1 research outputs found
A Statistically Modelling Method for Performance Limits in Sensor Localization
In this paper, we study performance limits of sensor localization from a
novel perspective. Specifically, we consider the Cramer-Rao Lower Bound (CRLB)
in single-hop sensor localization using measurements from received signal
strength (RSS), time of arrival (TOA) and bearing, respectively, but
differently from the existing work, we statistically analyze the trace of the
associated CRLB matrix (i.e. as a scalar metric for performance limits of
sensor localization) by assuming anchor locations are random. By the Central
Limit Theorems for -statistics, we show that as the number of the anchors
increases, this scalar metric is asymptotically normal in the RSS/bearing case,
and converges to a random variable which is an affine transformation of a
chi-square random variable of degree 2 in the TOA case. Moreover, we provide
formulas quantitatively describing the relationship among the mean and standard
deviation of the scalar metric, the number of the anchors, the parameters of
communication channels, the noise statistics in measurements and the spatial
distribution of the anchors. These formulas, though asymptotic in the number of
the anchors, in many cases turn out to be remarkably accurate in predicting
performance limits, even if the number is small. Simulations are carried out to
confirm our results