Lower bounds of localization uncertainty in sensor networks

Localization is a key application for sensor networks. We propose a Bayesian method to analyze the lower bound of localization uncertainty in sensor networks. Given the location and sensing uncertainty of individual sensors, the method computes the minimum-entropy target location distribution estimated by the network of sensors. We define the Bayesian bound (BB) as the covariance of such distribution, which is compared with the Cramer-Rao bound (CRB) through simulations. When the observation uncertainty is Gaussian, the BB equals the CRB. The BB is much simpler to derive than the CRB when sensing models are complex. We also characterize the localization uncertainty attributable to the sensor network topology and the sensor observation type through the analysis of the minimum entropy and the CRB. Given the sensor network topology and the sensor observation type, such characteristics can be used to approximately predict where the target can be relatively accurately located.