Combination of GNSS satellite clock offsets from L-band ground-tracking and inter-satellite link measurements

Satellite clock offset products are fundamental to high-precision Global Navigation Satellite Systems (GNSS) applications. Clock series derived from L-band Orbit Determination and Time Synchronization (ODTS) method generally exhibit good short-term stability but suffer from pronounced day-boundary discontinuities (DBDs). Furthermore, the orbit modeling errors absorbed into the clock estimates degrade the clock long-term stability. Inter-satellite link (ISL) technology provides an additional source of clock estimated information. Clock offsets derived from geometry-free ISL observables are almost immune to orbit errors and therefore offer better long-term stability. However, the limited ranging precision introduces larger random noise into ISL clocks, leading to the poorer short-term stability. Consequently, combining the above two measurement types is a logical strategy to optimize the overall clock solution. To exploit their complementary characteristics, we apply the Vondrak-Cepek (V-C) filter to combine 31 days of ISL clock offsets with the time derivatives of ODTS clocks provided by Deutsche GeoForschungsZentrum (GFZ). The results demonstrate that the V-C filter effectively suppresses observation noise without distorting the true signals. The combined clock product preserves the continuity of ISL clocks while maintaining the low noise level of the ODTS solution. After quadratic detrending, the combined clock residual is about 0.10 ns, comparable to those of ISL and significantly better than the GFZ value of 0.15 ns. In terms of overlapping Allan deviation, the combined clocks closely follow the GFZ performance at short averaging times and approach or even surpass the ISL stability at long intervals, achieving a balanced compromise between short- and long-term performance. The improvement in stability arises from both the complementary fusion of the two datasets and the smoothing properties of the filter. This study provides a new perspective on GNSS satellite clock combination and a practical method for fully exploiting the strengths of different clock products.