BDS-3 Multi-Frequency UDUC PPP-AR Using a Transformer-Based Improved Stochastic Model

Traditional stochastic models that rely solely on elevation angle and signal-to-noise ratio (SNR) struggle to adapt to the precision differences in BDS-3 multi-frequency observations, making it difficult to support high-precision positioning in complex scenarios. To address the issues that existing models fail to adapt to the differentiated error characteristics of BDS-3 five-frequency observations, lack adaptive modeling capabilities, and cannot support high-precision five-frequency PPP-AR in complex environments, this study proposes a Transformer-based adaptive stochastic model for five-frequency precise point positioning ambiguity resolution (PPP-AR). Satellite elevation angle, the SNR, and position dilution of precision (PDOP) are used as inputs, while observation noise labels derived from pseudorange post-fit residuals support supervised training. The predicted noise standard deviations are introduced into the observation covariance matrix for adaptive weighting. To distinguish generalization from memorization, the model was evaluated using observations from different days. On day of year (DOY) 244, the Transformer model achieved a mean post-convergence three-dimensional root-mean-square (3D RMS) error of 0.029 m, outperforming the comparison models, which yielded errors of 0.0037–0.0039 m. It also reduced the mean convergence time to 20.33 min, compared with 21.22–22.17 min for the comparison models. At the HARB station, the Transformer and elevation angle models both converged in 7 min, only one 30 s epoch faster than the multilayer perceptron (MLP) and SNR models. At the GAMG station, the ambiguity fix rate reached 31.25%, exceeding those of the elevation angle and SNR models by 18.28 and 15.40 percentage points, respectively. The results for DOY 245 and DOY 246 further support short-term transferability, but not long-term temporal generalization. Overall, the proposed model improves aggregate positioning accuracy and convergence efficiency while maintaining competitive ambiguity fixing performance.