Research On Constraint Principal Curves Algorithms For Fusion Of Railway GPS Tracks

ABSTRACT:High-Precision digital map with limited storage is the prerequisite of train positioning. When generating the railway tracks of digital map, using differential GPS can get precise GPS data but cost a lot. So, we can use low-accuracy GPS receiver to collect GPS data and can get a high-precision track from these low-accuracy data by a fusion algorithm, which can reduce the cost of generating digital map and improve the accuracy of the railway tracks in digital map. Research on the fusion algorithm for railway GPS tracks has a important significance. Most of the existing algorithms have not take the fixed points in the railway lines into consideration, and their computing speed, accuracy, fitness and other performances are need to be further improved.The Principal curves theory was put forward by Professor Hastie from Stanford University in1980s. In recent years, it has developed greatly, and has been successfully applied to image recognition, skeleton of the handwriting, data reduction, controlling trajectory and so on. Based on these, and combined with the fixed constraint points in the railway lines, this paper will apply the principal curves algorithms to fuse the GPS tracks. The main research work is as follows:Firstly, through the further study on the principal curves theory, and combined with the fixed constraint points in the railway lines, we propose the constraint K-segment principal curves, and three adaptive constraint K-segment principal curves algorithms based on local optimization, which is called CPCL algorithms, including constraint K-segment principal curves algorithm based on simple averaging (CPCLa); constraint K-segment principal curves algorithm based on line search (CPCLs) and improved constraint K-segment principal curves algorithm based on line search (CPCLi). By MATLAB, we develop software for fusing the GPS tracks using the proposed three algorithms.Then, we use three data sets of different shapes to simulate the algorithms, including sinusoidal, zigzag and spiral data sets. By comparing with the soft K-segment principal curves (KPCv) algorithm and the Max Point Method (MPM), we analyze the three proposed algorithms’performance indexes:fitness, error, computing speed, occupied storage space and so on. The results show that, CPCLa, CPCLs and CPCLi have stronger fitness, higher precision, faster computing speed, whose principal curves occupy less storage space and are more smooth.Finally, we use a measured GPS data set of highway and two measured GPS data sets of railway to verify and analyze the practical application of the three proposed algorithms. The results show that all of the three proposed algorithms can generate high-precision GPS trajectory from multiple low-accuracy GPS data. All of them have good practicability, and have good performance in computing speed, precision, storage space, smoothness and fitness. Among them, CPCLi can generate the highest accurate principal curve and has the best overall performance; CPCLa has the fastest computing speed; the principal curve generated by CPCLs has the minimum vertices.