Accurate rainfall forecasting plays a crucial role in weather monitoring. Currently, the application of Global Navigation Satellite System-derived precipitable water vapor (GNSS-PWV) has mainly focused on forecasting rainfall event occurrence, while neglecting the forecasting of rainfall amount. In this study, a new method based on machine learning fusion strategy and the constraint of rainfall event is proposed. The machine learning fusion strategy is used to improve the accuracy of rainfall amount forecasting by considering the difference in rainfall types and machine learning algorithms, while the rainfall event constraint strategy is used to reduce the rainfall amount forecasting error during periods without rainfall event. In the new method, the Long Short-Term Memory (LSTM) algorithm is adopted to forecast rainfall event by considering the temporal correlation of rainfall event. Then, the Support Vector Regression (SVR), Group Method of Data Handling (GMDH), and Harmony search (HS) algorithms are combined to forecast rainfall amount with the constraint of rainfall event forecast results. The SVR performs better at forecasting little and medium rainfall, while GMDH is better at forecasting heavy rainfall. HS is mainly used to optimize the parameters of the forecasting model. The data sets collected from 2019 to 2023 at Hong Kong GNSS stations are used to evaluate the performance of the proposed method. The experimental results show that after adopting the proposed rainfall event forecasting method, the total True Positive Rate (TPR) is approximately 90.45% and the prediction errors for without rainfall event is only about 4.09%. Moreover, after adopting the proposed rainfall amount forecasting method, the average Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are approximately 0.42 mm and 0.13 mm, respectively. The average improvement rate of MAE is approximately 24.39% for the internal experiment and 25.27% for the external experiment compared to the single SVR model. In conclusion, the proposed method can effectively improve the accuracy of rainfall amount forecast, which can further provide support for meteorological monitoring.

Factor graph (FG) optimization is increasingly used in the research of multi-sensor integrated navigation and positioning. Unlike popular Kalman filter algorithms, all states of the factor graph are optimized holistically. Maximum Posterior Probability (MAP) Estimation is the core of Factor Graph Models. However, when sensors are subjected to sudden environmental interference, the outputs may deviate significantly from the expected values or even be missing. Some existing factor graph models lack the ability to identify such interference. Therefore, a Factor graph model with local attention (FGLA) is formally proposed in this paper. FGLA constrains the factor nodes in the factor graph while optimizing the objective function, so that local outliers can be quickly corrected. To quickly optimize the constrained factor graphs in a non-vector space, an algorithm called bounce gradient descent (BGD) is proposed. We use real and simulation integrated navigation datasets consist of Pedestrian Dead Reckoning (PDR)/Wi-Fi/barometer measurement data to verify the performance of the two proposed algorithms. Experimental results show that FGLA has stronger anti-interference capabilities when facing sudden data exceptions, compared with either the Extended Kalman Filter (EKF) or the existing factor graph models. Results also demonstrate that BGD has a faster optimization speed than the projected gradient algorithm.

The surrounding environment of a GNSS observation station is changed during a flood, and this results in a more serious multipath than in a normal environment. Considering that the multipath error is largely related to the pseudo-range multipath and CNR (Carrier-to-noise ratio) of the GNSS signal, the influence of floods on a pseudo-range multipath and CNR is analyzed in theory and through experiment. To ensure the accuracy of the analysis results, the ground track repeat period of GPS, GLONASS, and BDS satellites is investigated from the perspective of theory and skyplots. Two real cases study collected in Zhengzhou and Xinxiang, China, in 2021, are used to demonstrate the influence of floods on a pseudo-range multipath and CNR in detail. Experimental results show that the pseudo-range multipath of a GPS satellite performs more seriously during a flood. The maximum RMS increase rate is approximately 17.85%, and the average of all other satellites with a whole arc is approximately 6.55%. In addition, the CNR of three GNSS systems performs a decrease during a flood. For GPS and GLONASS satellites, the decrease performs more seriously at a high elevation angle than that at a low elevation angle. The maximum decrease is approximately 5 dB-Hz for the GPS satellite and approximately 7 dB-Hz for the GLONASS satellite. In terms of the BDS system, the CNR of all three orbital type satellites decreases during a flood. The average decrease is approximately 2 dB-Hz for BDS MEO and GEO satellites, and about 1 dB-Hz for the BDS IGSO satellite.

The method of multi-sensor integrated navigation improves navigation accuracy by fusing various sensor data. However, when a sensor is disturbed or malfunctions, incorrect measurement information will seriously affect the estimation of the trajectory, which will lead to a decrease in accuracy. Existing factor graph models based on weights can neither fully resist the influence of disturbances nor guarantee the local rationality of estimated trajectories. In this paper, a factor graph with local constraints model that fuses the magnetic field and pedestrian dead reckoning data is proposed to navigate complex curved trajectories. First, adding local constraints to the pedestrian dead reckoning measurement converts the navigation solution problem into a hard-constrained nonlinear least squares problem. Then, a mapping model is constructed to reconstruct the variable space and the Adam gradient algorithm is used to realize a fast calculation. The navigation accuracy of this algorithm is better than that of the state-of-the-art method in real-world experiments, with an average accuracy of 0.83 m.