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

2025-06-13

AI Summary

State estimation for stochastic dynamic systems under non-Gaussian noise remains challenging due to the breakdown of Gaussian assumptions underlying classical filters. Method: This paper proposes a Kalman Filter-guided Recurrent Neural Network (KF-RNN), the first to embed the Joseph form of the covariance update within an RNN architecture and jointly optimize a Gaussian negative log-likelihood objective, ensuring mathematical consistency in uncertainty propagation and statistical reliability. Contribution/Results: The method preserves recursive, real-time inference while delivering high-accuracy state estimates and rigorously calibrated error covariance quantification. Experiments under non-Gaussian white noise demonstrate a 32% reduction in state estimation error and a 47% decrease in covariance calibration error compared to baselines—outperforming both conventional Kalman filters and state-of-the-art deep estimators.

Technology Category

Intelligent Robots: State EstimationMachine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Stochastic Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Improving state estimation in noisy stochastic dynamical systems
• Enhancing Kalman filter performance under non-Gaussian conditions
• Ensuring consistent uncertainty quantification in data-driven filtering

Innovation

• Deep learning-augmented Kalman filtering
• Recursive Joseph's formula for covariance
• Optimizes Gaussian negative log-likelihood