## 1 Introduction  
Compared with PPP (precise point positioning) technology, PPP that is based on real-time kinematic (RTK) network (PPP-RTK) technology can enable rapid integer ambiguity resolution (IAR) by exploiting precise atmospheric delay information that is provided by a regional network [1; 2; 3] and has unique advantages in convergence, accuracy, and real-time communication. As a result, PPP-RTK technology has received considerable attention. Compared with representation in an observation space in an RTK network, PPP-RTK provides state-space data that can be modeled and broadcast to users according to the different physical characteristics of the corrections. Obtaining accurate atmospheric delay information for users by means of an interpolation model in PPP-RTK is one of the keys to achieving high-precision real-time positioning. The atmospheric delay errors which are related to distance increase with increasing distance between user stations and reference stations. Therefore, the commonly used interpolation models all consider the correlation and uniformity of space. The most commonly used distance interpolation models are the distance-based linear interpolation model (LIM) [4], inverse distance-based linear interpolation method (DIM) [5], linear combination model (LCM) [6; 7], low-order surface model (LSM) [8; 9], least-squares collocation (LSC) method [10; 11], and kriging interpolation method [12; 13]. [PERSON] et al. [14] compared these methods and concluded that their performance was not significantly different. [PERSON] et al. [15] analyzed the interpolation accuracy of different interpolation models and gave the best reference results under different scales and terrain scenarios. [PERSON] et al. [16] proposed the modified LCM (MLCM), which is based on the LCM but with a different method for selecting the reference for interpolation coordinates. The MLCM method changes the reference coordinate from any reference station of the LCM method to the user station. Otherwise, the two methods are theoretically equivalent. [PERSON] et al. [17] considered the latitude and longitude anisotropy of the ionospheric total electron content (TEC) distribution by introducing latitude and longitude adjustment factors to improve the accuracy of inverse distance weighting interpolation. [PERSON] et al. proposed a version of LIM that was based on coinciding ionospheric pierce points (CIPPs) to improve the interpolation accuracy of ionospheric delays in low-latitude regions [18]. The inter-satellite single difference (SD) ionospheric delay is typically provided to the user. Unless specified otherwise, SD is the single difference between satellites. [PERSON] et al. [19] constructed an atmospheric delay model using the longitude and latitude of the network center and IPP, and broadcast the atmospheric delay correction coefficient for users (referred to as the USM). This method requires at least four stations and four satellites to solve the model coefficients. In regional enhanced PPP, the common function-based ionospheric interpolation methods such as LCM, DIM, LSM, LIM, and USM have advantages and disadvantages, and have application examples. There are few studies on the model of ionospheric delay that is expressed by the atmospheric delay coefficient based on the IPP in the region enhancement algorithm, which is worthy of further exploration. This paper proposes an interpolation model that uses the atmospheric delay coefficient to represent the SD ionospheric delay, based on the mean position of the ionospheric pierce point (IPP) of the satellite pair and the center position of the network, which is called the differenced surface model (DSM). When the number of stations is at least three, the ionospheric delay model coefficients of any single-difference satellite pair can be calculated. In this study, the interpolation performance of DIM, USM, and the new DSM model was compared for different scenarios.