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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 258694, 11 pages
http://dx.doi.org/10.1155/2013/258694
Research Article

Practical Constraint K-Segment Principal Curve Algorithms for Generating Railway GPS Digital Map

1State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, No. 3 Shang Yuan Cun, Hai Dian District, Beijing 10044, China
2Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira Taipa, Macau

Received 23 June 2013; Accepted 30 October 2013

Academic Editor: Yingwei Zhang

Copyright © 2013 Dewang Chen and Long Chen. 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

In order to obtain a decent trade-off between the low-cost, low-accuracy Global Positioning System (GPS) receivers and the requirements of high-precision digital maps for modern railways, using the concept of constraint K-segment principal curves (CKPCS) and the expert knowledge on railways, we propose three practical CKPCS generation algorithms with reduced computational complexity, and thereafter more suitable for engineering applications. The three algorithms are named ALLopt, MPMopt, and DCopt, in which ALLopt exploits global optimization and MPMopt and DCopt apply local optimization with different initial solutions. We compare the three practical algorithms according to their performance on average projection error, stability, and the fitness for simple and complex simulated trajectories with noise data. It is found that ALLopt only works well for simple curves and small data sets. The other two algorithms can work better for complex curves and large data sets. Moreover, MPMopt runs faster than DCopt, but DCopt can work better for some curves with cross points. The three algorithms are also applied in generating GPS digital maps for two railway GPS data sets measured in Qinghai-Tibet Railway (QTR). Similar results like the ones in synthetic data are obtained. Because the trajectory of a railway is relatively simple and straight, we conclude that MPMopt works best according to the comprehensive considerations on the speed of computation and the quality of generated CKPCS. MPMopt can be used to obtain some key points to represent a large amount of GPS data. Hence, it can greatly reduce the data storage requirements and increase the positioning speed for real-time digital map applications.