Hierarchical Distributed Architecture for the Least Allan Variance Atomic Timing

TL;DR

The paper addresses GNSS-dependent timing resilience by proposing a hierarchical distributed architecture that leverages a MAC ensemble to maintain consistent synchronization and minimize the Allan variance $\sigma_A^2(m \tau)$ of the generated time scale under both GNSS availability and failure. The lower layer achieves GNSS-free synchronization through edge-state Kalman filtering and a distributed controller, while the upper layer alternates between GNSS-based anchoring in normal operation and optimal floating control in emergencies to steer the generated time scale toward minimal long-term AVAR, with the AVAR characterized by $\sigma_A^2(m \tau) = \frac{q^{\sf T} \varGamma(m \tau) q}{(m \tau)^2}$ and $\varGamma(m \tau) = (m \tau) \Sigma_1 + \frac{(m \tau)^3}{3} \Sigma_2$. A state-space expansion decouples synchronization from the unobservable global time, enabling explicit optimization of AVAR via $q_A(\tau) = \frac{\varGamma^{-1}(\tau) \mathds{1}_N}{\mathds{1}_N^{\sf T} \varGamma^{-1}(\tau) \mathds{1}_N}$ and providing stability guarantees for both anchoring and floating modes. Numerical illustrations demonstrate improved short-term stability and GNSS resilience, highlighting practical relevance for high-precision timing in critical infrastructure.

Abstract

In this paper, we propose a hierarchical distributed timing architecture based on an ensemble of miniature atomic clocks. The goal is to ensure synchronized and accurate timing in a normal operating mode where Global Navigation Satellite System (GNSS) signals are available, as well as in an emergency operating mode during GNSS failures. At the lower level, the miniature atomic clocks employ a distributed control strategy that uses only local information to ensure synchronization in both modes. The resulting synchronized time or generated time scale has the best frequency stability, as measured by the Allan variance, over the short control period. In the upper layer, a supervisor controls the long-term behavior of the generated time scale. In the normal operating mode, the supervisor periodically anchors the generated time scale to the standard time based on GNSS signals, while in the emergency operating mode, it applies optimal floating control to reduce the divergence rate of the generated time scale, which is not observable from the measurable time difference between the miniature atomic clocks. This floating control aims to explicitly control the generated time scale to have the least Allan variance over the long control period. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the architecture in high-precision, GNSS-resilient atomic timing.

Figures (8)

• Figure 1: Diagram of the hierarchical atomic timing architecture in normal and emergency operation. At the lower level, the MACs provide GNSS-independent distributed synchronization, while at the upper level, the supervisor controls the GTS by switching between anchoring and floating control in response to evolving situations.
• Figure 2: The network of 10 MACs and 2 anchors.
• Figure 3: Clock reading deviations under the distributed control strategy.
• Figure 4: Clock reading deviations anchored by GNSS signals in the normal operating mode.
• Figure 5: The AVAR of the MACs that are free-running (FR), controlled by the distributed synchronization strategy alone (DS), and the free-running ensemble mean $\Phi(q_{0})$ and $\Phi(q_{\infty})$.

Theorems & Definitions (5)

• Theorem 1
• Corollary 2
• Theorem 3
• Lemma 1
• Theorem 4