Characterizing the Impact of SNR Heterogeneity on Time-of-Arrival based Localization Outage Probability

TL;DR

This paper analyzes how variations in signal-to-noise ratios among anchors affect the probability of localization outage in time-of-arrival systems, providing a more accurate error distribution model considering SNR heterogeneity.

Contribution

It introduces a distance-dependent SNR model for anchor-target links and derives an accurate approximation for the error ccdf, improving upon previous homogeneous SNR assumptions.

Findings

SNR heterogeneity significantly impacts localization error distribution.

The proposed model offers more accurate outage probability estimates.

Ignoring SNR heterogeneity can lead to underestimating localization errors.

Abstract

In localization, an outage occurs if the positioning error exceeds a pre-defined threshold, $\epsilon_{\rm th}$. For time-of-arrival based localization, a key factor affecting the positioning error is the relative positions of the anchors, with respect to the target location. Specifically, the positioning error is a function of (a) the distance-dependent signal-to-noise ratios (SNRs) of the anchor-target links, and (b) the pairwise angles subtended by the anchors at the target location. From a design perspective, characterizing the distribution of the positioning error over an ensemble of target and anchor locations is essential for providing probabilistic performance guarantees against outage. To solve this difficult problem, previous works have assumed all links to have the same SNR (i.e., SNR homogeneity), which neglects the impact of distance variation among the anchors on the positioning error. In this paper, we model SNR heterogeneity among anchors using a distance-dependent pathloss model and derive an accurate approximation for the error complementary cumulative distribution function (ccdf). By highlighting the accuracy of our results, relative to previous ones that ignore SNR heterogeneity, we concretely demonstrate that SNR heterogeneity has a considerable impact on the error distribution.