Ziv-Zakai bound for rate-constrained time-delay estimation in a wireless sensor network

Source localization is an important application of wireless sensor networks, and time-delay estimation is an essential step in several location finding algorithms. Various performance bounds for time-delay estimation have been developed for the case where the complete data from all individual sensors is considered available at the fusion center. In a wireless sensor network however, there exists a constraint on the number of bits that may be wirelessly exchanged between the sensors. This paper investigates performance bounds on time-delay estimation under a rate constraint, where the estimation is performed at the fusion center using signals that have been encoded with the available rate R. The Ziv-Zakai bound, which has been shown to subsume other bounds such as the Barankin and the Cramer-Rao bound as special cases, is obtained for the rate-constrained case and used to analyze the relation between the communication bit-rate and the variance of the time-delay estimation error.