  Various algorithms combine deep neural networks (DNNs) and Kalman filters
(KFs) to learn from data to track in complex dynamics. Unlike classic KFs,
DNN-based systems do not naturally provide the error covariance alongside their
estimate, which is of great importance in some applications, e.g., navigation.
To bridge this gap, in this work we study error covariance extraction in
DNN-aided KFs. We examine three main approaches that are distinguished by the
ability to associate internal features with meaningful KF quantities such as
the Kalman gain (KG) and prior covariance. We identify the differences between
these approaches in their requirements and their effect on the training of the
system. Our numerical study demonstrates that the above approaches allow
DNN-aided KFs to extract error covariance, with most accurate error prediction
provided by model-based/data-driven designs.
