Unsupervised Learned Kalman Filtering
This work addresses the challenge of state estimation in dynamic systems for applications like tracking, offering an incremental improvement by extending KalmanNet to unsupervised learning for better adaptability.
The paper tackles the problem of learning KalmanNet's mapping without ground-truth states by using an unsupervised approach that exploits its hybrid architecture to compute loss from internal features, achieving similar performance to supervised learning when noise statistics are unknown and enabling adaptation to changing state-space models without additional data.
In this paper we adapt KalmanNet, which is a recently pro-posed deep neural network (DNN)-aided system whose architecture follows the operation of the model-based Kalman filter (KF), to learn its mapping in an unsupervised manner, i.e., without requiring ground-truth states. The unsupervised adaptation is achieved by exploiting the hybrid model-based/data-driven architecture of KalmanNet, which internally predicts the next observation as the KF does. These internal features are then used to compute the loss rather than the state estimate at the output of the system. With the capability of unsupervised learning, one can use KalmanNet not only to track the hidden state, but also to adapt to variations in the state space (SS) model. We numerically demonstrate that when the noise statistics are unknown, unsupervised KalmanNet achieves a similar performance to KalmanNet with supervised learning. We also show that we can adapt a pre-trained KalmanNet to changing SS models without providing additional data thanks to the unsupervised capabilities.