Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification

• URL: http://arxiv.org/abs/2506.11639v1
• Date: Fri, 13 Jun 2025 10:11:32 GMT
• Title: Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification
• Authors: Hassan Mortada, Cyril Falcon, Yanis Kahil, Mathéo Clavaud, Jean-Philippe Michel,
• Abstract summary: This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation.<n> Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these assumptions, prompting the rise of data-driven filtering techniques. This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation with consistent error covariance quantification. Our approach propagates error covariance using the recursive Joseph's formula and optimizes the Gaussian negative log-likelihood. Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator.

Related papers

• Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems [2.5245286741414663]
  This paper establishes long-time accuracy of ensemble Kalman filters.<n>Our theory covers a wide class of partially-observed chaotic dynamical systems.<n>We prove long-time accuracy of ensemble Kalman filters with surrogate dynamics.
  arXiv  Detail & Related papers  (2024-12-18T20:35:21Z)
• Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observability [59.758009422067]
  We propose a standalone Kalman filter layer that performs closed-form Gaussian inference in linear state-space models.<n>Similar to efficient linear recurrent layers, the Kalman filter layer processes sequential data using a parallel scan.<n> Experiments show that Kalman filter layers excel in problems where uncertainty reasoning is key for decision-making, outperforming other stateful models.
  arXiv  Detail & Related papers  (2024-09-25T11:22:29Z)
• Tensor network square root Kalman filter for online Gaussian process regression [5.482420806459269]
  We develop, for the first time, a tensor network square root Kalman filter, and apply it to high-dimensional online Gaussian process regression. In our experiments, we demonstrate that our method is equivalent to the conventional Kalman filter when choosing a full-rank tensor network. We also apply our method to a real-life system identification problem where we estimate $414$ parameters on a standard laptop.
  arXiv  Detail & Related papers  (2024-09-05T06:38:27Z)
• Outlier-robust Kalman Filtering through Generalised Bayes [45.51425214486509]
  We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models. Our method matches or outperforms other robust filtering methods at a much lower computational cost.
  arXiv  Detail & Related papers  (2024-05-09T09:40:56Z)
• Split-KalmanNet: A Robust Model-Based Deep Learning Approach for SLAM [101.32324781612172]
  Simultaneous localization and mapping (SLAM) is a method that constructs a map of an unknown environment and localizes the position of a moving agent on the map simultaneously. Extended Kalman filter (EKF) has been widely adopted as a low complexity solution for online SLAM. We present a robust EKF algorithm using the power of deep learning for online SLAM, referred to as Split-KalmanNet.
  arXiv  Detail & Related papers  (2022-10-18T07:10:38Z)
• Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models [84.18625250574853]
  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.
  arXiv  Detail & Related papers  (2021-10-10T08:52:18Z)
• 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)
• Neural Kalman Filtering [62.997667081978825]
  We show that a gradient-descent approximation to the Kalman filter requires only local computations with variance weighted prediction errors. We also show that it is possible under the same scheme to adaptively learn the dynamics model with a learning rule that corresponds directly to Hebbian plasticity.
  arXiv  Detail & Related papers  (2021-02-19T16:43:15Z)

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.