A mathematical model for the atomic clock error in case of jumps

TL;DR

This paper develops an extended mathematical model for atomic clock errors that incorporates jumps and instability increases, providing exact solutions for improved simulation, prediction, and system impact analysis.

Contribution

It introduces a novel extension of stochastic differential equations to model atomic clock errors with jumps and instability, including an exact iterative solution.

Findings

Provides an exact iterative solution for clock error modeling.

Enhances simulation and prediction accuracy for atomic clocks.

Improves understanding of clock error impact in satellite navigation systems.

Abstract

We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative solution that can be useful for clock simulation, prediction, and interpretation, as well as for the understanding of the impact of clock error in the overall system in which clocks may be inserted as, for example, the Global Satellite Navigation Systems.