Inclusion of data uncertainty in machine learning and its application in geodetic data science, with case studies for the prediction of Earth orientation parameters and GNSS station coordinate time series

Abstract

Data uncertainty plays an important role in the field of geodesy. Even though deep learning is becoming increasingly important for geodetic applications due to its high accuracy, it typically does not consider the data uncertainty. As we demonstrate in this study, we propose to include the uncertainty of data in deep neural network architectures to achieve a better generalization. This is advantageous for big data applications as well as for small datasets. Inspired by weighted and total least squares, we formulate the problem for both input and target uncertainties, and combine it with the Bayesian learning method. This results in a new form of the loss function in machine learning. As an alternative approach, we consider data uncertainties by including them as additional features. For comparison purposes, we use models without the consideration of data uncertainty as a benchmark. To show the efficacy of the proposed method, we apply it to the prediction of Earth Orientation Parameters (EOPs, namely polar motion, dUT1, and LOD) and Global Navigation Satellite System (GNSS) station coordinate time series. We demonstrate that the least-squares-inspired method outperforms both the benchmark and the feature-inspired method for both the studies. In the EOPs study, the improvement can be more than 50% in the study interval. In the study of GNSS station coordinate time series, which is presented for 1000 stations across the globe, the improvement on an average basis is around 12%. The results demonstrate the advantage of using uncertainty information in the machine learning algorithms, when applied to geodetic time series.