Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models

TL;DR

This paper explores how KalmanNet, a hybrid deep learning and model-based state estimator, can reliably estimate uncertainty in dynamical systems, matching classic Kalman filter performance when dynamics are known and outperforming it under model mismatch.

Contribution

It demonstrates that KalmanNet can compute an interpretable uncertainty measure from its internal features, bridging the gap between deep learning and traditional uncertainty quantification.

Findings

KalmanNet estimates uncertainty comparable to Kalman filter when dynamics are known.

KalmanNet provides more accurate uncertainty estimates under model mismatch.

The internal features of KalmanNet can be used to compute the error covariance matrix.

Abstract

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.