# Joint Ranging and Clock Synchronization for Dense Heterogeneous IoT Networks

## TL;DR

This paper introduces a unified framework for joint range and clock-skew estimation in dense IoT networks, addressing the limitations of existing methods by incorporating clock-skew effects into the measurement model and proposing an efficient estimation algorithm.

## Contribution

It develops a novel data model that includes clock-skew effects and formulates joint estimation as a 2-D frequency problem, along with a new protocol and WLS algorithm for accurate synchronization and ranging.

## Key findings

- The proposed estimator is asymptotically efficient, approaching the Cramer Rao lower bound.
- The joint estimation method outperforms existing estimators that ignore clock-skew effects.
- Numerical experiments validate the effectiveness of the proposed approach.

## Abstract

Synchronization and ranging in internet of things (IoT) networks are challenging due to the narrowband nature of signals used for communication between IoT nodes. Recently, several estimators for range estimation using phase difference of arrival (PDoA) measurements of narrowband signals have been proposed. However, these estimators are based on data models which do not consider the impact of clock-skew on the range estimation. In this paper, clock-skew and range estimation are studied under a unified framework. We derive a novel and precise data model for PDoA measurements which incorporates the unknown clock-skew effects. We then formulate joint estimation of the clock-skew and range as a two-dimensional (2-D) frequency estimation problem of a single complex sinusoid. Furthermore, we propose: (i) a two-way communication protocol for collecting PDoA measurements and (ii) a weighted least squares (WLS) algorithm for joint estimation of clock-skew and range leveraging the shift invariance property of the measurement data. Finally, through numerical experiments, the performance of the proposed protocol and estimator is compared against the Cramer Rao lower bound demonstrating that the proposed estimator is asymptotically efficient.