy of SBAS-InSAR settlement monitoring. The experimental results verify the feasibility and effectiveness of using the level monitoring results to correct the deformation monitoring results of SBAS InSAR, and provide effective reference information for improving the accuracy of the deformation monitoring results by multi-source fusion processing.

In coal mining areas, surface subsidence poses significant risks to human life and property. Fortunately, surface subsidence caused by coal mining can be monitored and predicted by using various methods, e.g., probability integral method and deep learning (DL) methods. Although DL methods show promise in predicting subsidence, they often lack accuracy due to insufficient consideration of spatial correlation and temporal nonlinearity. Considering this issue, we propose a novel DL-based approach for predicting mining surface subsidence. Our method employs K-means clustering to partition spatial data, allowing the application of a gate recurrent unit (GRU) model to capture nonlinear relationships in subsidence time series within each partition. Optimization using snake optimization (SO) further enhances model accuracy globally. Validation shows our method outperforms traditional Long Short-Term Memory (LSTM) and GRU models, achieving 99.1% of sample pixels with less than 8 mm absolute error.

In the process of mineral resource extraction, monitoring surface deformation is crucial for ensuring the safety of engineering and ground infrastructure. Monitoring complete three-dimensional surface deformation is particularly significant. Traditional synthetic aperture radar (InSAR) technology provides deformation components only along the line of sight (LOS) and often lacks sufficient effective data in vegetation-covered mining areas and mining subsidence centers. To address this, this study proposes a method (SBAS-PIM) that combines SBAS-InSAR with the probabilistic integral method (PIM). This method leverages high-coherence points in mining areas and GNSS data from vegetation-covered regions to invert the parameters required by PIM, thus obtaining three-dimensional surface deformation results. The proposed method allows for the acquisition of three-dimensional deformation data with fewer InSAR points and GNSS data, significantly reducing labor costs and addressing the gap in InSAR monitoring of three-dimensional surface deformation in densely vegetated areas. Additionally, it accounts for the mutual influence of multiple adjacent working faces. Finally, through the application to a mining area in Heze, China, the maximum displacements in the vertical, east–west, and north–south directions were obtained as −2011, −418, and − 281 mm, respectively. The correlation coefficients between the vertical and east–west directions and GNSS data were both greater than or equal to 0.9, indicating that this method can effectively monitor the three-dimensional surface deformation of the mining area.

With the accelerated urbanization process in Qingdao, urban land subsidence has damaged infrastructure and hindered the sustainable development. To prevent disasters caused by urban land subsidence, large-scale, long-term monitoring, mechanism analysis, and risk assessment are essential. This study proposes an improved time series Interferometric Synthetic Aperture Radar (InSAR) method, extracting Permanent Scatterers (PS) and Distributed Scatterers (DS) based on a two-layer network. Using Sentinel-1 dataset, Qingdao's land subsidence from 2019 to 2024 was monitored. The results were validated using multi-source data, and a comprehensive analysis of the spatiotemporal distribution and causes of subsidence was conducted ,alongside a risk matrix based on the Hurst index. Results show that combining PS and DS increases measurement density. From 2019 to 2024, Qingdao's land was generally stable, with subsidence mainly along Jiaozhou Bay , reaching a maximum rate of −84 mm/year due to urbanization and land reclamation. Two mechanisms were identified at Jiaozhou Bay Bridge: linear and seasonal cyclic subsidence. The urban land risk matrix revealed that most sampling points in seven subsidence areas remain in a dangerous state. This study systematically investigated  Qingdao's land subsidence, evaluated urban stability, and provided insights and solutions for subsidence prevention and control.

Unmanned vehicles need to know their location and direction information accurately to plan and navigate their paths. However, the positioning system is susceptible to interference from a variety of factors, which leads to increased positioning errors, thereby affecting the accuracy of unmanned vehicle positioning. An unmanned vehicle fusion positioning technology based on the \"5G + Beidou\" integrated positioning system was proposed. While using the \"5G + Beidou\" base station for positioning, the 3D point cloud image was fused, and the high-precision real-time positioning was carried out through the vehicle's autonomous navigation algorithm. This paper first analyzed the current situation and characteristics of GNSS technology and studied the key technologies and principles of the \"5G + Beidou\" integrated positioning system. Then, aiming at the difficulty of 5G base station deployment, the GNSS system parameter optimization scheme based on a multidimensional fusion structure was designed. Finally, in the experiment, it was verified that the fusion system could achieve higher precision positioning results compared with traditional single-dimensional GNSS and multi-dimensional GNSS. The technical advantages of \"5G + Beidou\" were used for data fusion processing of unmanned vehicles, and a positioning method based on the combination of 3D point cloud image and high-precision map was proposed. Through some experiments, it was concluded that the fusion location method could control the error below 0.1, which showed the accuracy of the fusion location.

