## 1 Introduction  
For a long time, there has been significant interest in monitoring underwater environments to collect oceanographic data and to explore underwater resources. These harsh underwater environments have limited human access and most of them remain poorly understood. Recent advances in hardware and network technology had enabled sensor networks capable of sensing, data processing, and communication. A collection of sensor nodes, which have a limited sensing region, processing power, and energy, can be randomly deployed and connected to form a network in order to monitor a wide area. Sensor networks are particularly promising for use in underwater environments where access is difficult [1; 2; 3]. In underwater acoustic sensor networks (UASN), localization of sensor nodes is essential because it is difficult to accurately deploy sensor nodes to predetermined locations. In addition, all the information collected by sensor nodes may be useless unless the location of each sensor node is known [4]. To localize unknown nodes, static beacons [5; 6; 7; 8; 9; 10; 11] or a mobile beacon [12; 13; 14; 15; 16] can be used; typically, buoys are used for static beacons and an autonomous underwater vehicle (AUV) for a mobile beacon. The use of a mobile beacon has a similar effect to the use of many static beacons. For this reason, localization using a mobile beacon is inherently more accurate and cost-effective than localization using static beacons. Further, the vehicle can be conveniently maneuvered on the sea surface or underwater, based on a planned or random path, as shown in Figure 1.  
Localization schemes can also be classified as range-based or range-free schemes. Range-based schemes use the distance and/or angle information measured by the Time of Arrival (ToA), Time Difference of Arrival (TDoA), Angle of Arrival (AoA), or Received Signal Strength Indicator (RSSI) techniques. In underwater environments, range-based schemes that use the ToA and TDoA techniques have been proposed [5; 6; 7; 8; 9; 10; 13; 14; 15]. Time synchronization between sensor nodes is typically required for the ToA and TDoA techniques [6]. However, precise time synchronization is challenging in underwater environments [17]. In addition, even though the ToA and TDoA techniques are used without time synchronization, the techniques are based on the speed of sound and this varies with temperature, pressure, salinity, and depth. In contrast to range-based schemes, range-free schemes localize a sensor  
Figure 1: Movement of a mobile beacon for localization in underwater environments. node by deducing distance information instead of measuring distances [11,12,16]. Because range-free schemes do not require additional devices in order to measure distances and do not suffer from distance measurement errors, range-free schemes are a promising approach for underwater sensor networks [16]. Localization is one of the challenges associated with underwater sensor networks and many studies have focused on localization in recent years. Among these studies, LDB is a range-free localization scheme with a mobile beacon [16]. In LDB, sensor nodes can localize themselves through passively listening to beacons sent by an AUV that has an acoustic directional transceiver. Because sensor nodes just receive the beacons from the AUV without inter-node communications, LDB is energy-efficient because it reduces the energy consumption due to transmitting; the power consumed by transmitting is often 100 times higher than the power consumed by receiving [18]. In addition, because a sensor node can localize itself using its own received beacons from the AUV independently of the other sensor nodes, LDB has fine-grained accuracy even in sparse networks. The depth of a sensor node is directly determined by using a cheap pressure sensor.