## 4 Performance Evaluations
### Simulation Results  
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. Figure 7(a) compares the average location error as a function of the beacon distance and Figure 7(b) compares the ratio of localized sensor nodes with location errors below 10 m. The average location error of LDB is shown to fluctuate more and to be larger than that of LoMoB. As the beacon distance increases, the performance gap between LoMoB and LDB tends to widen. Figure 7 demonstrates that LoMoB is less vulnerable to the beacon distance than LDB. 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. Figure 8(a) compares the average location error as a function of the standard deviation \(\sigma_{r}\) in the radius of the circle and Figure 8(b) compares the ratio of localized sensor nodes with location errors below 10 m. As shown in the figures, the average location error increases as irregularities in the radius of the circle increase. LoMoB has \(32.4\%\)-\(45.8\%\) smaller location errors than LDB. The ratios of localized sensor nodes show a maximum difference of 7.4%. LoMoB is verified to be more tolerant to irregularities in the radius of the circle formed by the transceiver's beam than LDB. Figure 8: Localization accuracy as a function of standard deviation \(\sigma_{r}\) in the radius of the circle formed by the transceiver’s beam. (**a**) Average location error; (**b**) Ratio of localized sensor nodes. Figure 7: Localization accuracy as a function of beacon distance. (**a**) Average location error; (**b**) Ratio of localized sensor nodes. 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. Figure 9(a) compares the average location error according to the standard deviation \(\sigma_{m}\) in the location error of a mobile beacon and Figure 9(b) compares the ratio of localized sensor nodes with location errors below 10 m. LoMoB improves the average location error by \(21.5\%\)-\(32.4\%\) compared to LDB. The ratios of localized sensor nodes show a maximum difference of 4.3%. In addition, Figure 10 shows the average location error of LDB and LoMoB applying a simple mean and the weighted mean; if all the weights are equal, then the weighted mean is the same as the simple mean. LoMoB applying a simple mean and the weighted mean improves the average location error by \(14.3\%\)-\(26.9\%\) and \(21.5\%\)-\(32.4\%\), respectively. This indicates that the use of all the potential locations in LoMoB is the main factor to improve LDB and the use of the weights results in additional increase in the localization accuracy. Figure 10: Comparison between simple mean and weighted mean. Figure 9: Localization accuracy as a function of standard deviation \(\sigma_{m}\) in the location error of a mobile beacon. (**a**) Average location error; (**b**) Ratio of localized sensor nodes. 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.