Abstract: Objectives: Traditional stochastic models are unsuitable for the complex noise of smartphones. The development of stochastic models is a primary method to improve smartphone signal quality for precise positioning. This study proposes an adaptive stochastic model based on Random Forest (RF) to construct a mapping model among Signal-to-Noise Ratio (SNR), elevation angle, Doppler value, and pseudorange noise. The model's performance is validated in various typical scenarios, including static open, semi-open, obstructed, and urban canyon environments. It is demonstrated that the RF-based adaptive stochastic model is superior to traditional SNR models and other machine learning methods like XGBoost and LightGBM, in terms of positioning accuracy and robustness.Methods: (1) SNR, elevation angle, Doppler values, and satellite system information are extracted from raw smartphone GNSS observations as input features, while pseudorange observation noise is used as the target variable. (2) The correlation and importance of features with pseudorange noise are analyzed to identify the optimal feature subset. (3) RF, XGBoost, and LightGBM machine learning algorithms are respectively employed to establish three adaptive stochastic models. (4) Huawei Mate 40 and Honor 30 Pro smartphones are used as receivers to conduct experiments in four representative scenarios: static open, semi-open playground, high-rise obstruction, and urban canyon vehicular tracks. The positioning performance of the RF model is systematically compared with that of the traditional SNR model, XGBoost, and LightGBM.Results: In static open environments, the RF-based stochastic model improves the 2D positioning accuracy of the Mate 40 and Honor 30 Pro by 60.00% and 65.00%, respectively, outperforming the traditional SNR model (60.00%, 65.00%), XGBoost (51.70% and 50.10%), and LightGBM (24.90% and 47.10%). In the semi-open playground environment, the RF model further improves the 2D accuracy of the 30 Pro by 35.08%. In the urban canyon vehicular experiment, the RF model increases the 2D and 3D accuracy of the Mate 40 by 52.45% and 50.29% in open road sections. In obstructed sections, the RF model still achieves improvements of 23.06% in 2D accuracy and 22.06% in 3D accuracy, whereas the improvements obtained by XGBoost and LightGBM are only about 17% and 16%, respectively. In the high-rise and tree-obstructed environment, the RF model improves the 2D accuracy of the Mate 40 by 78.56%, significantly outperforming XGBoost (42.24%) and LightGBM (42.15%). The Honor 30 Pro also has an accuracy enhancement of 32.10% using the RF model.Conclusions: Through multi-scenario and multi-terminal experimental validation, the adaptive stochastic model based on RF is superior to traditional SNR models as well as XGBoost and LightGBM methods in both positioning accuracy and robustness.