An optimized BP neural network for modeling zenith tropospheric delay in the Chinese mainland using coupled particle swarm and genetic algorithm

Tropospheric delay influences high-precision navigation positioning and precipitable water vapor retrieval with the Global Navigation Satellite System (GNSS). Existing Zenith Tropospheric Delay (ZTD) models often struggle to accurately capture the non-linear variations in tropospheric delay. Therefore, this study employs the coupled Particle Swarm Optimization (PSO) algorithm with the Genetic Algorithm Back Propagation (GABP) neural network, combined with ERA5 reanalysis meteorological data, to develop an optimized model (PSO-GABP) for ZTD in the Chinese mainland. Nevertheless, ZTD data at the target point are obtained through four different methods: the integration method, model method, and GPT3 models at varying resolutions (EZTD_P, EZTD_S, GPT3_1, and GPT3_5). The analysis reveals the following: (1) The Root Mean Square (RMS) errors of the ZTD values obtained through these different methods are 1.86 cm, 3.42 cm, 3.99 cm, and 4.09 cm, respectively, when verified against GNSS_ZTD data from 2016. The optimized model yields ZTD values with the RMS error of 0.98 cm, 1.96 cm, 2.34 cm, and 2.36 cm, representing improvements of 47.3%, 42.7%, 41.4%, and 42.3% compared to the pre-optimization results. These improvements are significant; (2) The predictive capability of the constructed ZTD model is evaluated using GNSS_ZTD data from 2019 as a reference. The PSO_EZTD_P model demonstrates excellent accuracy and practicality in the Chinese mainland. As a result, the tropospheric delay optimization model based on the PSO-GABP neural network can provide valuable references for real-time GNSS navigation positioning and precipitable water vapor detection in the Chinese mainland.