Monitoring and correction of errors in state space representation products using PPP float ambiguity deviations and phase residuals in a wide-area network

Abstract Real-time Precise Point Positioning with Ambiguity Resolution (PPP-AR) critically depends on high-quality State Space Representation (SSR) products for satellite orbit, clock, and code/phase bias corrections. These products, however, often contain errors that can severely degrade user positioning performance. Existing network-based quality monitoring methods primarily rely on phase residuals to detect product errors. However, phase residuals are only effective in revealing SSR product errors after ambiguities have been fixed. Before ambiguities are fixed, the stable or slowly varying components of SSR product errors are absorbed into the float ambiguities, rendering such phase residuals insufficient to fully reveal SSR product errors. As a result, the products with unfixed ambiguities are typically tagged as unreliable due to their uncertain quality. This practice however reduces the availability of SSR products and limit user PPP-AR performance, particularly in challenging environments where fewer satellites are visible. To address this limitation, this study proposes a method that effectively monitors SSR product quality by jointly considering the deviations of float ambiguities from their true integer values and phase residuals associated with float ambiguities. Unlike the ambiguity-fixed phase residuals, these indicators are derived directly from the float PPP solution and provide a unified measure of SSR product errors, regardless of whether the ambiguities remain float or are subsequently fixed. Furthermore, by leveraging the spatial common-mode characteristics of the SSR product errors across a wide-area network, the method derives the corrections to mitigate product error. After correction, the ambiguity-float phase residuals serve as a unified quality indicator applicable to both ambiguity-fixed and ambiguity-float SSR products, enabling reliable quality assessment and anomaly detection. Validation using one month of real-time SSR products from CNES demonstrates that the proposed method significantly improves the availability and reliability of SSR products. Compared with traditional monitoring methods based on ambiguity-fixed phase residuals, the proposed method achieves a comparable and slightly higher ambiguity fixing rate (95.56% versus 92.83%), while significantly reducing the incorrect fixing rate from 0.69 to 0.09%. This improvement substantially mitigates the positioning degradation caused by incorrect ambiguity fixing, reducing the three-dimensional Root Mean Square Error (RMSE) from 15.1 to 4.6 cm.