Robust Particle Filter for Magnetic Field-based Train Localization

Kurzfassung

Increasing urbanization and climate change require transportation systems that have a small carbon footprint and a large transport capacity. Both requirements can be addressed with a highly automated railway system that uses trains powered by renewable energy sources. For the automation of a railway system with a large capacity, one crucial requirement is a reliable localization system that is able to localize all trains in the track network. As the braking distances of trains are beyond the measurement range of most sensors, the train positions in a large area have to be determined and distributed over a communication channel in real time to enable safe operation. Based on this real time information, it is then possible to automate train control and reduce the headways from the absolute to the relative braking distance. Headway reduction increases the capacity of existing track networks without building new tracks. This is particularly important in urban areas, where space is scarce and expensive. The challenge in the development of an appropriate localization system is to provide reliable position information in the whole track network independent of the environment. While in most parts of the track network global navigation satellite system (GNSS) signals are available and provide satisfying navigation solutions, there are also parts where shadowing and multipath renders GNSS signals unavailable, e.g., in tunnels and urban canyons. In our research, we therefore propose the use of magnetic field-based localization to complement GNSS in difficult environments. Magnetic field localization is based on the fact that ferromagnetic material in the vicinity of a railway track introduces distortions in the Earth magnetic field. These distortions are persistent over time and therefore can be used for localization when stored in a map. In our prior work, we proposed multiple approaches for magnetic localization of trains and showed their feasibility based on measurements collected with different types of trains [1,2]. Furthermore, we already addressed practical issues such as magnetometer calibration [3] enabling the use of the same magnetic map for different trains and magnetometers. Until now, research was mainly concerned with the development of position estimation methods when the magnetometer measurements are affected only by sensor noise or small noise-like errors. Unfortunately, in practice this assumption is often violated and the measurements contain large correlated errors. This type of error is caused by different events like other trains in the vicinity of the magnetometer, changes in the magnetic landscape due construction or the use of magnetic brakes. First attempts to handle such errors can be found in [2], where multiple noise models and a particle filter were used to reduce the effect of measurement errors on the position estimation. In this paper, we now propose an alternative approach. Instead of using different noise models, an error detection method is developed that is tightly integrated into the particle filter estimating the position. The proposed error detection is based on a likelihood ratio test (LRT) that decides between the hypothesis that i) the magnetometer measurements are obtained from the known magnetic field map with some additive noise and the hypothesis that ii) the data is not obtained from the map and hence is contaminated with large correlated errors. To calculate the test statistic, the likelihoods of the competing hypotheses are obtained by marginalizing the joint probability density of the measurements and corresponding positions with respect to the predicted particle cloud. Loosely speaking, in the LRT we check if the magnetic map at the predicted particle positions fit to the magnetometer measurements or not. In the latter case an error is detected. If an error is detected, the corresponding measurements are not used for updating the particle weights. When errors are present for a longer duration, the particle filter performs only predictions and the particles keep expanding. This can lead to a degraded accuracy or even divergence of the filter. To mitigate this issue, the use of aiding sensors like an odometer is considered. In practice, it can be also observed that errors do not affect all sensor axes of the magnetometer. Therefore, an LRT is performed for each magnetometer axis separately allowing for partial weight updates. For the performance of the LRT, a proper choice of the involved likelihoods is crucial. While the likelihood for the hypothesis that the data is generated from the map is easily found, choosing the likelihood for the counterhypothesis is not trivial. The paper therefore explores different options. To show the feasibility of the error detection, an evaluation based on real train measurements will be carried out. In the evaluation, the performance of the error detection for different likelihoods is compared and the benefit of the error detection is investigated. [1] Siebler, Benjamin, Heirich, Oliver, Sand, Stephan, "Bounding INS Positioning Errors with Magnetic-Field-Signatures in Railway Environments," in Proceedings of the 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, September 2017, pp. 3224-3230. [2] Siebler, Benjamin, Heirich, Oliver, Sand, Stephan, Hanebeck, Uwe D., "Joint Train Localization and Track Identification based on Earth Magnetic Field Distortions," 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS), Portland, Oregon, April 2020, pp. 941-948. [3] Siebler, Benjamin, Lehner, Andreas, Sand, Stephan, Hanebeck, Uwe D., "Evaluation of Simultaneous Localization and Calibration of a Train Mounted Magnetometer," Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, Missouri, September 2021, pp. 2285-2293.