Spatial Interpolation of GNSS Troposphere Wet Delay by a Newly Designed Artificial Neural Network Model

Abstract

Global Navigation Satellite System (GNSS) signals arrive at the Earth in a nonlinear and slightly curved way due to the refraction effect caused by the troposphere. The troposphere delay of the GNSS signal consists of hydrostatic and wet parts. In particular, tropospheric wet delay prediction and interpolation are more difficult than those of the dry component due to the rapid temporal and spatial variation of the water vapor content. Wet delay estimation and interpolation with a sufficient accuracy is an important issue for all parameters obtained by GNSS positioning techniques. In particular, in real-time positioning applications, errors caused by interpolation of the wet troposphere delay are reflected in the height component of about 1 to 2 cm. Furthermore, the amount of water vapor in the troposphere is very important information in weather forecast applications obtained as a function of wet delay. Therefore, real-time monitoring of the troposphere can be achieved with a higher resolution and accuracy by utilizing neural network models for interpolation of the wet tropospheric delay. In addition, in the absence of the GNSS station, wet delays can be interpolated by means of the surrounding stations to the desired location. In this study, a back propagation artificial neural network (BPNN) model based on meteorological parameters obtained from The New Austrian Meteorological Measuring Network (TAWES) was used to interpolate wet troposphere delay. Analysis was carried out at 40 reference stations of the Echtzeit Positionierung Austria (EPOSA) GNSS Network covering the whole of Austria. The interpolation of zenith wet delays based on the artificial neural network was performed by using latitude, longitude, altitude and meteorological parameters (temperature, pressure, weighted mean temperature, and water vapor pressure). These parameters were then subtracted from the artificial neural network model one by one and six different artificial neural networks were designed. In addition, the linear interpolation method (LIN) and inverse distance weighted interpolation method (IDW) were used as conventional interpolation methods. In order to investigate the effect of the network density on interpolation methods, three networks, including 40, 30, and 20 reference stations, were formed and the increased distance effect on interpolation methods was evaluated. In addition, analyses were conducted in winter, spring, and summer to evaluate the seasonal effects on interpolation methods. According to the statistical analysis, the root mean square error (RMSE) values of the IDW, LIN, and BPNN methods were found to be 12.6, 13.4, and 5.9 mm, respectively.

Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution

“…Despite the previous studies which mainly focus on some specific areas using the OFC model, e.g., the French (Oliveira et al 2017), China Hubei (Shi et al 2014, or the large region using the grid model, e.g., in mainland China (Zheng et al 2018;Zhang et al 2018) and Australia (Li et al 2021), the performance of the polynomial model in wide-area has not been fully investigated. Zus et al (2019) and Selbesoglu (2019) applied their interpolation model in the German and Turkey region using a relatively dense network of stations, but the corresponding impact on the positioning was not given. Moreover, the previous studies mainly focus on the GPS-only PPP or RTK service and the GPS + BDS solutions, whereas the performance of Galileo and GPS + Galileo PPP-AR with regional tropospheric augmentation has not been reported yet.…”

A Systematic Review of Machine Learning Techniques for GNSS Use Cases

“…Others include [106,107] using Gaussian Process Regression (GPR), and [108] using SVM. Prediction of tropospheric wet delay from GNSS observations has also been performed using ML algorithms like in [109][110][111][112][113] using ANN, and [114] using BP neural network.…”

On the Correlation of Solar Activity and Troposphere on the GNSS/EGNOS Integrity. Fuzzy Logic Approach

“…Precipitation is less frequently described in the literature as a factor affecting the satellite signal. According to stateof-the-art research [55][56][57], such a factor is air humidity and, often, temperature. In practice, these two factors have a negligible effect on signal integrity.…”