On the Limits of Single Anchor Localization: Near-Field vs Far-Field

TL;DR

This paper investigates the fundamental limits of single-anchor localization in near-field and far-field scenarios using Fisher information analysis, revealing different estimability of position and orientation parameters.

Contribution

It provides a Fisher information theoretical comparison of localization limits in near-field versus far-field conditions, highlighting the different estimability of orientation and position.

Findings

Near-field allows joint estimation of 3D orientation and position.

Far-field only allows joint estimation of 2D orientation and position.

Simulation shows 3D orientation can be estimated without beamforming in near-field.

Abstract

It is well known that a single anchor can be used to determine the position and orientation of an agent communicating with it. However, it is not clear what information about the anchor or the agent is necessary to perform this localization, especially when the agent is in the near-field of the anchor. Hence, in this paper, to investigate the limits of localizing an agent with some uncertainty in the anchor location, we consider a wireless link consisting of source and destination nodes. More specifically, we present a Fisher information theoretical investigation of the possibility of estimating different combinations of the source and destination's position and orientation from the signal received at the destination. To present a comprehensive study, we perform this Fisher information theoretic investigation under both the near and far field propagation models. One of the key insights is that while the source or destination's $3$D orientation can be jointly estimated with the source or destination's $3$D position in the near-field propagation regime, only the source or destination's $2$D orientation can be jointly estimated with the source or destination's $2$D position in the far-field propagation regime. Also, a simulation of the FIM indicates that in the near-field, we can estimate the source's $3$D orientation angles with no beamforming, but in the far-field, we can not estimate the source's $2$D orientation angles when no beamforming is employed.