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

TLDR

Position information is critical for commercial, public safety, and military applications, and future location‑aware networks aim for sub‑meter accuracy using wideband transmissions. This paper determines the fundamental limits of localization accuracy in wideband wireless networks under harsh multipath conditions. The authors develop a general framework that characterizes localization accuracy via the squared position error bound (SPEB) and equivalent Fisher information (EFI), deriving a concise expression directly from the full received waveforms rather than extracted metrics. The framework unifies anchor information and a priori agent knowledge, revealing that the SPEB derived from the full waveforms constitutes the fundamental accuracy limit.

Abstract

The availability of position 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 submeter 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 (EFI) 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 that 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.