Information theoretic bounds for sensor network localization

We investigate the fundamental performance limits of target localization, where a network of sensors observe and cooperatively estimate the 2D location of a target. Taking a general view of a sensor as any device whose observations depend statistically on target position, we consider the binary hypothesis testing problem of choosing between the correct target location and an incorrect location at a distance r from it, given the outputs of all sensors in the network. By considering a random placement of sensors in an infinitely large sensing area, we obtain upper and lower bounds on the error probability of this hypothesis testing problem. The error bounds depend only on the type of sensor and are independent of the detailed geometry of the sensor network deployment. This provides a compact comparison of the localization performance of sensors whose characteristics might differ widely (e.g., received signal strength, proximity and time of arrival sensors). Also the bounds decrease exponentially with the density of sensors, and the rate of decrease is shown to have a simple geometric interpretation.