This paper presents a novel theoretical framework for atomic time scale
generation, called explicit ensemble mean synchronization, which unifies clock
synchronization and time scale generation within a control-theoretic paradigm.
By exploiting an observable canonical decomposition of a standard atomic clock
ensemble model, the system is decomposed into two complementary components: the
observable part, which represents the synchronization deviation, and the
unobservable part, which captures the synchronization destination. Within this
structure, we mathematically prove that standard Kalman filtering, widely used
in current time scale generation, can be interpreted as a special case of the
proposed framework that optimizes long-term frequency stability in terms of the
Allan variance. Furthermore, by applying appropriate state feedback control to
each component based on the Kalman filtering, both clock synchronization and
optimal time scale generation are achieved within a unified framework. This
framework provides a principled basis for robust timekeeping systems that goes
beyond conventional approaches in both scope and performance.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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