# Pairwise Node Localization From Differences in Their UWB Channels to Observer Nodes

### Authors

Gregor Dumphart, Robin Kramer, Robert Heyn, Marc Kuhn, and Armin Wittneben

### Reference

IEEE Transactions on Signal Processing, 2022.

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### Abstract

We consider the problem of localization and distance estimation between a pair of wireless nodes in a multipath propagation environment, but not the usual way of processing a channel measurement between them. We propose a novel paradigm which compares the two nodes' ultra-wideband (UWB) channels to other nodes, called observers. The main idea is that the dissimilarity between the channel impulse responses (CIRs) increases with $d$ and allows for an estimate $\hat{d}$. Our approach relies on extracting common multipath components (MPCs) from the CIRs. This is realistic in indoor or urban scenarios and if $d$ is considerably smaller than the observer distances.
We present distance estimators which utilize the rich location information contained in MPC delay differences. Likewise, we present estimators for the relative position vector which process both MPC delays and MPC directions. We do so for various important cases: with and without time synchronization, delay measurement errors, and knowledge of the MPC association between the CIRs. The estimators exhibit great technological advantages: they do not require line-of-sight conditions, observer location knowledge, or environment knowledge.
We study the estimation accuracy with a numerical evaluation based on random sampling and, additionally, with an experimental evaluation based on measurements in an indoor environment. The proposal shows the potential for great accuracy in theory and practice. We describe how the paradigm could incorporate novel measurements into cooperative localization frameworks for spatio-temporal tracking. This could enable affordable wireless network localization in dynamic multipath settings.