Fundamental Limits of Wideband Localization - Part I: A General Framework

TL;DR

This paper establishes a fundamental framework for analyzing the limits of wideband wireless localization accuracy in complex environments, using a novel information-theoretic approach based on received waveforms.

Contribution

It introduces a general methodology to quantify localization accuracy via the squared position error bound (SPEB) using equivalent Fisher information, considering all waveform information.

Findings

Provides a succinct expression for SPEB based on waveform analysis.

Unifies localization information from anchors and prior knowledge.

Offers insights into the fundamental limits of wideband localization accuracy.

Abstract

The availability of positional information is of great importance in many commercial, public safety, and military applications. The coming years will see the emergence of location-aware networks with sub-meter accuracy, relying on accurate range measurements provided by wide bandwidth transmissions. In this two-part paper, we determine the fundamental limits of localization accuracy of wideband wireless networks in harsh multipath environments. We first develop a general framework to characterize the localization accuracy of a given node here and then extend our analysis to cooperative location-aware networks in Part II. In this paper, we characterize localization accuracy in terms of a performance measure called the squared position error bound (SPEB), and introduce the notion of equivalent Fisher information to derive the SPEB in a succinct expression. This methodology provides insights into the essence of the localization problem by unifying localization information from individual anchors and information from a priori knowledge of the agent's position in a canonical form. Our analysis begins with the received waveforms themselves rather than utilizing only the signal metrics extracted from these waveforms, such as time-of-arrival and received signal strength. Hence, our framework exploits all the information inherent in the received waveforms, and the resulting SPEB serves as a fundamental limit of localization accuracy.