Clock Rigidity and Joint Position-Clock Estimation in Ultra-Wideband Sensor Networks

TL;DR

This paper introduces a new clock rigidity theory for ultra-wideband sensor networks, linking graph properties to the feasibility of joint position and clock estimation using TOA measurements.

Contribution

It develops a novel clock rigidity framework and establishes conditions for unique joint position-clock estimation based on graph rigidity properties.

Findings

Clock frameworks are uniquely determined up to translation and scaling if infinitesimally clock rigid.

A clock framework's rigidity is linked to the underlying graph's bearing rigidity with redundant edges.

Simulation results validate the proposed joint estimation methods.

Abstract

Joint position and clock estimation is crucial in many wireless sensor network applications, especially in distance-based estimation with time-of-arrival (TOA) measurement. In this work, we consider a TOA-based ultra-wideband (UWB) sensor network, propose a novel clock rigidity theory and investigate the relation between the network graph properties and the feasibility of clock estimation with TOA timestamp measurements. It is shown that a clock framework can be uniquely determined up to a translation of clock offset and a scaling of all clock parameters if and only if it is infinitesimally clock rigid. We further prove that a clock framework is infinitesimally clock rigid if its underlying graph is generically bearing rigid in 2-dimensional space with at least one redundant edge. Combined with distance rigidity, clock rigidity provides a graphical approach for analyzing the joint position and clock problem. It is shown that a position-clock framework can be uniquely determined up to some trivial variations corresponding to both position and clock if and only if it is infinitesimally joint rigid. Simulation results are presented to demonstrate the clock estimation and joint position-clock estimation.