Upper bound of time synchronization error in two dimensional acoustic target localization using wireless sensor networks

Accuracy and power saving are two important quality of service (QoS) metrics in most applications of wireless sensor networks (WSNs) especially in acoustic target localization. The middleware layer of WSNs is responsible to properly manage the network-level resources and accurately setting the network parameters in support of these two application-level QoS metrics. A critical middleware-level task for such support is time synchronization. In this paper a probabilistic model of acoustic target localization is presented and is used to determine the probability mass function (pmf) of time delay between sensing times of sound waves of target object by two randomly selected sensing nodes. This pmf permits us to define upper bound of time synchronization error of the WSN. It can be used for determining the accuracy of target localization and amount of power consumption of the system based on the upper bound of time synchronization error which is set by the middleware level. This pmf can be used in applying tradeoffs between power consumption and accuracy of target localization results.