Unsupervised Learned Kalman Filtering

TL;DR

This paper introduces an unsupervised learning approach for KalmanNet, enabling it to adapt to unknown noise statistics and changing models without ground-truth data, maintaining high tracking performance.

Contribution

It presents an unsupervised training method for KalmanNet, allowing adaptation to unknown noise and model variations without requiring labeled data.

Findings

Unsupervised KalmanNet matches supervised performance when noise statistics are unknown.

The method enables model adaptation without additional data.

KalmanNet can track states effectively in changing environments.

Abstract

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.