A Statistically Modelling Method for Performance Limits in Sensor Localization
Abstract
In this paper, we study performance limits of sensor localization from a novel perspective. Specifically, we consider the CramerRao Lower Bound (CRLB) in singlehop 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 $U$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 chisquare 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 arXiv:
 arXiv:1109.2984
 Bibcode:
 2011arXiv1109.2984H
 Keywords:

 Computer Science  Systems and Control;
 Mathematics  Optimization and Control
 EPrint:
 Automatica, Volume 49, Issue 2, 2013, Pages 503509