# Performance Analysis of Undifferenced NRTK Considering Time-Varying Characteristics of Atmosphere
## 1 Introduction  
The BeiDou Global Navigation Satellite System (BDS) provides positioning, navigation, and timing services, including four types of positioning services: radio determination satellite service (RDSS), an active positioning based on radio measurement, standard point positioning (SPP) based on the BDS-3 Satellite-Based Augmentation System (BDSBAS); and precise point positioning (PPP) through B2b signals of geostationary orbit (GEO) satellites (PPP-B2b) [1]. PPP and real-time kinematic (RTK) are two typical methods of high-precision positioning. PPP relies on high-precision international GNSS service (IGS) satellite orbit and clock products, which have problems such as long initialization time and difficulty in ambiguity resolution [2]. RTK positioning uses observation difference to eliminate or weaken observation errors, which is the main means of high-precision positioning. However, as the distance increases between the reference station and the user station, the residual spatial correlation error affects the efficiency of the integer ambiguity resolution [3]. Network RTK (NRTK) can provide error correction information for users within the coverage area of reference stations, improve the ambiguity fixing efficiency and positioning accuracy, expand the positioning range, and improve the positioning reliability compared to conventional RTK [4]. Therefore, NRTK has become a research hotspot in the field of high-precision positioning. NRTK uses the carrier phase observation of multiple reference stations in a region to generate error correction information and eliminate user error, so as to obtain high-precision positioning results. Unlike existing PPP-RTK models using state-space error modeling observation error [5], NRTK represents satellite orbit errors as distance errors when using broadcast ephemeris, and estimates them together with satellite clock and satellite hardware delay errors using un-differential (UD) error interpolation methods, making error correction process more simple and more efficient. It can effectively eliminate satellite-related errors for users in real-time within a certain area. Undifferentiated NRTK uses the UD error correction value of observation, so users do not need to choose a primary reference station to achieve observation combination of double differential (DD). The error correction value of a satellite at a reference station includes whole error correction information of observation; having independent error correction information for each reference station makes it easy to broadcast and receive it through the network. It is very advantageous to use the UD error correction value of the observation. It can not only make full use of the reference station network to correct the observation error of a user, but also by using the undifferenced error correction value in the area covered by high-precision positioning, the user can easily unify with single-station positioning models. A requirement for undifferenced NRTK to provide reliable positioning is the successful fixing of the ambiguity of the reference station. When using an un-combined observation model, the atmospheric delay error is estimated as an unknown parameter. As the unknown parameter increases, the strength of the equation weakens, which increases the difficulty of ambiguity solution [6; 7]. Ionospheric errors can be corrected by obtaining ionospheric prior values from external sources [8]. The ionospheric delay information determined by modeling or the interpolation of a regional observation stations network can effectively eliminate ionospheric errors, and the corrected reference station network ambiguity can be quickly fixed [9; 10]. Although the global ionospheric map (GIM) generated through global stations has a large coverage range, its accuracy is poor due to the influence of reference station spacing, making the correction ability for ionospheric errors very limited [11; 12].