In 5G networks information about localization of a user equipment (UE) can be used not only for emergency calls or location-based services, but also for the network optimization applications, e.g., network management or dynamic spectrum access by using Radio Environment Maps (REM). However, some of these applications require much better localization accuracy than currently available in 4G systems. One promising localization method is Global Navigation Satellite System (GNSS)-based Real-Time Kinematics (RTK). While the signal received from satellites is the same as in traditional GNSS, a new reception method utilizing real-time data from a nearby reference station (e.g., 5G base station) results in cm-level positioning accuracy. The aim of this paper is to obtain a model of the RTK localization error for smartphone-grade GNSS antenna under open-sky conditions, that can be used in 5G network simulators. First, a tutorial-style overview of RTK positioning, and satellite orbits prediction is provided. Next, an RTK localization simulator is implemented utilizing GNSS satellites constellations. Results are investigated statistically to provide a simple, yet accurate RTK localization error framework, which is based on two Gauss-Markov process generators parametrized by visible satellites geometry, UE motion, and UE-satellite distance error variance.