Modeling And Predicting GNSS Tropospheric Delay Based On Machine Learning Algorithms

Tropospheric delay is caused by neutral atmospheric refraction,which is not only one of the main error sources of GNSS measurement but also an effective data source for detecting atmospheric water vapor.In this paper,the models of zenith direction tropospheric delay correction(ZTD)are built for forecasting based on machine learning algorithms,and the atmospheric precipitable water vapor(PWV)is retrieved with ZTD predictions.The high-temporal-resolution tropospheric delay model is of great significance for achieving high-precision GNSS services and promoting the development of GNSS meteorology.At the same time,it provides new ideas for modeling tropospheric delay of the GNSS signal with the help of machine learning algorithms.The main study contents and results are as follows:1 、 Using BP neural network and LSSVM algorithm,the BPNN-ZTD model and LSSVM-ZTD model are built based on 20 IGS stations respectively to forecast ZTD in the time domain.Among them,ZTD is predicted by the BPNN-ZTD model in the centimeter level,and the high-frequency signal is predicted with poor accuracy.The LSSVM-ZTD model is proposed with considering the correlation of training samples,where ZTD can be predicted in two-hour with the accuracy of the sub-centimeter level.In 2019,the average RMSE of the ZTD predictions of 11 stations is 6.0mm,and the average availability(bias is within ±5mm)is63.93%.The RMSE is about 24 mm lower than the ZTD predictions of the BPNN-ZTD model,and the availability is improved by about 50%.2、Two ERA5 data is adopted to estimate ZTD on 85 IGS stations in Europe.With the reference of IGS-ZTD,the consistency of ERA5P-ZTD cacluted by integration is better than that of ERA5S-ZTD obtained by Saastamoinen model.According to the three cases of no background data,ERA5S-ZTD as the background data and ERA5P-ZTD as the background data,three regional ZTD models(EST-ZTD1,EST-ZTD2 and EST-ZTD3)are built using LSSVM algorithm.The results show that the model is established with better accuracy when adding the background data as constraint.The periodic bias between ERA5S-ZTD and IGS-ZTD is compensated by the EST-ZTD2 model.The average monthly RMSE of 10 test stations is 22.9mm in 2018,the accuracy of EST-ZTD2 model is 19.1% higher than that of ERA5S-ZTD.The average monthly RMSE of EST-ZTD3 model is 9.0mm,the accuracy is improved by 1.6% over the accuracy of ERA5P-ZTD on average,and the improvement can reach 40% in some stations.It mainly depends on the distribution of training stations and the correlation between test stations and training stations in the study area.3、The North American GNSS-ZTD data is used to evaluate the BPNN,radial basis function(RBF)neural network and LSSSM algorithm from aspects of the modeling accuracy,efficiency,stability and applicability.The results show that: the RBF algorithm is the best for modeling when small-szie training samples are used.The accuracy and stability of the LSSVM algorithm is equivalent to that of the RBF algorithm,but the efficiency is low;The BP algorithm has advantages in modeling large-size training samples.4、With atmospheric parameter products provided by Suomi Net network,the RBF algorithm is adopted to built the regional ZTD prediction model RBF-ZTD referencing the modeling methods of LSSVM-ZTD and EST-ZTD1.The prediction accuracy of the RBF-ZTD model is significantly affected by the spatial distribution of the stations,and the difference of monthly RMSE is more than 10 mm in different regions.The average monthly RMSE is 21.3mm in the northwest region,where the distribution of stations is densely and uniform.The average monthly RMSE and annual RMSE of the whole study area are 30.9mm and 31.9mm respectively.Suominet meteorological data and GPT2 W meteorological data are used to retrieval PWV based on ZTD predictions,and the average monthly RMSE is 4.9mm and 5.7mm respectively;the accuracy of obtained PWV relies on that of ZTD predictions.