Constraining Parameter Variance Components for Multi-GNSS Satellite Ultra-Rapid Clock Offset Estimation

Multi-GNSS ultra-rapid clock offset products provide a critical time reference for real-time and near-real-time positioning, navigation, and timing (PNT) services. However, conventional estimation methods, which typically rely on white noise and empirical models, are unable to accurately capture the stochastic behavior of satellite clock offsets due to their predefined noise assumptions. To achieve more precise estimation, this paper proposes a novel model that incorporates constraints derived from the variance components of the clock offsets. First, a discrete state transition equation is formulated for the satellite clock offset, explicitly incorporating its frequency deviation and drift parameters. Second, by introducing both the clock offsets and their state parameters into the epoch-wise estimation equation, we construct a mathematical model that characterizes the atomic clock behavior. Third, singular value decomposition is applied to estimate the variance components of the clock offsets and their state parameters, with the noise model being updated on an epoch-wise basis. Experimental results reveal that the estimated variance components of multi-GNSS satellite clock offsets deviate significantly from the prior noise derived from conventional long-term clock products. The proposed method improves the clock offset estimation accuracy by 3.7%-22.7%. Furthermore, static precise point positioning (PPP) solutions combining GPS and BDS-3 observations show positioning accuracy improvements of 6.8%, 20.0%, and 8.9% in the east, north, and up directions, respectively, alongside convergence time reductions of 11.0%, 6.6%, and 3.2%. In general, the proposed ultra-rapid clock offset estimation model, constrained by the variance components of the multi-GNSS clocks, constitutes a valuable supplement to the existing quality-improvement strategies for clock products at the Analysis Centers (ACs).