Browsing by Subject "Outer approximation"

Now showing 1 - 3 of 3

Open Access
Distributed bounding of feasible sets in cooperative wireless network positioning
(IEEE, 2013) Gholami, M. R.; Wymeersch, H.; Gezici, Sinan; Ström, E. G.
Locations of target nodes in cooperative wireless sensor networks can be confined to a number of feasible sets in certain situations, e.g., when the estimated distances between sensors are larger than the actual distances. Quantifying feasible sets is often challenging in cooperative positioning. In this letter, we propose an iterative technique to cooperatively outer approximate the feasible sets containing the locations of the target nodes. We first outer approximate a feasible set including a target node location by an ellipsoid. Then, we extend the ellipsoid with the measured distances between sensor nodes and obtain larger ellipsoids. The larger ellipsoids are used to determine the intersections containing other targets. Simulation results show that the proposed technique converges after a small number of iterations.
Open Access
Spectra of self-similar Laplacians on the Sierpinski gasket with twists
(World Scientific Publishing Co. Pte. Ltd., 2008) Blasiak, A.; Strichartz, R. S.; Ugurcan, B. E.
We study the spectra of a two-parameter family of self-similar Laplacians on the Sierpinski gasket (SG) with twists. By this we mean that instead of the usual IFS that yields SG as its invariant set, we compose each mapping with a reflection to obtain a new IFS that still has SG as its invariant set, but changes the definition of self-similarity. Using recent results of Cucuringu and Strichartz, we are able to approximate the spectra of these Laplacians by two different methods. To each Laplacian we associate a self-similar embedding of SG into the plane, and we present experimental evidence that the method of outer approximation, recently introduced by Berry, Goff and Strichartz, when applied to this embedding, yields the spectrum of the Laplacian (up to a constant multiple). © 2008 World Scientific Publishing Company.
Open Access
Static positioning using UWB range measurements
(IEEE, 2010) Gholami, M.R.; Ström, E.G.; Sottile F.; Dardari, D.; Conti, A.; Gezici, Sinan; Rydström, M.; Spirito, M.A.
The performance of several existing and partly new algorithms for positioning of sensor node based on distance estimate is compared when the distance estimates are obtained from a measurement campaign. The distance estimates are based on time-of-arrival measurements done by ultrawideband devices in an indoor office environment. Two different positioning techniques are compared: statistical and geometrical. In statistical category, distributed weighted-multidimensional scaling (dwMDS), least squares, and sum product algorithm are evaluated and in geometrical technique projections approach and outer approximation (OA) method are investigated. No method shows the best performance in all cases, while in many situations, sum product algorithm, dwMDS, nonlinear least square, projection approach, OA, and weighted least square work well. Copyright © The authors.