Relative train localization with magnetic field measurements

In this paper a new method for relative train localization in global navigation satellite system (GNSS) denied areas is proposed. The proposed localization system is long-term stable and based solely on magnetometer and odometer measurements. The system utilizes that the magnetic field shows strong and time persistent variations along a railway track. Two trains driving on the same track will observe the same magnetic field variations but with a certain shift. This shift depends on the relative position of the trains and their speed. By measuring the train speed with an odometer it becomes possible to estimate the relative position by comparing the magnetometer and odometer measurements of two trains. In this paper we use cross-correlation to obtain the relative position estimate from a batch of measurements. A subsequent Kalman filter is used to smooth the estimate and to incorporate prior knowledge of the train dynamics. We further derive the Cramer-Rao lower bound (CRLB) for the relative position estimate to investigate the theoretically achievable localization accuracy and to approximate the variance of the relative position estimate in the update step of the Kalman filter. In an evaluation the feasibility and accuracy of the approach is shown based on measurement data collected with a train driving in a rural area. The results indicate that with the proposed method the relative position can be estimated with sub-meter accuracy.