Development and evaluation of the refined zenith tropospheric delay (ZTD) models

Abstract

The tropospheric delay is a significant error source in Global Navigation Satellite System (GNSS) positioning and navigation. It is usually projected into zenith direction by using a mapping function. It is particularly important to establish a model that can provide stable and accurate Zenith Tropospheric Delay (ZTD). Because of the regional accuracy difference and poor stability of the traditional ZTD models, this paper proposed two methods to refine the Hopfield and Saastamoinen ZTD models. One is by adding annual and semi-annual periodic terms and the other is based on Back-Propagation Artificial Neutral Network (BP-ANN). Using 5-year data from 2011 to 2015 collected at 67 GNSS reference stations in China and its surrounding regions, the four refined models were constructed. The tropospheric products at these GNSS stations were derived from the site-wise Vienna Mapping Function 1 (VMP1). The spatial analysis, temporal analysis, and residual distribution analysis for all the six models were conducted using the data from 2016 to 2017. The results show that the refined models can effectively improve the accuracy compared with the traditional models. For the Hopfield model, the improvement for the Root Mean Square Error (RMSE) and bias reached 24.5/49.7 and 34.0/52.8 mm, respectively. These values became 8.8/26.7 and 14.7/28.8 mm when the Saastamoinen model was refined using the two methods. This exploration is conducive to GNSS navigation and positioning and GNSS meteorology by providing more accurate tropospheric prior information.

Assessment of the Water Vapor Tomography Based on Four Navigation Satellite Systems and Their Various Combinations

“…Affected by water vapor along the signal ray, ZWD is the wet component of zenith total delay (ZTD) which is the primary parameter retrieved from GNSS observation. To obtain ZWD, the zenith hydrostatic delay (ZHD) should be subtracted from ZTD [38]. In this paper, the Saastamoinen model is used to calculate the accurate ZHD using the pressure measurements as follows [39]:…”

Characteristic differences in tropospheric delay between Nevada Geodetic Laboratory products and NWM ray-tracing

“…Numerous scholars have found and validated that NWM enhances the wet tropospheric correction retrieval of SA (Vieira et al 2022), improves the troposphere delays in SLR (Boisits et al 2020), provides more accurate gradient information to VLBI (Hofmeister and Böhm 2017), reduces GNSS positioning convergence time, and exhibits better overall robustness (Lu et al 2016(Lu et al , 2017Vaclavovic et al 2017;Deo and El-Mowafy 2018). Multiple tropospheric delay models (Schüler 2014;Li et al 2014Li et al , 2015Yang et al 2021), temperature and pressure models (Boehm et al , 2015Lagler et al 2013;Landskron and Böhm 2018b), weighted mean temperature models (Zhu et al 2022), mapping function models (Urquhart et al 2014;Zus et al 2015), and tropospheric gradient models have been developed based on different NWMs; they are typically used for correction or as a priori inputs in the above techniques (Wang et al 2022).…”

Retrieval of tropospheric delays from multi-GNSS observations in the polar region: effect factors and performance

“…Therefore, a reasonable model should be selected and the optimal parameters should be set to estimate the exact ZTD value. The Hopfield and Saastamoinen models are optimized by adding both annual and semi-annual periodic terms and artificial neural networks based on counter-term propagation in order to reach a model with a stable ZTD [11]. To determine the suitable model for Antarctica, nine different combined models were assessed and the results showed that the deviations of the GPT2, GPT2w and GPT3 + Saastamoinen models were 0.20, −0.22 and −0.29 cm.…”