Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Error characteristics of ad hoc positioning systems (aps)
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
An Analysis of Error Inducing Parameters in Multihop Sensor Node Localization
IEEE Transactions on Mobile Computing
On the cover time and mixing time of random geometric graphs
Theoretical Computer Science
Cramér-Rao-type bounds for localization
EURASIP Journal on Applied Signal Processing
Scaled Gromov hyperbolic graphs
Journal of Graph Theory
Estimation and control with relative measurements: algorithms and scaling laws
Estimation and control with relative measurements: algorithms and scaling laws
Cooperative localization bounds for indoor ultra-wideband wireless sensor networks
EURASIP Journal on Advances in Signal Processing
Relative location estimation in wireless sensor networks
IEEE Transactions on Signal Processing
Estimation From Relative Measurements: Electrical Analogy and Large Graphs
IEEE Transactions on Signal Processing
Betweenness centrality and resistance distance in communication networks
IEEE Network: The Magazine of Global Internetworking
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In this paper, we study the problem of estimating vector-valued variables from noisy "relative" measurements, which arises in sensor network applications. The problem can be posed in terms of a graph, whose nodes correspond to variables and edges to noisy measurements of the difference between two variables. The optimal (minimum variance) linear unbiased estimate of the node variables, with an arbitrary variable as the reference, is considered. This paper investigates how the variance of the estimation error of a node variable grows with the distance of the node to the reference node. A classification of graphs, namely, dense or sparse in Rd, 1 ≤ d ≤ 3, is established that determines this growth rate. In particular, if a graph is dense in 1-D, 2-D, or 3-D, a node variable's estimation error is upper bounded by a linear, logarithmic, or bounded function of distance from the reference. Corresponding lower bounds are obtained if the graph is sparse in 1-D, 2-D, and 3-D. These results show that naive measures of graph density, such as node degree, are inadequate predictors of the estimation error. Being true for the optimal linear unbiased estimate, these scaling laws determine algorithm-independent limits on the estimation accuracy achievable in large graphs.