# MS Location Estimation Based on the Artificial Bee Colony Algorithm
## 5 Simulation Results  
To examine the performance of the proposed location algorithm in the NLOS environment, computer simulations should be implemented. The performance of the proposed location algorithm was compared with other algorithms, such as TSA, LLOP, RSA, and GA. In this paper, the three BSs coordinates were set to BS1: (0, 0), BS2: (1732 m, 0), and BS3: (866 m, 1500 m). For each test, the random real MS location was chosen with a uniform distribution in the range surrounded by the points BS\({}_{1}\), \(I\), \(J\), and \(K\) as shown in Figure 3. In total, 10,000 tests were performed independently and all numerical quantities are presented in meters. Before the ABC algorithm was implemented, some control parameters were defined. The control parameters were set to colony size = 100, and \(Limit=10\). Another control parameter is maxcycles, defined as the max cycles of iteration. The control parameter of maxcycles does not need to be discussed in this research. Rather than apply the fixed parameter, we utilized the convergence mechanism to decide the moment for stopping the iterations. Many test functions were used to observe the performance in [39]. The objective function we used in this paper is just like a Griewank function. The corresponding global optimum solution is the global minimum value, which is the bottom of the surface for this function, as shown in Figure 4. It can be observed that the food source in the ABC algorithm is strongly multimodal when the objective function value decreases with dimensionality. The bees search in the limited range until the optimal solution can be found. The optimal solution is the prediction of the MS location. Figure 3: Cell layout showing the relationship between the base stations (BSs) and the inter-BS distances. The NLOS error is the main reason that causes location accuracy with a bad performance. NLOS effects were taken into account for the analysis of simulations in this paper. Two typical error models were applied, one is the circular disk of scatters model (CDSM) [40] and another one is a uniformly distributed noise model [24]. CDSM is the first introduced error model, which simulates the NLOS propagation environment. It assumes that the path of signal transmission between MS and BSs is not a straight path. One scatter spreading around MS in the circular disk is considered to obstruct the signal transmission. The signal is changed to go through a single reflection on the points of scatter. Therefore, the measured distance is reformulated by calculating the sum of two distances, including the distance between BSs and the scatters, and the distances between MS to the scatters. The measured distance would be increased according to the triangle theorem shown as Figure 5. \(P\) presents the scatter point. The real travel path is between MS and BS, but the measured ranges are the sum of \(r_{b}\) and \(r_{s}\) after the signal is interfered with by the scatter point. The AOA measurement is also affected in the CDSM error model. \(\theta_{n}\) is the AOA measurement error. The scatter points in the circular disk are considered as the lower range error with a higher probability to appear. The maximum error value is when the scatter point is on the circumference. Thus, range error depends on the scatter radius; a bigger scatter radius with a larger measured error. Figure 6 shows the average location error of the proposed ABC-based location algorithm compared with other existing methods in the CDSM error model. All methods increased the average error, with the longer radius of scatter. However, the proposed ABC-based algorithm has a lower average location error than TSA, LLOP, and RSA. The curve of the method we proposed has a relatively smooth  
Figure 4: The surface plot of the objective function. Figure 5: Geometry of circular disk of scatters model (CDSM). curve. Compared with TSA, LLOP, and RSA, the simulation results show that the proposed algorithm has the best performance on the location accuracy and supports the estimation of MS location with the best accuracy.