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

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.