The linear combination of multi-frequency carrier-phase and pseudorange observations can form the combined observations with special properties. The type and number of combined frequencies will directly affect the characteristics of the combined observations. BDS-2 and BDS-3 broadcast three and five signals, respectively, and the study of their linear combination is of great significance for precision positioning. In this contribution, the linear combination form of multi-frequency carrier-phase observations in cycles and meters is sorted out. Seven frequency combination modes are formed, and some special combinations for positioning are searched. Then, based on the principle of minimum combined noise, a simpler search method for the optimal real coefficients of ionosphere-free (IF) combination based on the least squares (LS) principle is proposed. The general analytical expressions of optimal real coefficients for multi-frequency geometry-based and ionosphere-free (GBIF), geometry-free and ionosphere-free (GFIF), and pseudorange multipath (PMP) combinations with the first-order ionosphere delay taken into account are derived. And the expression derivation process is given when both the first-order and second-order ionospheric delays are eliminated. Based on this, the characteristics of the optimal real coefficient combination in various modes are compared and discussed. The various combinations reflect that the accuracy of the combined observations from dual-frequency (DF) to five-frequency (FF) is gradually improving. The combination coefficient becomes significantly larger after taking the second-order ionospheric delay into account. In addition, the combined accuracy of BDS-3 is better than that of BDS-2. When only the first-order ionosphere is considered, the combination attribute of (B1C, B1I, B2a) is the best among the triple-frequency (TF) combinations of BDS-3. When both the first-order and second-order ionospheric delays are considered, the (B1C, B3I, B2a) combination is recommended.

Coal mining induces surface subsidence, making rapid and precise monitoring of this subsidence a key area of current research. To address the limitations of D-InSAR technology in capturing large-gradient deformations in the central subsidence basin and the challenges facing UAVs in accurately monitoring small deformations at the basin’s edge, we propose a method for inverting the expected parameters of surface subsidence by synergistically integrating InSAR and UAV monitoring. We determined the cumulative subsidence of monitoring points along the dip and strike observation line of the Banji 110,801 working face between 10 April 2021 and 28 June 2022, employing D-InSAR and UAV techniques. By leveraging the complementary strengths of both monitoring techniques, we fused the two types of monitoring data and verified the error of the fusion data to be within 10 cm through leveling data verification. Simulation experiments utilizing the probability integration method and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm confirmed that the 10 cm data source error remains within the required limits for probability integration parameter inversion. Finally, the BFGS algorithm was employed to invert the parameters of the probability integration method based on the fusion data results. Subsequently, these inversion parameters were used to predict the subsidence at the monitoring point and were compared with the level measured data. The results demonstrate that the use of collaborative InSAR and UAV monitoring technology for inverting the expected parameters of surface subsidence in the mining area yields superior results, aligning with the actual patterns of ground surface movement and deformation. This study addresses the global need for unmanned monitoring of mining-related subsidence. It employs InSAR and UAV technologies in a synergistic approach to monitor surface subsidence in mining regions. This approach harnesses the strengths of multiple data sources and presents a novel concept for the unmanned monitoring of surface subsidence in mining areas, contributing to environmental protection efforts.

Atmospheric water vapor is an essential source of information that predicts global climate change, rainfall, and disaster-natured weather. It is also a vital source of error for Earth observation systems, such as the global navigation satellite system (GNSS). The Zenith Tropospheric Delay (ZTD) plays a crucial role in applications, such as atmospheric water vapor inversion and GNSS precision positioning. ZTD has specific temporal and spatial variation characteristics. Real-time ZTD modeling is widely used in modern society. The conventional back propagation (BP) neural network model has issues, such as local, optimal, and long short-term memory (LSTM) model needs, which help by relying on long historical data. A regional/single station ZTD combination prediction model with high precision, efficiency, and suitability for online modeling was proposed. The model, called K-RBF, is based on the machine learning algorithms of radial basis function (RBF) neural network, assisted by the K-means cluster algorithm (K-RBF) and LSTM of real-time parameter updating (R-LSTM). An online updating mechanism is adopted to improve the modeling efficiency of the traditional LSTM. Taking the ZTD data (5 min sampling interval) of 13 international GNSS service stations in southern California in the United States for 90 consecutive days, K-RBF, R-LSTM, and K-RBF were used for regions, single stations, and a combination of ZTD prediction models regarding research, respectively. Real-time/near real-time prediction results show that the root-mean-square error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and training time consumption (TTC) of the K-RBF model with 13 station data are 8.35 mm, 6.89 mm, 0.61, and 4.78 s, respectively. The accuracy and efficiency of the K-RBF model are improved compared with those of the conventional BP model. The RMSE, MAE, R2, and TTC of the R-LSTM model with WHC1 station data are 6.74 mm, 5.92 mm, 0.98, and 0.18 s, which improved by 67.43%, 66.42%, 63.33%, and 97.70% compared with those of the LSTM model. The comparison experiments of different historical observation data in 24 groups show that the real-time update model has strong applicability and accuracy for the time prediction of small sample data. The RMSE and MAE of K-RBF with 13 station data are 4.37 mm and 3.64 mm, which improved by 47.70% and 47.20% compared to K-RBF and by 28.48% and 31.29% compared to R-LSTM, respectively. The changes in the temporospatial features of ZTD are considered, as well, in the combination model.

