Adaptive clock modeling for real-time GPS/Galileo PPP timing of LEO satellites

Abstract

Low Earth Orbit (LEO) satellite-borne Global Navigation Satellite System (GNSS) observations play an important role in precise orbit determination and timing applications. However, owing to the complex onboard environment and limitations in data-link conditions, observation interruptions and degraded observation quality frequently occur. In Precise Point Positioning (PPP), the receiver clock offset is typically modeled as a white-noise process. Such a model, however, has limited capability to characterize the time-varying behavior of the receiver clock offset, particularly during observation outages and subsequent recovery. In these situations, abrupt state transitions and weakened prior constraints can degrade the effectiveness of clock modeling and lead to substantial estimation errors. To address these limitations, an adaptive receiver clock model is developed within a Kalman-filter-based PPP framework. The proposed model incorporates clock offset prediction during observation outages and adaptive reconstruction of clock constraints after data recovery, thereby enabling smoother state propagation and more robust re-estimation of the receiver clock offset. Onboard GNSS observations from the GRACE-FO C/D and Sentinel-6A satellites were used to evaluate the proposed approach. PPP-based timing solutions were generated for DOY 258–290 in 2023, and their timing stability was assessed using the Modified Allan Deviation (MDEV). The results demonstrate that, compared with the conventional white-noise model, the proposed adaptive clock model substantially improves the continuity and stability of receiver clock offset estimation. In particular, at an averaging time of 1,280 s, the mean MDEV values averaged over the three selected study periods decrease from 5.90 × 10 −13 , 5.45 × 10 −13 , and 8.66 × 10 −13 to 1.95 × 10 −13 , 1.68 × 10 −13 , and 7.51 × 10 −13 for GRACE-FO C, GRACE-FO D, and Sentinel-6A, respectively, corresponding to reductions of 66.95%, 69.17%, and 13.28%. These results demonstrate that the proposed adaptive clock model provides an effective strategy for improving high-precision timing and onboard GNSS data processing for LEO satellites.