# MS Location Estimation Based on the Artificial Bee Colony Algorithm
## 5 Simulation Results
The second common NLOS propagation model is the uniformly distributed noise model [27]. In this NLOS error model, the measured distance is the true distance, which adds an error value. The NLOS error value is distributed uniformly in the range (0, \(U_{i}\)), where 0 and \(U_{i}\) are the lower bound and the upper bound of the error for each BS. An example of a uniformly distributed noise model is shown in Figure 7. The measured distance is the sum of the real distance \(R\) and the NLOS error with a uniform distribution for each BS. In Figure 8, the simulation shows the performances of the proposed algorithm and other methods with the NLOS error of various upper bound values. Obviously, the proposed algorithm has the lowest average location error in the uniformly distributed noise model. Figure 6: Average location error versus the different radius of scatters. Figure 7: Example of the uniformly distributed noise model. In a previous study, we proposed the positioning algorithm combined with GA [33]. A positioning method based on the ABC algorithm is used to precisely locate the MS as well as accelerate the convergence time, which is a bottleneck of the one based on GA. Therefore, the comparison of ABC and GA is an important issue. The error effect of CDSM and the uniformly distributed noise model on the average location error was compared with GA and ABC, as shown in Tables 1 and 2, respectively. Both the GA and ABC algorithms provide a more accurate estimation of the MS location. It can be observed that the ABC-based algorithm has a better performance than GA-based in the two NLOS error models. Another important ability is the efficiency of positioning, as how to provide the most accurate MS location in the shortest time is a critical and practical issue. Consequently, in order to provide the MS location estimation efficiently, the speed of convergence is a significant indicator. The algorithm with faster convergence can reduce the consumption time and computational complexity for positioning. As a result, the proposed algorithm not only reduces the time for positioning but also saves redundant hardware resources. Figure 9 demonstrates the proposed ABS-based algorithm has a quick convergence in various error models. In each error model, the proposed algorithm has the fast converging ability to obtain the best solution by the swarm intelligence of bees. The average convergence cycles/generations and the time taken for the procedure are recorded in Table 3. The results show that not only are the iteration cycles/generations of the ABC algorithm less than GA but also the ABC algorithm needs less \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Radius of scatter (m\(\backslash\)m) & 100 & 200 & 300 & 400 & 500 \\ \hline GA-based algorithm & 64.32 & 121.71 & 174.5 & 232.71 & 292.93 \\ \hline ABC-based algorithm & 62.84 & 117.37 & 173.91 & 231.56 & 290.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average location errors versus the radius of scatters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Upper bound (m\(\backslash\)m) & 200 & 300 & 400 & 500 & 600 & 700 \\ \hline GA-based algorithm & 65.59 & 94.97 & 123.58 & 154.82 & 186.58 & 218.2 \\ \hline ABC-based algorithm & 65.16 & 93.37 & 122.74 & 153.49 & 185.14 & 218 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average location errors versus the upper bound of the NLOS errors. Figure 8: Average location error versus the upper bound of non-line-of-sight (NLOS) errors. time to implement the optimization problem when the number of loops is fixed. Compared to GA, the ABC algorithm has a relatively simple and fast-converging iterative procedure. It can be observed from our simulation results that the proposed ABC-based location algorithm can improve the location accuracy and speed up the positioning execution time by its excellent optimization ability.