@MISC{_sensorselection, author = {}, title = {Sensor Selection in Arbitrary Dimensions}, year = {} }

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Abstract

Abstract — We address the sensor selection problem which arises in tracking and localization applications. In sensor selection, the goal is to select a small number of sensors whose measurements provide a good estimate of a target’s state (such as location). We focus on the bounded uncertainty sensing model where the target is a point in the d dimensional Euclidean space. Each sensor measurement corresponds to a convex, polyhedral subset of the space. The measurements are merged by intersecting corresponding sets. We show that, on the plane, four sensors are sufficient (and sometimes necessary) to obtain an estimate whose area is at most twice the area of the best possible estimate (obtained by intersecting all measurements). We also extend this result to arbitrary dimensions and show that a constant number of sensors suffice for a constant factor approximation in arbitrary dimensions. Both constants depend on the dimensionality of the space but are independent of the total number of sensors in the network. Note to Practitioners In many applications, sensing and communication constraints may render using all available sensors infeasible. In such scenarios, select-ing a small number of sensors – whose collaborative performance in estimating the state of a target is comparable to the best possible achievable error – becomes important. This paper focuses on sensors whose measurements can be specified as an intersection of halfspaces (e.g. cameras, whose measurements correspond to cones). It is proven that a “small ” set of good sensors can be selected from an arbitrary set of measurements in any dimension d. Of practical importance are the two cases: d = 2 (where four sensors suffice for a good estimate) and d = 3 (eight sensors are enough). Index Terms — Sensor networks: camera networks and sensor