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

TL;DR

Recursive KalmanNet combines deep learning with Kalman filtering principles to improve state estimation accuracy and uncertainty quantification in non-ideal, noisy environments, outperforming traditional and existing data-driven methods.

Contribution

It introduces a novel recurrent neural network that integrates Kalman filtering concepts with recursive covariance propagation for enhanced state estimation.

Findings

Outperforms traditional Kalman filter in non-Gaussian noise scenarios

Provides consistent error covariance estimates

Achieves superior accuracy compared to existing deep learning estimators

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.