The global navigation satellite system (GNSS) and inertial navigation system (INS) integrated navigation system have been widely used in Intelligent Transportation Systems (ITSs). However, the positioning error of integrated navigation systems is rapidly divergent when GNSS outages occur. Motion constraint and back propagation (BP) neural networks can provide additional knowledge to solve this issue. However, the predictions of a neural network have outliers and motion constraint is difficult to adapt according to the motion states of vehicles and boats. Therefore, this paper fused a BP neural network with motion constraints, and proposed a motion-constrained GNSS/INS integrated navigation method based on a BP neural network (MC-BP method). The pseudo-measurement of the GNSS was predicted using a fitting model trained by the BP neural network. At the same time, the prediction outliers were detected and corrected using motion constraint. To assess the performance of the proposed method, simulated and real data experiments were conducted with a vehicle on land and a boat offshore. A classical GNSS/INS integration algorithm, a motion-constrained GNSS/INS algorithm, and the proposed method were compared through data processing. Compared with the classical GNSS/INS integration algorithm and the motion-constrained GNSS/INS algorithm, the positioning accuracies of the proposed method were improved by 90% and 64%, respectively, in the vehicle land experiment. Similar performances were found in the offshore boat experiment. Using the proposed MC-BP method, improved meter-level-positioning results can be achieved with the GNSS/INS integration algorithm when GNSS outages occur.

Tropospheric delay is a significant error source in Global Navigation Satellite Systems (GNSS) positioning. Slant Path Delay (SPD) is commonly derived by multiplying Zenith Tropospheric Delay (ZTD) with a mapping function. However, mapping functions, assuming atmospheric isotropy, restrict the accuracy of derived SPDs. To improve the accuracy, a horizontal gradient correction is introduced to account for azimuth-dependent SPD variations, treating the atmosphere as anisotropic. This study uncovers that, amidst atmospheric dynamics and spatiotemporal changes in moisture content, the SPD deviates from that based on traditional isotropy or anisotropy assumption. It innovatively introduces the concept that SPD exhibits non-isotropy with respect to azimuth angles. Hypothesis validation involves assessing SPD accuracy using three mapping functions at five International GNSS Service (IGS) stations, referencing the SPD with the ray-tracing method. It subsequently evaluates the SPD accuracy with horizontal gradient correction based on Vienna Mapping Function 3 (VMF3) estimation. Lastly, the non-isotropic of SPD is analyzed through the ray-tracing method. The results indicate the smallest residual (1.1–82.7 mm) between the SPDs with VMF3 and those with the ray-tracing. However, introducing horizontal gradient correction yields no significant improvement of SPD accuracy. Considering potential decimeter-level differences in SPD due to non-isotropic tropospheric delay across azimuth angles, a precise grasp and summary of these variations is pivotal for accurate tropospheric delay modeling. This finding provides vital support for future high-precision tropospheric delay modeling.

Tropospheric delay is a major error source that affects the performance of the Global Navigation Satellite Systems (GNSS) Real Time Kinematic (RTK) positioning especially for the medium/long-range baseline. Although high precision tropospheric delay can be estimated by GNSS carrier phase measurement, together with position and ambiguity, a relatively long period of convergence time is necessary. In this study, we develop a new GPS/BDS RTK algorithm constrained with a tropospheric delay parameters from Numerical weather prediction (NWP) model for medium/long-range baselines. The accuracy of the tropospheric delays derived from NWP is assessed through comparisons with the results of GAMIT (GNSS at MIT). The positioning performance with standard GPS RTK, standard GPS/BDS RTK, the developed NWP-constrained GPS RTK and NWP-constrained GPS/BDS RTK over medium/long-range baselines are compared in terms of the initialization time and the positioning accuracy. Experiment results show that the mean differences between the NWP and GAMIT zenith tropospheric delay (ZTD) are between −5.50 mm and 5.60 mm, and the RMS values of the NWP ZTD residuals are from 24.02 mm to 32.62 mm. A reduction in the initialization time of over 41% and 58% for medium- and long-range baselines can be achieved with the NWP-constrained RTK (both GPS alone and GPS/BDS RTK solutions) compared to the standard RTK solution, respectively. An improvement of over 30% can be found with the GPS/BDS RTK compared with that of the GPS alone RTK for both standard and the NWP-constrained modes. The positioning precision of NWP-constrained GPS/BDS RTK is better than 3 cm in the horizontal direction and better than 5 cm in the vertical direction, which satisfies the requirement of the precise positioning service.

In order to study and forecast extreme weather, a comprehensive and systematic analysis of the spatial and temporal relationship between Precipitable Water Vapor (PWV), predicted by Numerical Weather Predication (NWP) data, and precipitation, is necessary. The goal of this paper was to study the temporal and spatial relationship between PWV and precipitation during the so-called ‘July 20’ (18–21 July 2021) heavy rainstorm in Zhengzhou. Firstly, the PWV data provided by 120 radiosonde stations uniformly distributed throughout the world, and two IGS stations in China, in 2020, was used to evaluate the accuracy of PWV estimation by ERA5 and MERRA-2 data, and the factors affecting the accuracy of NWP PWV were explored. Secondly, ERA5 PWV and the precipitation data of six meteorological stations were used to qualitatively analyze the relationship between PWV and precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou. Finally, a quantitative study was conducted by an eigenvalue matching method. The main experimental results were as follows. Compared with MERRA-2 PWV, the accuracy of ERA5 PWV was slightly higher. Latitude, altitude and season were the influencing factors of the NWP PWV estimation accuracy. The change trend of ERA5 PWV was consistent with both 24 h cumulative precipitation and surface precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou. The average optimal matching degree and optimal matching time between NWP PWV and surface precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou was 56.6% and 3.68 h, respectively. The maximum optimal matching degree was 80.3%. The spatial–temporal relationship between NWP PWV and surface precipitation was strong.