Symmetric probabilistic values for identifying informative sensors

In this paper, we show how the notion of symmetric probabilistic values from cooperative game theory can be used in a sensor network to identify the sensors that are relatively more informative than others. We note that parameter estimation in a sensor network can be modeled as a cooperative game, where a metric of estimation accuracy assigns a value to each subset of sensors. Symmetric probabilistic values are then known to be indicators of the relative power of players in cooperative games. Motivated by this, we define a power index for sensors based symmetric probabilistic values. While generally any metric of estimation accuracy can be used for computing power indices, it is noted that by choosing the determinant of the Fisher information matrix, the computational complexity associated with power indices gracefully increases with the number of sensors. The formulas are explicitly provided for computing the Banzhaf value and the Shapley value, two well-known symmetric probabilistic values. A target whose parameter is being estimated by the sensor network can use power indices to identify and act against the informative sensors. As an important application in this regard, the power indices of sensors are computed in bearings-only and range-only target localization.