Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models
This addresses the challenge of reliable uncertainty characterization in data-driven tracking systems, which is incremental as it builds on the existing KalmanNet framework.
The paper tackled the problem of uncertainty estimation in deep learning-based state tracking by proposing a method to compute error covariance from KalmanNet's internal features, showing it matches Kalman filter uncertainty when dynamics are known and provides more accurate error estimation under model mismatch.
Providing a metric of uncertainty alongside a state estimate is often crucial when tracking a dynamical system. Classic state estimators, such as the Kalman filter (KF), provide a time-dependent uncertainty measure from knowledge of the underlying statistics, however, deep learning based tracking systems struggle to reliably characterize uncertainty. In this paper, we investigate the ability of KalmanNet, a recently proposed hybrid model-based deep state tracking algorithm, to estimate an uncertainty measure. By exploiting the interpretable nature of KalmanNet, we show that the error covariance matrix can be computed based on its internal features, as an uncertainty measure. We demonstrate that when the system dynamics are known, KalmanNet-which learns its mapping from data without access to the statistics-provides uncertainty similar to that provided by the KF; and while in the presence of evolution model-mismatch, KalmanNet pro-vides a more accurate error estimation.