Research on the ensemble timescale algorithm incorporated with an optical clock

To bridge the gap between the optical clock (OC) technological advancements and their practical implementation, this study develops an ensemble timescale algorithm that integrates discontinuously operated OCs with hydrogen maser (HM) ensembles using two-stage weighted least squares optimization. We conducted a systematic multi-scenario analysis by combining operational cycles of 1, 3, and 7 d with uptimes ranging from 1 to 24 h. This allowed us to quantify the effectiveness of the OC in estimating the frequency drift of HMs and their impact on timescale stability. Experimental validation demonstrates that OCs operating ⩾2 h d -1 , ⩾5 h every 3 d, or ⩾24 h/week achieve equivalent frequency drift assessment accuracy to a cesium fountain clock (CsF). Notably, with 12-hour daily operation, the OC-integrated timescale attains a stability of 1.07 × 10 −16 at 3.6 × 10 6 s, which represents a 192% and 839% improvement over CsF-integrated timescales and HM-only timescales. This research establishes a comprehensive theoretical and experimental validation for OC integration in timescale generation.