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Sensor Placement and Selection for Bearing Sensors with Bounded Uncertainty
"... We study the problem of placing sensors so as to accurately estimate the location of a target in a given environment. We focus on bearing sensors (such as cameras, microphone arrays) which are commonly used for target localization. We seek to discover and exploit the geometric structure associated w ..."
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We study the problem of placing sensors so as to accurately estimate the location of a target in a given environment. We focus on bearing sensors (such as cameras, microphone arrays) which are commonly used for target localization. We seek to discover and exploit the geometric structure associated with both the sensing model and the estimation process in order to obtain sensor placement schemes with performance guarantees. We use a geometric model to represent the sensing uncertainty: Each measurement yields an unbounded 2D wedge with angular width 2α around the measurement (α is an input parameter representing the maximum sensing noise). The wedge is guaranteed to contain the true location of the target. The target is localized by intersecting the wedges obtained from all sensors. The quality of the placement is given by the area or diameter of the intersection in the worstcase (i.e. regardless of the target’s location). We study the bicriteria optimization problem of placing a small number of sensors while guaranteeing a worstcase bound on the estimation error. Our main result is a constantfactor approximation for this problem: Let U ∗ D and UA ∗ be the diameter and area uncertainty achieved by an optimal algorithm using n ∗ sensors. We show that at most 9n ∗ sensors placed on a triangular grid has diameter uncertainty of at most 5.88U ∗ D and area uncertainty of at most 7.76U ∗ π π A, when the sensing noise 0 < 2α ≤ 2
Automatic Reduction of Combinatorial Filters
"... AbstractWe consider the problem of filtering whilst maintaining as little information as possible to perform a given task. The literature includes several illustrations of how adroit choices for state descriptions may lead to concise or even minimal filters tailored to specific tasks. We introdu ..."
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AbstractWe consider the problem of filtering whilst maintaining as little information as possible to perform a given task. The literature includes several illustrations of how adroit choices for state descriptions may lead to concise or even minimal filters tailored to specific tasks. We introduce an efficient algorithm which is able to reproduce these handcrafted solutions. Specifically, our algorithm accepts as input an arbitrary combinatorial filter, expressed as a transition graph, and outputs an equivalent filter that uses fewer information states to complete the same filtering task. We also show that solving this problem optimally is NPhard, and that the related decision problem is NPcomplete. These hardness results justify the potentially suboptimal output of our algorithm. In the experiments we describe, our algorithm produces optimal or nearoptimal reduced filters for a variety of problem instances. These reduced filters are of interest for several reasons, including their direct application on platforms with severely limited computational power and in systems that require communication over lowbandwidth noisy channels. Moreover, inspection of reduced filters may provide insights into the structure of a problem that can guide the design of the other elements of a robot system.