![]() Therefore, it is necessary to perform the regional refinement of the ZTD models, which can not only optimize the performance of the corresponding parameter models in a specific area, but also improve the accuracy of empirical ZTD models. The obvious regional differences in the accuracy with the Saastamoinen and Hopfield models are due to the fact that they were constructed based on global mean meteorological data and global climate analysis, which makes it difficult to describe the ZTD characteristics in certain areas. However, several studies confirmed that the Saastamoinen and Hopfield models tend to be poor when using the regional meteorological data in a local area (Yang et al., 2020c, 2021). Thus, the ZTDs estimated by the above two types of empirical models have generally poorer results than those with Saastamoinen and Hopfield model based on the measured meteorological data. The other empirical models, such as GPT series (Boehm et al., 2007 Bohm et al., 2015 Lagler et al., 2013 Landskron & Boehm, 2018), are first building the models of various meteorological quantities, and then estimating the ZTD with these estimated meteorological parameters and the formula of Saastamoinen model, Hopfield model, and other models. Some empirical models, such as GZTD series (Yang et al., 2020b Yao et al., 2013, 2016) and IGGtrop series (Li et al., 2012, 2015, 2018), are established by using the trend analysis on long-term ZTD values. Two types of ZTD models are commonly used: (1) ZTD models with the measured meteorological parameters at a site, such as Hopfield model, Saastamoinen model and Black model, which can achieve centimeter-level accuracy by inputting accurately measured meteorological parameters (Hopfield, 1969 Black & Eisner, 1984 Saastamoinen, 1972) (2) the empirical ZTD models, which feedback only by the location of a site and time of interest. A stable and accurate ZTD model is necessary to meet these requirements. An accurate ZTD is not only an important parameter for GNSS navigation and positioning (Duan et al., 1996 Meng, 2002 Zhang et al., 2017 Zumberge et al., 1997), but also the basis for retrieving Precipitable Water Vapor (PWV) in GNSS meteorology (Li et al., 2014 Yang et al., 2020a Zheng et al., 2018). We generally project the tropospheric delay into zenith direction by using a mapping function and utilize the Zenith Tropospheric Delay (ZTD) to describe the tropospheric influence on the signal propagation. ![]() It is a significant error source in GNSS positioning and navigation, for the delay varies from 2 to 20 m depending on the elevation angle of a satellite (Chen et al., 2020 Penna et al., 2001). This exploration is conducive to GNSS navigation and positioning and GNSS meteorology by providing more accurate tropospheric prior information.ĭuring propagating through the neutral atmosphere, Global Navigation Satellite System (GNSS) signals from a satellite to a receiver will be delayed and bent due to their interaction with dry gases and water particles, which is called tropospheric delay (Bevis et al., 1992 Yao et al., 2018). These values became 8.8/26.7 and 14.7/28.8 mm when the Saastamoinen model was refined using the two methods. 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. The results show that the refined models can effectively improve the accuracy compared with the traditional models. The spatial analysis, temporal analysis, and residual distribution analysis for all the six models were conducted using the data from 2016 to 2017. The tropospheric products at these GNSS stations were derived from the site-wise Vienna Mapping Function 1 (VMP1). 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. One is by adding annual and semi-annual periodic terms and the other is based on Back-Propagation Artificial Neutral Network (BP-ANN). 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. It is particularly important to establish a model that can provide stable and accurate Zenith Tropospheric Delay (ZTD). It is usually projected into zenith direction by using a mapping function. The tropospheric delay is a significant error source in Global Navigation Satellite System (GNSS) positioning and navigation.
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