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

• URL: http://arxiv.org/abs/2110.04738v1
• Date: Sun, 10 Oct 2021 08:52:18 GMT
• Title: Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models
• Authors: Itzik Klein, Guy Revach, Nir Shlezinger, Jonas E. Mehr, Ruud J. G. van Sloun, and Yonina. C. Eldar
• Abstract summary: We investigate the ability of KalmanNet, a proposed hybrid model-based deep state tracking algorithm, to estimate an uncertainty measure. 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 Kalman filter.
• Score: 84.18625250574853
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Measuring and Modeling Uncertainty Degree for Monocular Depth Estimation [50.920911532133154]
  The intrinsic ill-posedness and ordinal-sensitive nature of monocular depth estimation (MDE) models pose major challenges to the estimation of uncertainty degree. We propose to model the uncertainty of MDE models from the perspective of the inherent probability distributions. By simply introducing additional training regularization terms, our model, with surprisingly simple formations and without requiring extra modules or multiple inferences, can provide uncertainty estimations with state-of-the-art reliability.
  arXiv  Detail & Related papers  (2023-07-19T12:11:15Z)
• Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification [0.0]
  This paper presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime.
  arXiv  Detail & Related papers  (2023-04-13T08:57:33Z)
• The Implicit Delta Method [61.36121543728134]
  In this paper, we propose an alternative, the implicit delta method, which works by infinitesimally regularizing the training loss of uncertainty. We show that the change in the evaluation due to regularization is consistent for the variance of the evaluation estimator, even when the infinitesimal change is approximated by a finite difference.
  arXiv  Detail & Related papers  (2022-11-11T19:34:17Z)
• On Uncertainty in Deep State Space Models for Model-Based Reinforcement Learning [21.63642325390798]
  We show that RSSMs use a suboptimal inference scheme and that models trained using this inference overestimate the aleatoric uncertainty of the ground truth system. We propose an alternative approach building on well-understood components for modeling aleatoric and epistemic uncertainty, dubbed Variational Recurrent Kalman Network (VRKN) Our experiments show that using the VRKN instead of the RSSM improves performance in tasks where appropriately capturing aleatoric uncertainty is crucial.
  arXiv  Detail & Related papers  (2022-10-17T16:59:48Z)
• Diffusion Tensor Estimation with Uncertainty Calibration [6.5085381751712506]
  We propose a deep learning method to estimate the diffusion tensor and compute the estimation uncertainty. Data-dependent uncertainty is computed directly by the network and learned via loss attenuation. We show that the estimation uncertainties computed by the new method can highlight the model's biases, detect domain shift, and reflect the strength of noise in the measurements.
  arXiv  Detail & Related papers  (2021-11-21T15:58:01Z)
• Unsupervised Learned Kalman Filtering [84.18625250574853]
  unsupervised adaptation is achieved by exploiting the hybrid model-based/data-driven architecture of KalmanNet. We numerically demonstrate that when the noise statistics are unknown, unsupervised KalmanNet achieves a similar performance to KalmanNet with supervised learning.
  arXiv  Detail & Related papers  (2021-10-18T04:04:09Z)
• KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics [84.18625250574853]
  We present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics. We numerically demonstrate that KalmanNet overcomes nonlinearities and model mismatch, outperforming classic filtering methods.
  arXiv  Detail & Related papers  (2021-07-21T12:26:46Z)
• Approaching Neural Network Uncertainty Realism [53.308409014122816]
  Quantifying or at least upper-bounding uncertainties is vital for safety-critical systems such as autonomous vehicles. We evaluate uncertainty realism -- a strict quality criterion -- with a Mahalanobis distance-based statistical test. We adopt it to the automotive domain and show that it significantly improves uncertainty realism compared to a plain encoder-decoder model.
  arXiv  Detail & Related papers  (2021-01-08T11:56:12Z)
• Deep Learning based Uncertainty Decomposition for Real-time Control [9.067368638784355]
  We propose a novel method for detecting the absence of training data using deep learning. We show its advantages over existing approaches on synthetic and real-world datasets. We further demonstrate the practicality of this uncertainty estimate in deploying online data-efficient control on a simulated quadcopter.
  arXiv  Detail & Related papers  (2020-10-06T10:46:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.