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This paper describes a novel method for the estimation of the trajectorycurve and orientation of a rigid body moving along a railway track. Compared toother recent developments in the literature, the presented approach has thesignificant advantage of tracking the position and orientation of a railwayvehicle using inertial sensors only, excluding global position sensors (GNSS ortotal station) and also excluding global orientation sensors (magnetometers orinclinometers). The algorithm is based on a kinematic model of the relativemotion of the body with respect to the track. This kinematic model is used asthe system equations of a Kalman filter algorithm that includes in the statevector the coordinates used to define the position and orientation of the body.Two different Kalman filter approaches are described. In the first one, theposition and orientation are calculated independently. In the second one, bothposition and orientation are calculated as a coupled problem. Crucial to thesuccess of the results of the Kalman filters is the use of the correctcovariance matrices associated with the system process and the measurements.The calculated trajectory and orientation are applied in this research to theproblem of track geometry measurement. A scale track with known design geometryand irregularities is used to conduct experiments for tuning and evaluating thequality of the output of the algorithm. Results show that the developedalgorithm is accurate enough for this application. They also show that, usingeither of the two proposed Kalman filtering approaches, the constrained maximumlikelihood method for the estimation of the covariance matrices performssimilarly to the known-output method. This is very convenient because it allowsa straightforward application of the observation model in different scenarios.

Estimation of the trajectory and attitude of railway vehicles using inertial sensors with application to track geometry measurement