Clock synchronization over networks -- Identifiability of the sawtooth model

TL;DR

This paper investigates the identifiability of the sawtooth signal model in two-node clock synchronization, revealing that noise can enhance parameter estimation and providing simulation-based performance insights.

Contribution

It introduces a novel analysis of the sawtooth model for clock synchronization, showing noise can improve estimation conditions and offering performance benchmarks.

Findings

Noise improves estimation of phase and offset parameters.

Identifiability of the sawtooth model is established.

Simulation results provide performance references under realistic conditions.

Abstract

In this paper, we analyze the two-node joint clock synchronization and ranging problem. We focus on the case of nodes that employ time-to-digital converters to determine the range between them precisely. This specific design choice leads to a sawtooth model for the captured signal, which has not been studied before from an estimation theoretic standpoint. In the study of this model, we recover the basic conclusion of a well-known article by Freris, Graham, and Kumar in clock synchronization. More importantly, we discover a surprising identifiability result on the sawtooth signal model: noise improves the theoretical condition of the estimation of the phase and offset parameters. To complete our study, we provide performance references for joint clock synchronization and ranging using the sawtooth signal model by presenting an exhaustive simulation study on basic estimation strategies under different realistic conditions. With our contributions in this paper, we enable further research in the estimation of sawtooth signal models and pave the path towards their industrial use for clock synchronization and ranging.