State space

Quantum mechanics

Algorithm

Gaussian

Linear dynamical system

Linear system

Statistics

Extended Kalman filter

Computer science

Physics

State-space representation

Mathematics

Estimator

Mathematical analysis

Artificial intelligence

Kalman filter

Artificial neural network

Interpretability

State (computer science)

IEEE Transactions on Signal Processing

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.

KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics