Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
It is the error margin in the positioning of the receiver due to the spatial distribution of the satellites.
- 2.
References
Belhajem, I., Maissa, Y.B., Tamtaoui, A.: Improving vehicle localization in a smart city with low cost sensor networks and support vector machines. Mob. Netw. Appl. 23(4), 854–863 (2017). https://doi.org/10.1007/s11036-017-0879-9
Wang, L., Li, Z., Zao, J., Zhou, K., Wang, Z., Yuan, H.: Smart device-supported BDS/GNSS real-time kinematic positioning for sub-meter-level accuracy in urban location-based services. Sensors J. 16, 1–15 (2016)
Wörner, M., Schuster, F., Dölitzscher, F., Keller, C.G., Haueis, M., Dietmayer, K.: Integrity for autonomous driving: a survey. In: IEEE/ION Position, Location and Navigation Symposium (PLANS), pp. 666–671 (2016)
Blomenhofer, H., Ehret, W., Su, H., Blomenhofer, E.: Sensitivity analysis of the GALILEO integrity performance dependent on ground sensor station network. In: ION GNSS 18th International Technical Meeting of Satellite Division, pp. 1361–1373 (2005)
Karlsson, E., Mohammadiha, N.: A statistical GPS error model for autonomous driving. In: Proceedings of the IEEE Intelligent Vehicles Symposium, pp. 754–759 (2018)
Parakkal, P.G., Variyar., S.V.V.: GPS based navigation system for autonomous car. In: 2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI), pp. 1888–1893 (2017)
El Abbous, A., Samanta., N.: A modeling of GPS error distributions. In: European Navigation Conference (ENC), pp. 119–127 (2017)
Lee, G., Rodriguez, C., Madabhushi, A.: An empirical comparison of dimensionality reduction methods for classifying gene and protein expression datasets. In: Măndoiu, I., Zelikovsky, A. (eds.) ISBRA 2007. LNCS, vol. 4463, pp. 170–181. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72031-7_16
Joardar, S., Siddique., T.A., Alam, S., Hossam-E-Haider, M.: Analyses of different types of errors for better precision in GNSS. In: 3rd International Conference on Electrical Engineering and Information and Communication Technology, pp. 1–6 (2016)
Molnar, C.: Interpretable Machine Learning. https://christophm.github.io/interpretable-ml-book/limo.html. Accessed 2 Mar 2020
Radi, A., Nassar., S., Khedr, M., El-Sheimy, N., Molinari, R., Guerrier, S.: Improved stochastic modelling of low-cost GNSS receivers positioning errors. In: IEEE/ION Position, Location and Navigation Symposium (PLANS), pp. 108–117 (2018)
Tang, D., Lu, D., Baigen, C., Wang, J.: GNSS localization propagation error estimation considering environmental conditions. In: 16th International Conference on Intelligent Transportation Systems Telecommunications (ITST), pp. 1–7 (2018)
Zimmermann, F., Schmitz, B., Klingbeil, L., Kuhlmann, H.: GPS multipath analysis using Fresnel zones. Sensors J. 19, 25 (2018)
Bauer, S., Obst, M., Wanielik, G.: 3D environment modeling for GPS multipath detection in urban areas. In: International Multiconference on Systems, Signals and Devices (SSD), pp. 1–5 (2012)
Kuratomi, A.: GNSS position error estimated by machine learning techniques with environmental information input. M.Sc. Mechatronics, KTH, Sweden (2019)
Yang, S., Tabatowski-Bush, B., Xiang, W.: Build up a real-time LSTM positioning error prediction model for GPS sensors. In: 90th IEEE Vehicular Technology Conference (VTC), pp. 1–5 (2019)
Fan, C., Zhang, Y., Pan, Y., Li, X., Zhang, C., Yuan, R., et. al.: Multi-horizon time series forecasting with temporal attention learning. In: 25th SIGKDD Conference on Knowledge Discovery and Data Mining (ADST), pp. 2527–2535 (2019)
Amrhein, V., Korner-Nievergelt, F., Roth, T.: The earth is flat (p \(>\) 0.05): significance thresholds and the crisis of unreplicable research. PeerJ. 5, e3544 (2015)
Suzuki, T., Kitamura, M., Yoshiharu, A., Hashizume, T.: High accuracy GPS and GLONASS positioning by multipath mitigation using omnidirectional infrared camera. In: IEEE International Conference on Robotics and Automation, pp. 311–316 (2011)
Pereira, S., et al.: Enhancing interpretability of automatically extracted machine learning features: application to a RBM-random forest system on brain lesion segmentation. Med. Image Anal. 44, 228–244 (2018)
Boström, H., Linusson, H., Löfström, T., Johansson, U.: Accelerating difficulty estimation for conformal regression forests. Ann. Math. Artif. Intell. 81(1), 125–144 (2017). https://doi.org/10.1007/s10472-017-9539-9
Bostrom, H., Asker, L., Gurung, R., Karlsson, I., Lindgren, T., Papapetrou, P.: Conformal prediction using random survival forests. In: 16th IEEE International Conference on Machine Learning and Applications (ICMLA), Cancun, pp. 812–817 (2017). https://doi.org/10.1109/ICMLA.2017.00-57
Gong, H., Chen, C., Bialostozky, E., Lawson, C.: A GPS/GIS method for travel mode detection in New York City. Comput. Environ. Urban Syst. 36, 131–139 (2012)
Acknowledgements
We thank the company Waysure Sweden AB for supporting this research project, providing the real-world dataset, and their GNSS experts input for the feature selection process.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Kuratomi, A., Lindgren, T., Papapetrou, P. (2021). Prediction of Global Navigation Satellite System Positioning Errors with Guarantees. In: Dong, Y., Mladenić, D., Saunders, C. (eds) Machine Learning and Knowledge Discovery in Databases: Applied Data Science Track. ECML PKDD 2020. Lecture Notes in Computer Science(), vol 12460. Springer, Cham. https://doi.org/10.1007/978-3-030-67667-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-030-67667-4_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-67666-7
Online ISBN: 978-3-030-67667-4
eBook Packages: Computer ScienceComputer Science (R0)