# High-Precision Time Synchronization and Autonomous Maintenance for LEO Satellite Constellations Based on High-Stability Crystal Oscillators

## TL;DR

This paper introduces a low-cost, high-precision time synchronization method for LEO satellite constellations using crystal oscillators instead of atomic clocks or GNSS.

## Contribution

A novel autonomous time synchronization method using high-stability crystal oscillators and decentralized control for LEO constellations.

## Key findings

- The method achieves better than 5 ns (1σ) time synchronization performance in a Walker-Delta constellation.
- Peak-to-peak time error remains below 30 ns, meeting requirements for communication and timing services.
- The approach supports decentralized deployment and local physical time signal outputs for large-scale networks.

## Abstract

In recent years, the large-scale deployment of Low Earth Orbit (LEO) constellations has made autonomous time synchronization and reference maintenance within constellations a critical enabling technology. Achieving high-precision synchronization with low cost and low power consumption, without relying on onboard atomic clocks or Global Navigation Satellite System (GNSS) signals, remains a significant challenge. This paper proposes an autonomous time synchronization method for LEO constellations that relies solely on high-stability crystal oscillators as local oscillators. By leveraging satellite-to-ground and inter-satellite measurement links, the proposed approach enables constellation-wide time synchronization without external timing references. A satellite-to-ground link visibility time model is established based on orbital parameters and ground station visibility geometry. On this basis, a discrete state-space model is constructed, incorporating temperature-induced frequency perturbation compensation, frequency offset estimation, and control voltage regulation. A combined Kalman filtering and Linear Quadratic Regulator (LQR) control framework is employed to achieve precise time offset synchronization and long-term maintenance. Experimental results demonstrate that, under a Walker-Delta constellation configuration with an orbital altitude of 800 km and an inclination of 55°, the proposed method introduces a time synchronization performance better than 5 ns (1σ), with a peak-to-peak error below 30 ns. This level of performance satisfies the timing requirements of typical LEO constellation applications, including communication scheduling, high-rate modulation, and critical infrastructure timing services. Moreover, the proposed scheme supports decentralized deployment and provides local physical time signal outputs, making it well suited for large-scale satellite networks requiring high-precision autonomous time synchronization.