Residual-Guided Hybrid Stochastic Modeling: A Two-Stage Learning Framework for Urban GNSS Positioning Enhancement

The Global Navigation Satellite System (GNSS) has been widely adopted in navigation applications due to its high accuracy and convenience. However, in urban canyon environments, severe signal blockage caused by buildings and trees introduces substantial non-line-of-sight errors and multipath effects, leading to degraded and highly fluctuating positioning performance. To address this issue, this paper proposes a residual-guided hybrid stochastic modeling framework. The method operates in two stages: first, a pseudo-range correction estimation network takes GNSS parameters containing residuals as input to estimate pseudo-range correction; second, these estimated corrections together with elevation angle and carrier-to-noise ratio are fed into a hybrid stochastic model parameter estimation network to determine model parameters. This design adjusts the pseudo-range observations to reduce the positioning loss without requiring true pseudo-range errors, which are difficult to obtain in real-world scenarios. Meanwhile, the explicit modeling of relationships among pseudo-range correction, elevation angle, and carrier-to-noise ratio renders the stochastic model parameters interpretable. Experiments on public urban GNSS datasets demonstrate that the proposed method achieves competitive positioning performance against both conventional and learning-based baselines. It delivers notable accuracy improvements in light urban canyon environments, particularly on the KLT2 sequence, while maintaining robust and competitive performance in the more challenging TST and Mong Kok scenarios. These results validate the effectiveness of jointly estimating pseudo-range corrections and adaptive observation weights for enhancing positioning accuracy and robustness across diverse urban environments.