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.
翻译:在跟踪动态系统时,提供不确定性的衡量标准以及国家估计往往至关重要。 典型的国家估计数据,如卡尔曼过滤器(KF),根据对基本统计数据的了解,提供了时间上依赖的不确定性度量,然而,深层次的学习跟踪系统却在努力可靠地确定不确定性的性质。 在本文中,我们调查了最近提出的基于混合模型的深度状态跟踪算法KalmanNet估算不确定性的能力。 通过利用卡尔曼网络的可解释性质,我们证明错误共变矩阵可以根据其内部特征进行计算,作为一种不确定性计量。 我们证明,当系统动态为人所知时,KalmanNet从数据中学习其绘图,而没有获得与KF提供的类似的统计数据提供的不确定性;在进化模型匹配中,KalmanNet支持更准确的误差估计。