Browsing by Subject "Convex feasibility problem"

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    Upper bounds on position error of a single location estimate in wireless sensor networks
    (Hindawi Publishing Corporation, 2014) Gholami, M. R.; Ström, E. G.; Wymeersch, H.; Gezici, Sinan
    This paper studies upper bounds on the position error for a single estimate of an unknown target node position based on distance estimates in wireless sensor networks. In this study, we investigate a number of approaches to confine the target node position to bounded sets for different scenarios. Firstly, if at least one distance estimate error is positive, we derive a simple, but potentially loose upper bound, which is always valid. In addition assuming that the probability density of measurement noise is nonzero for positive values and a sufficiently large number of distance estimates are available, we propose an upper bound, which is valid with high probability. Secondly, if a reasonable lower bound on negative measurement errors is known a priori, we manipulate the distance estimates to obtain a new set with positive measurement errors. In general, we formulate bounds as nonconvex optimization problems. To solve the problems, we employ a relaxation technique and obtain semidefinite programs. We also propose a simple approach to find the bounds in closed forms. Simulation results show reasonable tightness for different bounds in various situations.