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Recent years have witnessed a growing interest in tracking algorithms thataugment Kalman Filters (KFs) with Deep Neural Networks (DNNs). By transformingKFs into trainable deep learning models, one can learn from data to reliablytrack a latent state in complex and partially known dynamics. However, unlikeclassic KFs, conventional DNN-based systems do not naturally provide anuncertainty measure, such as error covariance, alongside their estimates, whichis crucial in various applications that rely on KF-type tracking. This workbridges this gap by studying error covariance extraction in DNN-aided KFs. Webegin by characterizing how uncertainty can be extracted from existingDNN-aided algorithms and distinguishing between approaches by their ability toassociate internal features with meaningful KF quantities, such as the KalmanGain (KG) and prior covariance. We then identify that uncertainty extractionfrom existing architectures necessitates additional domain knowledge notrequired for state estimation. Based on this insight, we propose BayesianKalmanNet, a novel DNN-aided KF that integrates Bayesian deep learningtechniques with the recently proposed KalmanNet and transforms the KF into astochastic machine learning architecture. This architecture employs samplingtechniques to predict error covariance reliably without requiring additionaldomain knowledge, while retaining KalmanNet's ability to accurately track inpartially known dynamics. Our numerical study demonstrates that BayesianKalmanNet provides accurate and reliable tracking in various scenariosrepresenting partially known dynamic systems.

Bayesian KalmanNet: Quantifying Uncertainty in Deep Learning Augmented Kalman Filter