Real−time single−frequency precise point positioning (PPP) is a promising low−cost technique for achieving high−precision navigation with sub−meter or centimeter−level accuracy. However, its effectiveness depends heavily on the availability and quality of the real−time ionospheric state estimations required for correcting the delay in global navigation satellite system (GNSS) signals. In this study, the dynamic mode decomposition (DMD) model is used with global ionospheric vertical total electron content (vTEC) RMS maps to construct 24 h global ionospheric vTEC RMS map forecasts. These forecasts are assimilated with C1P forecast products, and L1 single−frequency positioning solutions are compared with different ionospheric correction models. The study examines the impact of assimilating predicted RMS data and evaluates the presented approach’s practicality in utilizing the IGRG product. The results show that the IGSG RMS prediction−based model improves positioning accuracy up to five hours ahead and achieves comparable results to other models, making it a promising technique for obtaining high−precision navigation.