Ionospheric scintillation refers to the phenomenon of rapid random fluctuations in the amplitude and phase of radio signals which can result in increasing of measurement noise and signal loss of lock. At present, the receiver tracking error stochastic (RTES) model can effectively reduce the influence of ionospheric scintillation on GNSS precision point positioning (PPP). However, the RTES model relies on the data products from specialized ionospheric scintillation monitoring receivers (ISMR). Compared with geodetic receivers widely distributed around the world, the number of ISMR monitoring stations is very limited, and the acquisition of ISMR data products is difficult. Using the GPS observation and scintillation data recorded by the Canadian high arctic ionospheric network (CHAIN) during 2014—2022, this study proposes a PPP stochastic model suitable for geodetic GNSS receivers in high latitudes, referred to as the high latitude receiver tracking error (HL_RTES) model. The HL_RTES model uses S4c index and rate of total electron content index (ROTI) to estimate the receiver tracking error variance, and the GPS positioning accuracy is improved by reweighting the observed values. The GPS observations of CHAIN station from February 1, 2023 to February 28, 2023 are used to conduct single-frequency mimics kinematic PPP experiment. Experimental results show that the performance of HL_RTES model and RTES model are comparable, and both can improve the PPP positioning accuracy under ionospheric scintillation; compared with EAS model, the monthly average RMS improvement rates of HL_RTES model in the horizontal, vertical and 3D directions are 33.3%, 42.8% and 38.3% respectively. In addition, using the data from the IGS stations INVK, KIRU, SCOR and URAL on February 15, 2023 to conduct experiment, it is found that the HL_RTES model can significantly mitigate the effects of high latitudes scintillation on PPP; compared with the EAS model, the improvement rates of HL_RTES model based PPP on the 3D RMS of the four stations are 57.2%, 32.9%, 43.8% and 31.4%, respectively.