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Journal of Applied Mathematics
Volume 2013, Article ID 953048, 10 pages
http://dx.doi.org/10.1155/2013/953048
Research Article

Calculation of Weighted Geometric Dilution of Precision

1Department of Information Management, Tainan University of Technology, Tainan, Taiwan
2Department of Digital Entertainment and Game Design, Taiwan Shoufu University, Tainan, Taiwan
3Department of Electronic Engineering, National Quemoy University, Kinmen, Taiwan
4Department of Communication Engineering, Chung-Hua University, Hsinchu, Taiwan

Received 20 April 2013; Revised 28 August 2013; Accepted 3 September 2013

Academic Editor: Anyi Chen

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.

Abstract

To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP), instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS) devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN) and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error.