The Sensor Selection Problem for Bounded Uncertainty Sensing Models

We address the problem of selecting sensors so as to minimize the error in estimating the position of a target. We consider a generic sensor model where the measurements can be interpreted as polygonal, convex subsets of the plane. In our model, the measurements are merged by intersecting corresponding subsets, and the measurement uncertainty corresponds to the area of the intersection. This model applies to a large class of sensors, including cameras. We present an approximation algorithm which guarantees that the resulting error in estimation is within factor 2 of the least possible error. In establishing this result, we formally prove that a constant number of sensors suffice for a good estimate-an observation made by many researchers. We demonstrate the utility of this result in an experiment where 19 cameras are used to estimate the position of a target on a known plane. In the second part of this paper, we study relaxations of the problem formulation. We consider 1) a scenario where we are given a set of possible locations of the target (instead of a single estimate) and 2) relaxations of the sensing model. Note to Practitioners-This paper addresses a problem which arises in applications where many sensors are used to estimate the position of a target. For most sensing models, the estimates get better as the number of sensors increases. On the other hand, energy and communication constraints may render it impossible to use the measurements from all sensors. In this case, we face the sensor selection problem: how to select a "good" subset of sensors so as to obtain "good" estimates. We show that under a fairly restricted sensing model, a constant number of sensors are always competitive with respect to all sensors and present an algorithm for selecting such sensors. In obtaining this result, we assume that the sensor locations are known. In future research, we will investigate methods that are robust with respect to errors in sensor localization/calibration