Performance limits in sensor localization

In this paper, we study the Cramér-Rao Lower Bound (CRLB) in single-hop sensor localization using measurements derived from received signal strength (RSS), time of arrival (TOA) and bearing, respectively, from a novel perspective. Differently from the existing work, we use a statistical sensor-anchor geometry modeling method, with the result that the trace of the associated CRLB matrix, as a scalar metric for performance limits of sensor localization, becomes a random variable. Given a probability measure for the sensor-anchor geometry, the statistical properties of the metric are analyzed to demonstrate properties of sensor localization. Using the Central Limit Theorems for U-statistics, we show that as the number of anchors increases, the 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. We provide formulas quantitatively describing the relationship among the mean and standard deviation of the 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.