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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 369694, 11 pages
Research Article

Neural Network for WGDOP Approximation and Mobile Location

1Department of Information Management, Tainan University of Technology, Tainan 71002, Taiwan
2Department of Communication Engineering, Chung-Hua University, Hsinchu 30012, Taiwan
3Department of Electronic Engineering, National Quemoy University, Quemoy 89250, Taiwan

Received 12 April 2013; Revised 17 June 2013; Accepted 17 June 2013

Academic Editor: Ker-Wei Yu

Copyright © 2013 Chien-Sheng Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers location methods that are applicable in global positioning systems (GPS), wireless sensor networks (WSN), and cellular communication systems. The approach is to employ the resilient backpropagation (Rprop), an artificial neural network learning algorithm, to compute weighted geometric dilution of precision (WGDOP), which represents the geometric effect on the relationship between measurement error and positioning error. The original four kinds of input-output mapping based on BPNN for GDOP calculation are extended to WGDOP based on Rprop. In addition, we propose two novel Rprop–based architectures to approximate WGDOP. To further reduce the complexity of our approach, the first is to select the serving BS and then combines it with three other measurements to estimate MS location. As such, the number of subsets is reduced greatly without compromising the location estimation accuracy. We further employed another Rprop that takes the higher precision MS locations of the first several minimum WGDOPs as the inputs into consideration to determine the final MS location estimation. This method can not only eliminate the poor geometry effects but also significantly improve the location accuracy.