In the evolving landscape of device-free localization techniques, Wi-Fi channel state information (CSI) emerges as a pivotal tool for environmental sensing. This study introduces a novel fingerprint localization algorithm. It employs an improved Hybrid Grey Wolf Particle Swarm Optimization (IPSOGWO) in combination with Multi-Output Support Vector Regression (MSVR) to enhance indoor positioning accuracy. To counteract the limitations of standard DBSCAN and PCA in noise reduction and feature extraction from complex nonlinear data, we propose an adaptive denoising algorithm based on spatial clustering (A-DBSCAN) and an autoencoder to efficiently denoise and extract features from CSI amplitude to improve the localization accuracy. Additionally, we introduce a new position update strategy, bolstering the optimization efficiency of the PSOGWO algorithm. This refined approach is instrumental in determining the globally optimal hyperparameters in MSVR, leading to enhanced model prediction accuracy. Two indoor scenario experiments were conducted to evaluate our method, yielding average localization errors of 0.59 m and 1.12 m, marking an improvement in localization performance compared to existing methods.

Surface subsidence induced by coal mining poses severe threats to global ecosystems and infrastructure. A critical challenge in subsidence prediction lies in the sensitivity of existing probabilistic integral parameter inversion methods to gross errors, leading to unstable predictions and compromised reliability. To address this limitation, we propose the IGGIII-BFGS algorithm that integrates robust estimation with unconstrained optimization method, enhancing resistance to gross errors during parameter inversion. Through systematic comparison of four robust estimation methods (Huber, L1, Geman–McClure, IGGIII) fused with BFGS, the IGGIII-BFGS method demonstrated superior stability and accuracy, reducing relative errors in key parameters (subsidence factor q, horizontal displacement coefficient b, and tangent of major influence angle tan β) to near-zero levels. Validation on the Huainan mining case study showed that the IGGIII-BFGS method achieved a 25.8% reduction in subsidence RMSE compared to standard BFGS, with predicted curves exhibiting strong agreement with field measurements. This advancement enables precise forecasting of subsidence and horizontal displacement, which hold significant value for the sustainable development of the surface ecological environment and social stability.

Global Navigation Satellite System (GNSS) observations are subject to various errors during their propagation process. A reasonable correction of these errors can improve the positioning, navigation, and timing (PNT) service capability. The impact of multipaths on pseudorange observations can reach a decimeters or even meters level. However, their mechanism is complex and there is currently no universally accepted high-precision correction model. The correlation between the pseudorange multipaths (MP) of BDS-2 satellites and satellite elevation has been confirmed, while there have been fewer analyses of the MP characteristics for different frequencies of BDS-3 satellites. The broadcasting of multi-frequency observations in BDS-3 should theoretically make the extracted MP more accurate compared to traditional methods. Based on this, in this contribution, a multi-frequency MP extraction algorithm based on the least squares principle is proposed, which can simultaneously eliminate the influence of higher-order ionospheric delay. The analytical expression for only eliminating first-order ionospheric delay is successfully derived. Subsequently, the characteristics of the MPs extracted from different frequency combinations and the impact of combination noise on the extraction accuracy are discussed. The influence of second-order ionospheric delay on the MPs for each frequency under different combination noises, as well as the periodic behavior exhibited in long-term observations of the BDS-3 medium earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites, are also analyzed. Finally, the correlations between the MPs of each frequency of BDS satellite and elevation are quantitatively analyzed based on observations from 35 stations. Overall, this work has positive implications for the study of the MP characteristics of BDS-3 and subsequent modeling efforts.