Lan, T.; Chen, J.; Geffert, A.; Becker, U.:
Deep-Learning-Based Position Error Estimation with Uncertainty Quantification for Satellite-Based Localization.
Navigation 2021, November 2021.


A major challenge of satellite-based localization on the ground is the signal degradation due to multipath, reflection and diffraction resulting from surrounding objects such as buildings and trees. The signal degradation leads to position errors. However, the estimation of such position errors is difficult since the models are complex and common assumptions are not valid anymore. The rapid increase in computation power has enabled the use of techniques like deep learning. The benefit of deep learning is that it does not require explicit modelling of the systems. Instead, it can be trained to approximate the models using a great amount of data. It is therefore potentially meaningful to apply deep learning on position error estimation of satellite-based localization. A drawback of deep learning is that its estimation quality is insufficient whenever it encounters unseen or rare-case data. However, estimation quality is not observable for online applications. Therefore, it would be helpful to acquire the uncertainty of estimations to decide upon their integrity or trustworthiness so that hazardously misleading estimations can be detected and excluded to avoid potential hazards.
In this contributed work, deep-learning-based position error estimation models dedicated for urban environments are developed. Moreover, the estimation uncertainty is quantified using ensemble learning. Within the scope of ensemble learning, a given number of position error estimators with different neural networks and parameters are developed. The estimations made by those models are further compared to determine the underlying uncertainty and to derive a prediction interval. The result is evaluated based on the coverage rate, i.e., what percentage of real position errors lies within the prediction interval determined by ensemble learning. With the proposed methodology, the feasibility of applying deep learning to position error estimation for satellite-based localization especially for safety-relevant applications will be analysed and discussed.