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In large-scale sensor networks, localization with mobile beacons is one of the most efficient ways to deploy sensor nodes as well as locate them. Direct communication with mobile beacons has an advantage of improvement in location accuracy by enabling sensor nodes to measure distances to the mobile beacons. Thus, it is important to improve the accuracy in the distance for high accurate positioning. In this letter, we propose a distance estimation scheme with weighted least squares in mobile beacon-based localization. First, we model distance measurements to a beacon node moving along the given linear tracks. Given our measurement model, the proposed scheme uses weighted least squares to minimize errors in distance measurements. Additionally we analyze the lower bound of errors in our distance estimation based on the Cramer-Rao bound. Simulation results show that our scheme can provide improved accuracy in both distance estimation and position estimation.