Frequency Stability-Aware Stochastic Modeling for Inter-System Bias in Multi-GNSS PPP

Global navigation satellite systems (GNSSs) exhibit differences in coordinate and time References, necessitating the consideration of inter-system bias (ISB) in multi-GNSS precise point positioning (PPP). Traditional ISB estimation models, such as white noise (ISB-WN), random walk (ISB-RW), and constant (ISB-CT) models, apply uniform Kalman filtering process noise across different receivers, precise products, and navigation systems, often neglecting ISB variations under diverse conditions. This study introduces a novel stochastic model that incorporates the frequency stability of ISB parameters (ISB-FS). By integrating the time-frequency characteristics of navigation system time references and the short-term stability of receiver hardware delays, the model employs overlapping Allan variance and a sliding window approach to adaptively update ISB process noise. An analysis involving ten stations from four manufacturers demonstrates that the ISB-FS model enhances multi-GNSS PPP solutions accuracy: positioning accuracy improves by approximately 3%, time transfer precision by 10%, and long-term frequency stability (245760 s) by up to 38%, while maintaining comparable Zenith tropospheric delay (ZTD) accuracy. This research offers a refined ISB estimation strategy, advancing the precision of multi-GNSS PPP solutions.