By relying on the advantages of a uniform site distribution and continuous observation of the Continuously Operating Reference Stations (CORS) system, real-time high-precision Global Navigation Satellite System/Precipitable Water Vapor (GNSS/PWV) data interpretation can be carried out to achieve accurate monitoring of regional water vapor changes. The study of the atmospheric water vapor content and distribution changes is the basis for the realization of rainfall forecasting and water vapor circulation research. Such research can provide data support for the effective forecasting of regional precipitation in megacities and the construction of a more sensitive flood prevention and warning system. Nowadays, a single model is often adopted for GNSS/PWV time series. This makes it challenging to match the high randomness characteristic of water vapor change. This study proposes a hybrid model that takes into account the linear and nonlinear aspects of water vapor data by using complete empirical mode decomposition (CEEMDAN) of adaptive noise, differential autoregressive integrated moving average (ARIMA), and the long-short-term memory network (LSTM). The CEEMDAN is used to decompose the water vapor data series. Then, the high- and low-frequency data are modeled separately, reducing the sequence’s complexity and non-stationarity. In selecting the prediction model, we use the ARIMA model for the high-frequency series and the ARIMA–GWO–LSTM ensemble model for the low-frequency sub-series and residual series. The model is verified using GNSS/PWV time series data collected at the Hong Kong CORS station in July 2021. The results show the following: (1) The LSTM model optimized by the grey wolf optimization algorithm (GWO) is comparable with the single LSTM model in the low-frequency sequence prediction process, and the error items are reduced by 30% after calculation. (2) During the process from CEEMDAN decomposition to the use of the combination model for prediction, the accuracy evaluation indexes of the station increase by more than 20%. The interpolation method can accurately determine the regional water vapor spatial variation, which is of practical significance for local rainfall forecasting. High-frequency data obtained by CEEMDAN decomposition demonstrate the dramatic changes in water vapor before and after the rainfall, which can provide ideas for improving the accuracy of rainfall forecasting.

Urban vitality (UV) is a critical indicator for measuring the level of sustainable urban development, closely associated with environmental factors such as population density, economic activity, and spatial utilization efficiency. However, traditional methods face significant limitations in capturing the heterogeneity and nonlinear relationships between urban vitality and its influencing factors. This study suggests an interpretable machine learning framework to address the aforementioned issues. It combines a gradient boosting decision tree (GBDT) model with the SHapley Additive exPlanation (SHAP) framework to examine the urban vitality distribution characteristics and factors that influence them in Beijing’s fifth ring road. The main findings include the following: Urban vitality within Beijing’s fifth ring road exhibits significant spatial clustering and positive correlations, with clear spatial heterogeneity. The plot ratio (PR) exerts a notable positive influence on urban vitality, while green space accessibility (DG) demonstrates the strongest negative impact. The building density (BD), in contrast, shows a strong negative correlation with urban vitality. Variables such as the NDVI, average housing price (AHP), and road network density (RND) contribute significantly to urban vitality, reflecting the combined effects of vegetation coverage, economic conditions, and transportation layout. The findings provide a quantitative analytical tool for urban planning, facilitating resource optimization, improving urban vitality, and supporting scientific and rational decision-making.

As micro-electro-mechanical systems (MEMS) technology continues its rapid ascent, a growing array of smart devices are integrating lightweight, compact, and cost-efficient magnetometers and inertial sensors, paving the way for advanced human motion analysis. However, sensors housed within smartphones frequently grapple with the detrimental effects of magnetic interference on heading estimation, resulting in diminished accuracy. To counteract this challenge, this study introduces a method that synergistically employs convolutional neural networks (CNNs) and support vector machines (SVMs) for adept interference detection. Utilizing a CNN, we automatically extract profound features from single-step pedestrian motion data that are then channeled into an SVM for interference detection. Based on these insights, we formulate heading estimation strategies aptly suited for scenarios both devoid of and subjected to magnetic interference. Empirical assessments underscore our method’s prowess, boasting an impressive interference detection accuracy of 99.38%. In indoor environments influenced by such magnetic disturbances, evaluations conducted along square and equilateral triangle trajectories revealed single-step heading absolute error averages of 2.1891° and 1.5805°, with positioning errors averaging 0.7565 m and 0.3856 m, respectively. These results lucidly attest to the robustness of our proposed approach in enhancing indoor pedestrian positioning accuracy in the face of magnetic interferences.

Indoor positioning using smartphones has garnered significant research attention. Geomagnetic and sensor data offer convenient methods for achieving this goal. However, conventional geomagnetic indoor positioning encounters several limitations, including low spatial resolution, poor accuracy, and stability issues. To address these challenges, we propose a fusion positioning approach. This approach integrates geomagnetic data, light intensity measurements, and inertial navigation data, utilizing a hierarchical optimization strategy. We employ a Tent-ASO-BP model that enhances the traditional Back Propagation (BP) algorithm through the integration of chaos mapping and Atom Search Optimization (ASO). In the offline phase, we construct a dual-resolution fingerprint database using Radial Basis Function (RBF) interpolation. This database amalgamates geomagnetic and light intensity data. The fused positioning results are obtained via the first layer of the Tent-ASO-BP model. We add a second Tent-ASO-BP layer and use an improved Pedestrian Dead Reckoning (PDR) method to derive the walking trajectory from smartphone sensors. In PDR, we apply the Biased Kalman Filter–Wavelet Transform (BKF-WT) for optimal heading estimation and set a time threshold to mitigate the effects of false peaks and valleys. The second-layer model combines geomagnetic and light intensity fusion coordinates with PDR coordinates. The experimental results demonstrate that our proposed positioning method not only effectively reduces positioning errors but also improves robustness across different application scenarios.