In this work, we combine the special structure of the separable nonlinear least squares problem with a variable projection algorithm based on singular value decomposition to separate linear and nonlinear parameters. Then, we propose finding the nonlinear parameters using the Levenberg–Marquart (LM) algorithm and either solve the linear parameters using the least squares method directly or by using an iteration method that corrects the characteristic values based on the L-curve, according to whether or not the nonlinear function coefficient matrix is ill posed. To prove the feasibility of the proposed method, we compared its performance on three examples with that of the LM method without parameter separation. The results show that (1) the parameter separation method reduces the number of iterations and improves computational efficiency by reducing the parameter dimensions and (2) when the coefficient matrix of the linear parameters is well-posed, using the least squares method to solve the fitting problem provides the highest fitting accuracy. When the coefficient matrix is ill posed, the method of correcting characteristic values based on the L-curve provides the most accurate solution to the fitting problem.

This study investigated the role of the number of differentialinterferograms and coherent threshold values on the accuracy of SBAS InSAR (small baseline subset interferometric synthetic aperture radar) results for specific applications in Jiyang Coal. Fifty-eight imageswere utilized to form fourdifferential interferogram timeseries with different numbers of interferograms and coherence thresholds. The four SBAS InSAR-monitored results, mining information of 15 working faces, and levelling-monitored results of 260 levelling points werecompared.The greater number of differential interferograms and lower coherent threshold values could better reflect the spatial distribution and variation trend of mining subsidence and demonstrate the advantages of SBAS InSAR. However, an excessive number of differential interferograms and excessively low coherent threshold values would increase the data processingdifficulty and the differences between SBAS InSAR- and levelling-monitoredresults. Location, spatial distributionandscopeofSBAS InSAR-monitored mining subsidence were consistent with the mining progress of the working faces.The accuracy ofSBASInSAR-monitored subsidence values followed a certain spatio-temporal variation law. The variation trend of absolute differences between SBAS InSAR-and levelling-monitored subsidence values was similar to the shape of the levelling-monitoredsubsidence basin, which was helpful to study the correction method of SBAS InSAR-monitored results.

Light detection and ranging (LiDAR) is commonly used to create high-resolution maps; however, the efficiency and convergence of parameter estimation are difficult. To address this issue, we evaluated the structural characteristics of received LiDAR signals by decomposing them into Gaussian functions and applied the variable projection algorithm of the separable nonlinear least-squares problem to the process of waveform fitting. First, using a variable projection algorithm, we separated the linear (amplitude) and nonlinear (center position and width) parameters in the Gaussian function model; the linear parameters are expressed with nonlinear parameters by the function. Thereafter, the optimal estimation of the characteristic parameters of the Gaussian function components was transformed into a least-squares problem only comprising nonlinear parameters. Finally, the Levenberg–Marquardt algorithm was used to solve these nonlinear parameters, whereas the linear parameters were calculated simultaneously in each iteration, and the estimation results satisfying the nonlinear least-square criterion were obtained. Five groups of waveform decomposition simulation data and ICESat/GLAS satellite LiDAR waveform data were used for the parameter estimation experiments. During the experiments, for the same accuracy, the separable nonlinear least-squares optimization method required fewer iterations and lesser calculation time than the traditional method of not separating parameters; the maximum number of iterations was reached before the traditional method converged to the optimal estimate. The method of separating variables only required 14 iterations to obtain the optimal estimate, reducing the computational time from 1128 s to 130 s. Therefore, the application of the separable nonlinear least-squares problem can improve the calculation efficiency and convergence speed of the parameter solution process. It can also provide a new method for parameter estimation in the Gaussian model for LiDAR waveform decomposition.