Performance limits in sensor localization

Abstract

In this paper, we study performance limits of sensor localization from a novel perspective. Specifically, we consider the Cramér-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 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 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. Index TermsCramér-Rao lower bound, received signal strength (RSS), time of arrival (TOA), bearing, U -statistics.

A Statistical Characterization of Localization Performance in Wireless Networks

“…Therefore, in this scenario, localization performance will only be based on the N anchors tasked. This is clearly reflected in the modified conditional distribution of S in (15).…”

“…Proof. Multiplying the modified conditional distribution of S, given in (15), by the marginal distribution of L from Corollary 6.1 gives the joint distribution of S and L. Then, setting L equal to a particular realization, , and summing over all realizations, gives us the marginal cdf of S, as desired.…”

“…With regards to the first step, there have been several attempts in the literature to obtain this conditional distribution. An excellent first attempt can be found in the series of papers, [13], [14], [15], in which approximations of this conditional distribution were presented for Received-Signal-Strength (RSS), Time-of-Arrival (TOA), and Angle-of-Arrival (AOA) based localization, respectively. These approximations were obtained through asymptotic arguments by driving the number of participating anchor nodes to infinity.…”

Effective Sensors Deployment with Localization Accuracy Constraints

“…Given the path-loss model (1) and the mutually independent assumption, ș CRLB Tr can be approximated by the following normal distribution as s is sufficiently large [1]. ¸¸¸¸¹ · © §1 · © § , the following inequality should be satisfied (11), denoted as * s , which is the minimal number of anchors(anchors at least) required to meet the given localization constraints.…”

“…Then how many anchors are needed to ensure the given localization constraints? In [1], under the uniformly and randomly deployment, the localization estimation errors are proved to be approximately following the normal distribution with mean related to the number of anchors, which provide a way to answer this question. The method to get the minimal number and the sufficient number of anchors are detailed in this paper.…”