Prediction of Global Navigation Satellite System Positioning Errors with Guarantees

Intelligent Transportation Systems employ different localization technologies, such as the Global Navigation Satellite System. This system transmits signals between satellite and receiver devices on the ground which can estimate their position on earth's surface. The accuracy of this positioning estimate, or the positioning error estimation, is of utmost importance for the efficient and safe operation of autonomous vehicles, which require not only the position estimate, but also an estimation of their operation margin. This paper proposes a workflow for positioning error estimation using a random forest regressor along with a post-hoc conformal prediction framework. The latter is calibrated on the random forest out-of-bag samples to transform the obtained positioning error estimates into predicted integrity intervals, which are confidence intervals on the positioning error prediction with at least 99.999% confidence. The performance is measured as the number of ground truth positioning errors inside the predicted integrity intervals. An extensive experimental evaluation is performed on real-world and synthetic data in terms of root mean square error between predicted and ground truth positioning errors. Our solution results in an improvement of 73% compared to earlier research, while providing prediction statistical guarantees.