# MS Location Estimation Based on the Artificial Bee Colony Algorithm
## 4 The Proposed ABC-Based Location Estimation  
Researchers have proposed various positioning methods to estimate the MS location more accurately, such as TSA, LLOP, and RSA. We also have provided the MS location estimation based on GA before [33]. The GA-based location method has a better performance than the RSA and other existing methods in our previous research. However, the general disadvantages of GA are the trapping in the local optimum and the lack of a mechanism to memorize the best individuals during the iterations [38]. Additionally, a poor local search ability, risk of a suboptimal solution, and delayed convergence are worrying problems also. To overcome the main disadvantages above, instead of GA, the ABC algorithm is implemented on function minimization in this paper. The employed selection operation is one important difference between the GA and ABC algorithm. The selection operation of GA depends on the fitness performance. In the ABC algorithm, new solutions are produced with equal chance. The iteration of the ABC algorithm is according to the self-adjusting operation and memory mechanism. Compared to GA, the ABC algorithm can get out of a local minimum and attain the global optimum with relative computational simplicity for multivariable function optimization [37]. Another advantage of ABC is its simplicity. Parameters of GA are hard to set prior, but ABC is easy to implement and there are few parameters to adjust. The ABC algorithm is expected to provide the estimated MS location more accurately and efficiently, and to converge faster. In this study, a novel positioning method based on the ABC algorithm for MS location estimation is developed and the results are compared with the other existing methods. In this section, the location model and objective function will be introduced first. Then, the proposed ABC-based location algorithm will be presented clearly. ABC is an optimum approach method that simulates the ability of bee colonies. ABC dynamically adjusts the value to fit a better solution based on the gathered environmental information. In this scheme, the ABC-based positioning algorithm is applied for optimal estimation. MS location estimation is accomplished by approaching a nonlinearoptimization under nonlinear constraints. The object of optimization will be designed according to the question waiting to be solved. In this paper, the ABC algorithm is proposed to decrease the NLOS error and promote the positioning accuracy for wireless location systems. The number of BSs is three due to the constraint on hearability. It is assumed that we have a transmitting MS, and TOA measurements are taken at each receiving BS. As shown in Figure 1, the coordinates for BS1, BS2, and BS3 are given by (0, 0), (\(X_{2}\), 0), and (\(X_{3}\), \(Y_{3}\)), respectively. (\(x\),\(y\)) is the MS coordinate waiting to be estimated. Then, the measured distance between the MS and the BS\({}_{i}\) is \(r_{i}\), \(i=1,2,3\). According to the geometric approach, each measured distance by a BS forms a circle, and the center of a circle is a BS. Multiple TOA measurements estimate MS location by the intersections of the circles. The following three equations indicate the circles for TOA measurement:  
\[\text{{Circle 1: }}x^{2}+y^{2}={r_{1}}^{2}, \tag{7}\]  
\[\text{{Circle 2: }}(x-X_{2})^{2}+y^{2}={r_{2}}^{2}, \tag{8}\]  
\[\text{{Circle 3: }}(x-X_{3})^{2}+(y\text{-}Y_{3})^{2}={r_{3}}^{2}. \tag{9}\]  
In an ideal case, the intersection of three circles would be a point. However, in a practical case, NLOS error is very common in our life. The accuracy of the estimated location degrades seriously because of the NLOS propagation environment. No matter what kind of ranging technique is used, the measured distance is greater than the true value. In the NLOS propagation environment, the measured distance is always increased due to the signal strength attenuation or propagation time delay. Therefore, the radius variation is always positive.