1 research outputs found
A Statistical Characterization of Localization Performance in Wireless Networks
Localization performance in wireless networks has been traditionally
benchmarked using the Cramer-Rao lower bound (CRLB), given a fixed geometry of
anchor nodes and a target. However, by endowing the target and anchor locations
with distributions, this paper recasts this traditional, scalar benchmark as a
random variable. The goal of this work is to derive an analytical expression
for the distribution of this now random CRLB, in the context of
Time-of-Arrival-based positioning.
To derive this distribution, this work first analyzes how the CRLB is
affected by the order statistics of the angles between consecutive
participating anchors (i.e., internodal angles). This analysis reveals an
intimate connection between the second largest internodal angle and the CRLB,
which leads to an accurate approximation of the CRLB. Using this approximation,
a closed-form expression for the distribution of the CRLB, conditioned on the
number of participating anchors, is obtained.
Next, this conditioning is eliminated to derive an analytical expression for
the marginal CRLB distribution. Since this marginal distribution accounts for
all target and anchor positions, across all numbers of participating anchors,
it therefore statistically characterizes localization error throughout an
entire wireless network. This paper concludes with a comprehensive analysis of
this new network-wide-CRLB paradigm.Comment: Submitted to IEEE Transactions on Wireless Communication