Accuracy of Magnetic Field-based Train Localization and the Impact of Unknown Calibration Parameters

Kurzfassung

Rail transport is very efficient in terms of greenhouse gas emissions, especially compared to road transport [1]. In the face of climate change it is therefore desirable to shift traffic from road to rail. To handle the additional traffic, the capacity of the existing railway network needs to be increased. Increasing the capacity by building new tracks is often not practical due high costs, long construction times or a lack of space, e.g., in dense urban areas. As an alternative, capacity can be increased by utilizing the existing track networks more efficiently by introducing a higher degree of automation. Automation allows to reduce the safety distance between consecutive trains from the absolute braking distance to the relative braking distance. Furthermore, automation enables new operational concepts such as virtual coupling that is expected to increase the network capacity considerably. In a virtually coupled train set the different trains can split up on-the-fly during motion since they are only coupled over a communication link and the distance between them is controlled automatically. For virtual coupling and automation in general, the locations of the trains in the network play a crucial role. Therefore, train localization is regarded as one of the core technologies in future railway systems and great efforts are made to establish GNSS in the railway environment. These efforts will be successful for most areas of the railway network but there will be always areas in which the performance of GNSS is not sufficient due to shadowing and multi path propagation. For a couple of years, we therefore advocate the use of distortions of the Earth magnetic field for train localization. The idea of magnetic field-based localization is derived from the observation that the Earth magnetic field along a railway track is strongly distorted by magnetic material in its vicinity. These distortions are characteristic for a certain position on the track and are persistent over time. Thus, the distortions can be seen as a magnetic fingerprint that can be used for train localization. Magnetic localization is a standalone technology, e.g., for tunnels, but can also serve as a redundant source of position information when GNSS is available. In our prior work we showed the general feasibility of magnetic train localization [2] and proposed a Bayesian Cramer-Rao lower bound (BCRLB) [3] to analyze the theoretically achievable position accuracy. In [3] we only considered the case of a perfectly calibrated magnetometer. This assumption is rarely fulfilled in practice, as standard calibration methods require a rotation of the magnetometer and the platform it is mounted on in a homogeneous magnetic field. For a train-mounted sensor, this is not feasibly without considerable effort. Hence, we developed a simultaneous localization and calibration (SLAC) algorithm [4]. The key idea of SLAC is that when a train passes through a distorted magnetic field, the changes in the magnetic field not only allow localization, but also excite all magnetometer axes such that the calibration parameters become observable. In this paper, we now combine the BCRLB from [3] with the idea of SLAC to obtain a more realistic bound for the accuracy of magnetic train localization. The newly derived bound allows to analyze the impact of the unknown calibration parameters on the position accuracy and shows how well the parameters can be estimated. The full paper will contain a detailed derivation of the bound and an evaluation based on real train measurements. In addition, the SLAC algorithm will be compared to the bound to see if it is close to the optimal result or if it should be improved. [1] European Environment Agency, "Rail and waterborne – Best for low-carbon motorised transport," Publications Office, 2021, https://data.europa.eu/doi/10.2800/85117 [2] B. Siebler, O. Heirich, S. Sand and U. D. Hanebeck, "Joint Train Localization and Track Identification based on Earth Magnetic Field Distortions," 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS) [3] B. Siebler, S. Sand and U. D. Hanebeck, "Bayesian Cramer-Rao Lower Bounds for Magnetic Fieldbased Train Localization," 2023 IEEE/ION Position, Location and Navigation Symposium (PLANS) [4] B. Siebler, A. Lehner, S. Sand and U. D. Hanebeck, "Simultaneous localization and calibration (SLAC) methods for a train-mounted magnetometer,” NAVIGATION, 70(1), 2023