Ensemble Timescale Generation Using a Fused Kalman Filter and Three-States Weighting Approach

Abstract

The growing demand for high-precision timekeeping has sparked great interest in how to generate stable timescales based on clock ensembles. While weighted-average algorithms are widely used for this purpose, their inherent limitation of assigning a single weight per clock hinders the simultaneous mitigation of multiple noise types, ultimately restricting timekeeping accuracy. To address this issue, this article proposes a Kalman filter plus three-states weighted-average (KPTW) algorithm, grounded in multiscale analysis. The method begins by employing a Kalman filter to estimate the clock bias, frequency deviation, and frequency drift of individual clocks, thereby decomposing different noise types into distinct clock states. Each state is then processed through a dedicated weighting strategy, enabling effective noise mitigation and drift reduction. The ensemble timescale is subsequently synthesized from these individually weighted states. Experimental results demonstrate that the proposed algorithm significantly enhances both short and long-term stability. Specifically, it achieves a 41.86% improvement in one-day stability compared with the AT1 algorithm, and an 83.19% improvement in one-month stability compared with the ALGOS algorithm. By supporting both externally referenced and self-sustaining operation modes, KPTW offers the versatility needed for broad adoption in time metrology labs.