Time Difference of Arrival Extraction from Two-Way Ranging

TL;DR

This paper addresses scalable passive localization by extracting Time Difference of Arrival (TDoA) information from active Two-Way Ranging (TWR), enabling passive listeners to estimate distances without synchronized anchors. It develops drift-aware estimators for both Single-Sided and Double-Sided TWR, deriving drift-corrected ToF formulas using relative drift factors and carrier frequency offset (CFO) when available. The key contributions include a common error estimation framework for SS-TWR and DS-TWR under clock drift, and the generalized extraction of TDoA information from listening to TWR for passive devices, including drift-corrected TDoA estimation. The results enable hyperbolic positioning with mobile or fully passive anchors, increasing scalability and update rates in dense UWB localization deployments.

Abstract

Two-Way Ranging enables the distance estimation between two active parties and allows time of flight measurements despite relative clock offset and drift. Limited by the number of messages, scalable solutions build on Time Difference of Arrival to infer timing information at passive listeners. However, the demand for accurate distance estimates dictates a tight bound on the time synchronization, thus limiting scalability to the localization of passive tags relative to static, synchronized anchors. This work describes the extraction of Time Difference of Arrival information from a Two-Way Ranging process, enabling the extraction of distance information on passive listeners and further allowing scalable tag localization without the need for static or synchronized anchors. The expected error is formally deducted. The extension allows the extraction of the timing difference despite relative clock offset and drift for the Double-Sided Two-Way Ranging and Single-Sided Two-Way Ranging with additional carrier frequency offset estimation.

Figures (4)

• Figure 1: TDoA inferred Hyperbolas: The time difference of arrival (TDoA) allows a tag to fix its position to a hyperbola relative to known anchors, allowing hyperbolic positioning with enough anchors. This work describes how TDoA information can be extracted from listening to the Two-Way Ranging of other devices, allowing for mobile anchors and an increase in the frequency and scalability for dense deployments.
• Figure 2: The message exchange in Two-Way Ranging (TWR) protocols: Measuring the round times and delays, active parties $A$ and $B$ can estimate the time-of-flight and therefore their distance despite clock offsets. The addition of a third (final) message extends the traditional Single-Sided TWR (SS-TWR) to Double-Sided TWR (DS-TWR) and mitigates the effect of relative clock drifts removing the need for carrier offset estimation as in SS-TWR.
• Figure 3: Inferred TDoA from SS-TWR: A passive listening node $L$ determine the difference in ToF between nodes $A$ and $B$ which conducted active ranging using SS-TWR. Estimating the carrier frequency offset mitigates the effect of clock drifts.
• Figure 4: Inferred TDoA from DS-TWR: A passive listening node $L$ can determine the difference in time-of-flight nodes $A$ and $B$ which conduct active ranging using DS-TWR. The two messages of $A$ allow $L$ to correct its relative clock drift.