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Localization is one of the most important issues associated with underwater acoustic sensor networks, especially when sensor nodes are randomly deployed. Given that it is difficult to deploy beacon nodes at predetermined locations, localization schemes with a mobile beacon on the sea surface or along the planned path are inherently convenient, accurate, and energy-efficient. In this paper, we propose a new range-free Localization with a Mobile Beacon (LoMoB). The mobile beacon periodically broadcasts a beacon message containing its location. Sensor nodes are individually localized by passively receiving the beacon messages without inter-node communications. For location estimation, a set of potential locations are obtained as candidates for a node's location and then the node's location is determined through the weighted mean of all the potential locations with the weights computed based on residuals.

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 [

To localize unknown nodes, static beacons [

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 [

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 [

In this section, we briefly explain LDB in the viewpoint of system environment, beacon point selection, and location estimation [

In LDB, an AUV with a directional transceiver moves at a fixed depth in water and broadcasts its location, which called a beacon, and the angle of its transceiver's beam (_{2} and the sensor node in blue can receive the beacons _{1}, _{2}, and _{3}. The conical beam forms circles with different radii according to the depth of the sensor nodes, as shown in _{A}_{s}

From the viewpoint of a sensor node located at (_{s}_{A}_{b}_{1} to _{6}. Among the series of received beacons, the first beacon is defined as the first-heard beacon point and the last beacon is defined as the last-heard beacon point. The location of a sensor node is estimated using only the beacon points, and not all the received beacons.

Because the sensor depth is known from the pressure sensor, the beacon points can be projected onto the horizontal plane in which the sensor node resides, as shown in

We describe location estimation based on the projected beacon points. As shown in _{0}), and the projected point of the beacon after the last-heard beacon point is defined as the projected post-heard beacon point _{7}).

Four circles are then drawn with radius _{b}

In this section, we explain the system environment, beacon point selection, and location estimation method for LoMoB. Because LoMoB can be applied to systems that use either a directional transceiver or an omnidirectional transceiver, we explain LoMoB for both systems. In addition, because LoMoB improves LDB, we explain LoMoB by comparing and contrasting it with LDB.

LoMoB considers a system that uses an omnidirectional transceiver in addition to a system that uses a directional transceiver [

A mobile beacon moves on the sea surface or underwater. When a mobile beacon has an omnidirectional transceiver, 3D movement of the mobile beacon is possible whereas a mobile beacon that has a directional transceiver is restricted to 2D movement at a fixed depth. The mobile beacon is assumed to know its own location and to broadcast a beacon containing its location information at regular distance intervals, which are called the beacon distance _{2} and the sensor node in blue can receive the beacons _{1} and _{2}. Here, the communication range

From the viewpoint of a sensor node, the sensor node can receive a beacon when the beacon is within the communication range of the sensor node; e.g., in _{1} to _{6}. The selection of beacon points from the received beacons is performed as in LDB. When a sensor node receives the first beacon from a mobile beacon, the first beacon is selected as a beacon point; _{1} in _{6} in

As shown in

Sensor nodes are assumed to have a pressure sensor, and therefore they are assumed to know their depth [^{th}_{s}_{i}^{th}

For a system using a directional transceiver, all the projected beacon points are located between the distances _{b}_{b}_{b}_{b}

In this subsection, we explain how to estimate the location of a sensor node based on the distances between the sensor node and the projected beacon points. First, potential locations are obtained as candidates for the location of the sensor node. Second, the location of the sensor node is estimated using the weighted mean of the potential locations.

After estimating the distances between a sensor node and projected beacon points, the following equations need to be solved for localization:
^{th}^{th}

Let us explain how to estimate the location of a sensor node based on the bilateration method with _{12}(1) is closer to the two circles with centers
_{12}(2) in _{jk}_{jk}_{jk}_{jk}_{jk}

In rare cases, the number of intersection points between two circles can be one or zero. If there is one intersection point, this single point becomes the potential location. If there is no intersection point, which occurs when the distance between the two beacon points

The location of a sensor node can be estimated using all the potential locations. The location of a sensor node can simply be estimated as the mean of all the potential locations. However, to improve the estimation accuracy, a weighted mean of the potential locations can be used instead. Here, the weight is determined based on a residual, which we define here. Given _{jk}_{jk}, ŷ_{jk}_{jk}_{jk}, ŷ_{jk}

Less than three beacon points may be acquired for some sensor nodes in certain circumstances. In this case, because the location of a sensor node cannot be estimated through _{12}(1) and _{12}(2) of two circles with centers

