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.

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.

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.

Accurate positioning of mining working faces and reliable acquisition of their spatial characteristics play a key role in controlling illegal mining, in addition to identifying underlying hazards in coal mine goafs. However, when errors are present in observation deformation data, the traditional approach used to precisely locate rectangular working faces and invert their spatial characteristics cannot be used to accurately describe the properties of mining working faces. To address this issue, based on the relationship between surface deformation and the mining-induced response of the underground working face, in combination with the weighted iterative robust genetic algorithm (GA), we construct a precise positioning method for mining working faces. The simulation test results of this method demonstrate that, compared with the conventional GA, it not only has lower fitting errors (reduced from 73.5 mm to 49.0 mm and from 80.8 mm to 48.8 mm, respectively) but also significantly decreases the maximum relative error in the mining characteristic parameter inversion results. By applying it in the actual case of Guqiao Mine’s 1414 (1) mining working face, the proposed method’s reliability is further validated. The obtained results offer practical support for underground goaf detection and mining supervision efforts.

Satellite clock bias (SCB) is a critical error source affecting the positioning and timing accuracy of Global Navigation Satellite Systems (GNSSs). The conventional back propagation neural network (BP) model, when applied to SCB prediction, is prone to local optima and exhibits rapid error divergence. To address these limitations, this study proposes and investigates two enhanced BP models: one optimized by the genetic algorithm (GA) and another by the mind evolutionary algorithm (MEA). A comprehensive comparative analysis is conducted against the standard BP model. Experiments utilize precise clock products from the International GNSS Service (IGS), with data from six representative satellites featuring different atomic clock types (IIR, IIR-M, IIF rubidium, and cesium clocks). The models are trained on 24 h of historical data and evaluated by forecasting clock biases for 2, 6, 12, and 24 h ahead. Prediction accuracy is assessed using root mean square error (RMS), range, and mean error. The results demonstrate that optimization algorithms significantly improve the BP neural network’s performance. The genetic algorithm optimized back propagation neural network (GABP) model demonstrates comprehensive superiority, achieving the highest accuracy across all forecast horizons and satellite types. For instance, in 24 h predictions, the average RMS error of the GABP model (6.516 ns) is merely 10.9% of the standard BP model’s error. Notably, for the cesium clock on satellite G24, the GABP model’s 24 h RMS (1.600 ns) is approximately 23 times lower than that of the mind evolutionary algorithm optimized back propagation neural network (MEABP) model. The GABP model also shows strong adaptability, maintaining high precision for both rubidium and cesium clocks and exhibiting gradual error growth with extended forecast duration, indicating excellent generalization and resistance to overfitting. To further evaluate generalization across different seasons and time periods, additional experiments were conducted using data from February–March, June, and October 2021 on six different satellites. The results consistently show that GABP outperforms MEABP and BP across all tested conditions. While the MEABP model outperforms the standard BP, it shows limitations in long-term forecasts, particularly for cesium clocks, due to tendencies for premature convergence and sensitivity to data noise. In conclusion, the GABP model, leveraging the robust global optimization capability of the genetic algorithm is validated as a highly effective and reliable solution for high-accuracy short- and long-term satellite clock bias prediction.

The emergence of large-gradient deformation within a short period is a typical characteristic of mining subsidence. InSAR phase unwrapping can readily fail as a consequence of this deformation characteristic, and it is challenging to achieve effective monitoring of mining subsidence over mining sites with InSAR techniques. To monitor mining subsidence, we developed an InSAR strategy with constraints derived from the IPIM (Improved Probability Integration Method). As the initial step, this method modifies the PIM model to improve its precision in predicting the surface deformation basin edge. Furthermore, by investigating the functional relationship between InSAR-observed line-of-sight (LOS) deformation and the three-dimensional surface displacement in subsidence regions, we develop a new IPIM-constrained InSAR observation condition equation for mining subsidence. Subsequently, taking the GA (genetic algorithm) as the optimization solver, we establish an IPIM parameter inversion model driven by the GA. In the final stage, using LOS displacement measurements acquired from InSAR observations, the surface displacement field over mining subsidence zones can be extracted using the presented InSAR monitoring scheme constrained by the IPIM forecasting model. Using field measurements collected at the 2111(3) working face of the Xieqiao Coal Mine, the error in subsidence fitting is ±178.76 mm. The presented technique has been validated as feasible and can supply fundamental datasets for geological hazard prevention and control in mining areas.