Estimation of the train travelled distance, velocity and acceleration by using GPS signals

Two models of railway centerline are considered. The first, "ideal", model is composed of straight line segments, cubic parabola transition curves and arcs of circles, defined by parametric equations. The second "nonideal", model represents a piecewise linear approximation of the "ideal" model. The goal of this paper is to estimate the travelled distance, velocity and acceleration by using a low-cost GPS receiver and to study the impact of the centerline uncertainty and the railroad curvature on these estimations. The Least Square (LS) algorithm based on a block of GPS measurements and a realistic dynamical train model is designed to estimate the travelled distance, the velocity and the acceleration of the train. The mean error and the second order moment are theoretically calculated for these estimations and compared with the results of Monte-Carlo simulations.