It is noteworthy that the main feature of LoMoB that can improve LDB is the use of the weighted mean of all the potential locations. In LDB, when a sensor node has four projected beacon points _{1}, _{1}, _{2}, and _{2}, as shown in _{1} and _{1} and one point between the two is estimated as the location of the sensor node based on _{2} and _{2}. Here, the error in the estimated location depends largely on the distance between _{1} and _{1} [_{1} and _{1} are located very close to each other, the location error is expected to be large. In this case, a better choice may be that _{2} and _{2} (or another two projected beacon points) are used for the two possible points, rather than _{1} and _{1}. However, the selection of two projected beacon points for the possible points has not yet been studied. If the errors of the beacon points _{1} and _{1} increase because of some factors such as irregularities in the radius of the circle formed by the transceiver's beam and the location error of a mobile beacon, the errors of the two possible points also increase, which results in an increase of the location error. Even though more beacon points, in addition to _{1}, _{1}, _{2}, and _{2}, are obtained, the localization accuracy is not improved because the additional beacon points are not used for localization. As in LDB, LoMoB obtains two intersection points based on two beacon points and determines one point between the two as a potential location for the location of the sensor node based on the other beacon points. However, compared to LDB, LoMoB estimates the location of a sensor node based on all the potential locations, not just one potential location. In addition, potential locations with a high weight contribute more to the estimation of the location of the sensor node than other potential locations. For these reasons, LoMoB is expected to improve LDB in challenging underwater environments even though LoMoB uses just four beacon points, as does LDB. If more than four beacon points are used, the localization accuracy is expected to improve further.

In this section, we first describe the simulation parameters, then introduce the metric to evaluate the localization accuracy and, finally, we compare the localization accuracy of LoMoB with that of LDB through simulations.

The sensing space for UASN is a rectangular parallelepiped of 1 km × 1 km × 100 m, in which 100 sensor nodes are randomly deployed. A mobile beacon is assumed to move linearly at a velocity of 1 m/s and broadcasts a beacon at every beacon interval,

In LoMoB and LDB, localization begins by selecting beacon points. Any projected beacon points that are not exactly on the circle formed by the transceiver's beam for a sensor node cause an estimation error of the distance between the projected beacon point and the sensor node, which results in an error in the estimated location. The beacon distance causes projected beacon points to be located not exactly on the circle formed by the beam. In addition, the phenomena such as reflection, diffraction, and refraction in underwater environments cause irregularities in the radius of the circle formed by the beam. To improve the reality of our simulations, irregularities in the radius of the circle are modeled as _{r}_{r}_{m}_{m}_{m}_{m}^{T} is the measured location of the mobile beacon located at _{m}^{T} and _{m}_{x}, e_{y}^{T} is a random vector whose _{x}_{y}

To compare the localization accuracy of LoMoB and LDB, we define the average location error as follows:
_{k}_{k}, ŷ_{k}_{k}_{k}, y_{k}

Because the average location error may be seriously affected by a small number of large location errors, the ratio of localized sensor nodes with location errors below a given threshold can be used as an additional metric for evaluating the localization accuracy. The ratio of localized sensor nodes below a given threshold allows the localization accuracy to be assessed in greater depth than the average location error alone.

Because the beacon distance, irregularities in the radius of the circle formed by the transceiver's beam, and the location error of a mobile beacon all influence the accuracy of distance estimation between a sensor node and a projected beacon point, the localization accuracy is analyzed with respect to these factors.

In real underwater environments, the radius of the circle formed by the transceiver's beam is expected to fluctuate. Irregularities in the radius of the circle cause sensor nodes to provide erroneous estimates of distances between the projected beacon points and a sensor node, in addition to the error associated with the beacon distance. _{r}

A mobile beacon is generally assumed to know its own location. In reality, the location information of a mobile beacon may be erroneous. As well as irregularities in the radius of the circle formed by the transceiver's beam, the location error of a mobile beacon needs to be considered because this also causes erroneous estimation of the distances between the projected beacon points and a sensor node. _{m}

The localization accuracy performance of LoMoB and LDB was compared through the average location error and the ratio of localized sensor nodes with location errors below 10 m according to the beacon distance, irregularities in the radius of the circle formed by the transceiver's beam, and the location error of a mobile beacon. The simulation results verify that LoMoB is more tolerant to estimation errors of the distances between the projected beacon points and a sensor node. Subsequently, LoMoB is more promising than LDB in harsh underwater environments.

In this paper, we proposed a range-free localization scheme for UASN with a mobile beacon that provides the potential locations with weighting factors according to residuals and estimates the location of a sensor node through the weighted mean of the potential locations. Because LoMoB localizes a sensor node based on the weights of the potential locations, it improves the localization accuracy and is more tolerant to errors in the estimation of the distance between projected beacon points and sensor nodes. Simulation results show that LoMoB significantly improves the localization accuracy of LDB, especially in underwater environments that cause irregularities in the radius of the circle formed by the transceiver's beam and the location error of a mobile beacon. Our simulations demonstrated that LoMoB is more robust with respect to errors in distance estimation than LDB.

This work was supported by the World-Class University Program through the National Research Foundation of Korea (R31-10026), and Grant (K20903001804-11E0100-00910) funded by the Ministry of Education, Science, and Technology (MEST), also by a grant (07SeaHeroB01-03) from Plant Technology Advancement Program funded by Ministry of Construction and Transportation.

Movement of a mobile beacon for localization in underwater environments.

System environment and beacon point selection and projection for LDB. (

Location estimation with projected beacon points based on geometric constraints. (

System environment, beacon point selection, and projection for LoMoB. (

Estimation of the sensor node location using projected beacon points.

Selection of a potential location between two intersection points.

Localization accuracy as a function of beacon distance. (

Localization accuracy as a function of standard deviation _{r}

Localization accuracy as a function of standard deviation _{m}

Comparison between simple mean and weighted mean.