## 1 Introduction  
Due to the high operational efficiency and algorithm simplicity, pseudorange-based Single Point Positioning (SPP) is still the most popular Global Navigation Satellite Systems (GNSS) positioning technology for custom-grade navigation where meter-level positioning accuracy is sufficient [1]. Compared with Precise Point Positioning (PPP) and Network Real Time Kinematic (NRTK), SPP does not restricted to convergence time and reference stations. One of the major error sources that degrades the SPP accuracy is the signal transmission delay caused by the troposphere [2]. The so-called tropospheric delay varies from about 2 m at the zenith to 20 m at lower elevation angles between receiver and satellite [3]. Typically, an empirical model is applied to mitigate the tropospheric delay and metewrith to improve the positioning accuracy [4, 5]. Usually, the residual tropospheric delay after model correction will be further estimated in PPP and NRTK applications, so as to mitigate the biases projecting to positioning. However, in SPP, the residual tropospheric delay is drowned in measurement noise, and cannot be further compensated by parameter estimation. Therefore, it is necessary to assess the biases produced by the residual tropospheric delay on SPP. Usually the tropospheric delay along the line-of-sight is mapped onto the zenith direction using the elevation-dependent mapping function [6]. Therefore, modeling the Zenith Tropospheric Delay (ZTD) is essential. Up till now, a variety of tropospheric delay models have been proposed and discussed. They are mainly divided into two classes: (1) the models relying on meteorological parameters as inputs, such as Hopfield model [7] and Saastamoinen model [8]; and (2) the models based on a look-up table to provide meteorological parameters, such as University of New Brunswick (UNB) series models and the European Geostationary Navigation Overlay System (EGNOS) model [9; 10]. Funded by the Austrian Science Fund, TU Wien provides abundant tropospheric products as open access data [11]. The released discrete troposphere delay models (e.g., VMF1 and VMF3) are based on actual data from Numerical Weather Models (NWMs) by the European Center for Medium-Range Weather Forecasts (ECMWF) [12], and are provided either in grid-wise or site-wise. Furthermore, other hybrid ZTD models, such as GZTD2 [13], IGGtrop_ri (i = 1, 2, and 3) [14], TropGrid2 [15], Improved Tropospheric Grid (ITG) [16], the improved wet delay model [17], IGGtrop_SH and IGGtrop_rH [18], WGTEM [19], and so on, have been successively developed, with the purpose of improving accuracy and simplifying calculation. ZTD is conventionally expressed as the sum of the Zenith Hydrostatic Delay (ZHD) and the Zenith Wet Delay (ZWD) [20]. Due to the high temporal and spatial variability of atmospheric water vapor, it is difficult to model the ZWD precisely [21], which accordingly limits the correction accuracies of different ZTD methods. Many investigations have been focusing on evaluating the correction accuracies of these models. [PERSON] and [PERSON] [22] compared several tropospheric models with the Saastamoinen model at six IGS stations and concluded that the models used in their study showed higher accuracies at mid-latitude regions than at the equator. [PERSON] et al. [16] concluded that the Saastamoinen+GPT2 model is 10% better than the UNB3m model, referring to the IGS-ZTD products. By using 1-year data from 27 IGS monitoring stations, [PERSON] et al. [23] concluded that the Saastamoinen+GPT2w model is superior to the Saastamoinen+GPT2 model. [PERSON] et al. [24] evaluated the accuracy of IGGtrop, EGNOS, and UNB3m models in China using 25 stations of the Crustal Movement Observation Network of China. The results show that the accuracy of IGGtrop is about 24% and 19% higher than that of EGNOS and UNB3m models, respectively. [PERSON] et al. [25] assessed the consistence between VMF-ZTD forecast grid products and IGS-ZTD products, and concluded that the difference is at the centimeter level. [PERSON] et al.