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

The idea of magnetic field-based train localization is derived from the observation that magnetic material in the vicinity of railway tracks introduces position-specific and time-invariant distortions in the Earth magnetic field. A map of the magnetic field thus can be used to estimate the position of a train by comparing the map to the measurements of a train-mounted magnetometer. In this paper, we derive and evaluate the Bayesian Cramer-Rao lower Bound (BCRLB) for magnetic field-based train localization ´ with simultaneous magnetometer calibration. The BCRLB gives a lower limit for the achievable position accuracy and allows to systematically analyze the impact of unknown but jointly estimated calibration parameters. Furthermore, the bound can be used to show the observability of all calibration parameters.