Sensor Placement and Selection for Bearing Sensors with Bounded Uncertainty

Date of Submission: 
February 24, 2012
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We consider the problem of placing sensors so as to effectively localize a target in a square workspace. In our model, each sensor returns a bearing measurement with bounded error: the true location of the target is guaranteed to be contained in a 2α-wedge around the measurement where α is a sensor noise parameter. The target is localized by intersecting the measurements (wedges) from all sensors. The estimation quality is given by the area of the intersection. We show that by placing sensors on a triangular grid, one can guarantee that the estimation quality is within a constant factor of the quality that can be achieved by any placement in the worst-case (regardless of target’s location and measurements obtained). We also show that this estimate can be obtained by activating a small number of sensors and thereby provide a mechanism for sensor selection as well.