Global navigation satellite system (GNSS) provides position, velocity, and timing information globally, but single-frequency receivers are limited by errors such as satellite orbit, clock, and especially ionospheric delay. While satellite-based augmentation system (SBAS) improves accuracy by supplying orbit, clock, and ionospheric corrections, realistic simulation tools are required to effectively develop and validate such systems. This study presents a MATLAB-based simulator that generates GNSS observations, computes corrections via precise orbit determination using extended Kalman filtering (EKF), and constructs grid-based ionospheric maps from dual-frequency measurements. The simulator, focused on positioning accuracy rather than integrity, is evaluated using a virtual quasi-zenith satellite system (QZSS) constellation with global positioning system (GPS) under intense ionospheric conditions in Japan. The performance of the simulator was analyzed at the MIZU ground station and further assessed across 36 virtual stations to demonstrate the spatial effectiveness of the correction information.