There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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.

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

The availability of position information is of great importance in many commercial, governmental, and military applications Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors) However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality We provide a geometrical interpretation of equivalent Fisher information (EFI) for cooperative networks This approach allows us to succinctly derive fundamental performance limits and their scaling behaviors, and to treat anchors and agents in a unified way from the perspective of localization accuracy Our results yield important insights into how and when cooperation is beneficial

http://publications.lib.chalmers.se/records/fulltext/local_133941.pdf

Fundamental Limits of Wideband Localization— Part II: Cooperative Networks

Ultra Wideband Signals and Systems in Communication Engineering

Sensor networks can benefit greatly from location-awareness, since it allows information gathered by the sensors to be tied to their physical locations. Ultra-wide bandwidth (UWB) transmission is a promising technology for location-aware sensor networks, due to its power efficiency, fine delay resolution, and robust operation in harsh environments. However, the presence of walls and other obstacles presents a significant challenge in terms of localization, as they can result in positively biased distance estimates. We have performed an extensive indoor measurement campaign with FCC-compliant UWB radios to quantify the effect of non-line-of-sight (NLOS) propagation. From these channel pulse responses, we extract features that are representative of the propagation conditions. We then develop classification and regression algorithms based on machine learning techniques, which are capable of: (i) assessing whether a signal was transmitted in LOS or NLOS conditions; and (ii) reducing ranging error caused by NLOS conditions. We evaluate the resulting performance through Monte Carlo simulations and compare with existing techniques. In contrast to common probabilistic approaches that require statistical models of the features, the proposed optimization-based approach is more robust against modeling errors.

/pdf/nlos-identification-and-mitigation-for-localization-based-on-2yysnz70nz.pdf

NLOS identification and mitigation for localization based on UWB experimental data

Understanding ultra-wide-band (UWB) propagation channels is a prerequisite for UWB system design as well as communication-theoretic and information-theoretic investigations. This paper surveys the fundamental properties of UWB channels, pointing out the differences to conventional channels. If the relative bandwidth is large, the propagation processes, and therefore path loss and shadowing, become frequency-dependent, and the well-known wide-sense stationary uncorrelated scattering model is not applicable anymore. If the absolute bandwidth is large, the shape of the impulse responses as well as the fading statistics change. This paper also describes methods for measuring UWB channels and extracing channel parameters. Throughout this paper, the relationship between channel properties and other areas of UWB research are pointed out.

A.F. Molisch

Papers

Ultra-Wide-Band Propagation Channels