  State estimation of dynamical systems in real-time is a fundamental task in
signal processing. For systems that are well-represented by a fully known
linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a
low complexity optimal solution. However, both linearity of the underlying SS
model and accurate knowledge of it are often not encountered in practice. Here,
we present KalmanNet, a real-time state estimator that learns from data to
carry out Kalman filtering under non-linear dynamics with partial information.
By incorporating the structural SS model with a dedicated recurrent neural
network module in the flow of the KF, we retain data efficiency and
interpretability of the classic algorithm while implicitly learning complex
dynamics from data. We demonstrate numerically that KalmanNet overcomes
non-linearities and model mismatch, outperforming classic filtering methods
operating with both mismatched and accurate domain knowledge.
