Session P3b: Methods and Algorithms for Timing Applications and Timescales

A Kuramoto Oscillator Ensemble Time Scale
Nate Ristoff, Hunter Kettering, James Camparo, The Aerospace Corporation
Location: Seaview A/B
Date/Time: Wednesday, Jan. 29, 4:23 p.m.

Resilient GPS (RGPS) will need a robust ensembling and time distribution methodology that is
scalable. Additionally, ensembles for cis-lunar and eventual Martian timekeeping will not only
need to be robust but simple and versatile. As we will discuss in this presentation, Kuramoto
oscillators significantly simplify the ensembling process, making it highly scalable and easily
adaptable to a crosslinked constellation in Earth or lunar orbit. The Kuramoto oscillator is a very
simple algorithm that utilizes phase measurement combined with clock feedback. It is based on a
phenomenon of non-linear feedback between oscillators, which leads to spontaneous
synchronization among the oscillators. Though the Kuramoto oscillator has been used to study a
variety of systems such as firefly blinking, neuron activity and coupled metronomes, to date there
have been no studies of Kuramoto oscillators in the context of high precision clocks (terrestrial or
space). Here we report on simulations of Kuramoto oscillators based on low SWaP Rb atomic
clocks, reporting the simulated time error buildup and the resulting time scale’s MDEV, and we
compare the Kuramoto oscillator ensemble algorithm to a simple frequency averaging algorithm.
The simulation results to be reported are very promising, and motivate our future work to construct
a hardware instantiation of a Kuramoto oscillator ensemble time scale.
Approved for public release. OTR 2024-01125