  This paper describes a novel method for the estimation of the trajectory
curve and orientation of a rigid body moving along a railway track. Compared to
other recent developments in the literature, the presented approach has the
significant advantage of tracking the position and orientation of a railway
vehicle using inertial sensors only, excluding global position sensors (GNSS or
total station) and also excluding global orientation sensors (magnetometers or
inclinometers). The algorithm is based on a kinematic model of the relative
motion of the body with respect to the track. This kinematic model is used as
the system equations of a Kalman filter algorithm that includes in the state
vector the coordinates used to define the position and orientation of the body.
Two different Kalman filter approaches are described. In the first one, the
position and orientation are calculated independently. In the second one, both
position and orientation are calculated as a coupled problem. Crucial to the
success of the results of the Kalman filters is the use of the correct
covariance matrices associated with the system process and the measurements.
The calculated trajectory and orientation are applied in this research to the
problem of track geometry measurement. A scale track with known design geometry
and irregularities is used to conduct experiments for tuning and evaluating the
quality of the output of the algorithm. Results show that the developed
algorithm is accurate enough for this application. They also show that, using
either of the two proposed Kalman filtering approaches, the constrained maximum
likelihood method for the estimation of the covariance matrices performs
similarly to the known-output method. This is very convenient because it allows
a straightforward application of the observation model in different scenarios.
