# Inter-Node Distance Estimation from Multipath Delay Differences of Channels to Observer Nodes

## TL;DR

This paper introduces novel distance estimators for wireless nodes based on multipath delay differences to observer nodes, enabling accurate indoor localization without requiring synchronization or line-of-sight.

## Contribution

It develops and analyzes new multipath-based distance estimators that work in rich multipath environments with or without synchronization, supporting multiple observers.

## Key findings

- Estimators perform well in realistic indoor environments.
- The method does not require precise synchronization or line-of-sight.
- Multiple observers improve estimation accuracy.

## Abstract

We study the estimation of distance d between two wireless nodes by means of their wideband channels to a third node, called observer. The motivating principle is that the channel impulse responses are similar for small d and drift apart when d increases. Following this idea we propose specific distance estimators based on the differences of path delays of the extractable multipath components. In particular, we derive such estimators for rich multipath environments and various important cases: with and without clock synchronization as well as errors on the extracted path delays (e.g. due to limited bandwidth). The estimators readily support (and benefit from) the presence of multiple observers. We present an error analysis and, using ray tracing in an exemplary indoor environment, show that the estimators perform well in realistic conditions. We describe possible localization applications of the proposed scheme and highlight its major advantages: it requires neither precise synchronization nor line-of-sight connection. This could make wireless user tracking feasible in dynamic indoor settings.