Relative Train Localization with Magnetic Field Measurements
Benjamin Siebler, Oliver Heirich, Stephan Sand, German Aerospace Center (DLR), Institute of Communications and Navigation, Germany
The capacity and flexibility in current railways system is limited by the large safety distances between consecutives trains. To lower the safety distances while guaranteeing a safe operation a higher degree of automation must be introduced into rail traffic. A new technique that can enable higher flexibility and increase the capacity of current track networks is virtual coupling. Virtual coupling uses a distance control loop to automatically keep a predefined distance between trains. This lowers the safety distances to a few meters and replaces the mechanical coupler between different trains. The replacement of the mechanical coupler with a control loop allows trains to drive in a platoon that can be split and merged while driving. For virtual coupling, the estimation of the relative position or respectively the distance between trains is crucial. This estimate must be available in all environments including tunnels, underground and urban areas. In these scenarios global satellite navigation system (GNSS) signals are completely blocked or at least strongly distorted. In this paper, we therefore propose a new method for relative train localization that uses solely magnetic field and train speed measurements. The method is based on the observation that ferromagnetic infrastructure elements in the railway environment introduce strong distortions into the earth magnetic field. Typically these infrastructure elements like rails, sleepers and poles, have fixed positions which results in position dependent magnetic distortions. Therefore the distortions can be seen as a magnetic signature characteristic for a specific part of the track network. In our prior work we showed that a georeferenced map of these signatures can be used to obtain a long-term stable estimate of the absolute train position by using only a magnetometer and an inertial measurement unit (IMU).
In this paper the focus is on estimating the distance between trains. More precisely, the so called on-track distance is estimated that accounts for the track geometry. The on-track distance is defined by the length of the track between two consecutive trains and therefore can be used directly as an input to the control loop of virtually coupled trains. In contrast to estimating the absolute position, the proposed relative localization approach does not require a prior recorded map of the magnetic field signatures. Instead a dynamic map is created online, containing only the magnetic field recorded on a few hundred meters of track. The map has a predefined length and when new magnetometer measurements are available old measurements are deleted. In the map each measurement is stored together with the distance the train has driven since the measurement was recorded. The newest magnetic field measurement has always distance zero and the oldest has a distance that is close to the map length. The map creation and update therefore requires the information how far the train has driven within the sampling time. This information is obtained by numerically integrating the speed of an odometer. The output of this integration will naturally contain errors and therefore also the distances stored in the map will have errors. But by limiting the length of the map also the error in the estimated driven distance is limited. After the map is updated, the update is shared among trains in the vicinity via direct train to train communications. For virtual coupling it is sufficient to share the map of the leading train. To enable relative localization each following train creates a magnetic field signature based on its own magnetic field measurements. This signature is created in the same way as the map but is shorter. When the trains are driving on the same track, which can be assumed in a virtual coupling context, they also measure the same magnetic field. Therefore, to
estimate the on-track distance only the position of the signature within the map of the leading train must be found. This can be achieved by calculating the cross correlation of the map and the signature. The most likely position of the signature is where the correlation function has its maximum value. To suppress outliers and to filter the on-track distance estimate from the correlator, the correlator estimate is used as a measurement in a Kalman filter. The Kalman filter includes a model for the dynamics of the on-track distance and considers the relative speed of the trains. In the update step of the filter, it is important that the value of the measurement noise variance of the on-track distance estimate is set to an appropriate value. To determine this value the Cramer-Rao lower bound (CRLB) for the on-track distance estimate of the correlator was derived. With the CRLB it is then possible to calculate the corresponding noise variance based on the collected measurements.
In initial tests with measurement data a meter level accuracy for the on-track distance could be achieved. For the full paper, the initial tests will be extended to a comprehensive evaluation based on measurements recorded on a regional train in Germany. The paper will further contain a detailed description of the proposed methods and a detailed derivation of the CRLB that is used in the update step of the Kalman filter.