Stochastic Model Refinement for Multi-GNSS Real-Time PPP Based on Orbit and Clock Extrapolation Error Statistics

Short-term outages of real-time state space representation (SSR) products degrade precise point positioning (PPP) accuracy. We propose a multi-GNSS PPP stochastic model refinement method based on historical statistics of additional signal-in-space range error (SISRE). System-level and satellite-level age-dependent models are constructed offline from joint range-domain statistics of orbit and clock extrapolation errors. Online, model outputs are converted into equivalent additional variances for direct variance inflation (DVI). Thirty days of Wuhan University SSR data are divided into non-overlapping 15-day training and test sets for modeling and cross-day validation. Within 10 min, BDS-3 and Galileo show relatively small extrapolation errors, GPS shows pronounced inter-satellite differences, and GLONASS shows higher overall errors. The training model and test reference model show similar error scales and age-dependent growth, indicating cross-day repeatability. Without additional downweighting, four-constellation simulated kinematic PPP experiments with 10 min outages yield a three-dimensional root mean square (3D RMS) positioning error of 13.26 cm. System-level and satellite-level DVI reduce this to 4.33 and 4.07 cm, respectively, corresponding to reductions of approximately 67% and 69%. Satellite-level DVI provides a further reduction of approximately 6%. Thus, the method improves PPP accuracy during short-term SSR outages, with modest satellite-level gains that vary by station, component, and outage window.