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Neural Aided Adaptive Innovation-Based Invariant Kalman Filter

Barak Diker, Itzik Klein

Abstract

Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are applied. To cope with real-world scenarios, adaptive noise estimation methods have been developed primarily for classical Euclidean formulations. However, these methods remain largely unexplored in the tangent Lie space, despite it provides a principled geometric framework with favorable error dynamics on Lie groups. To fill this gap, we combine invariant filtering theory with neural-aided adaptive noise estimation in real-world settings. To this end, we derive a novel theoretical extension of classical innovation-based process noise adaptation formulated directly within the Lie-group framework. We further propose a lightweight neural network that estimates the process noise covariance parameters directly from raw inertial data. Trained entirely in a sim2real framework via domain adaptation, the network captures motion-dependent and sensor-dependent noise characteristics without requiring labeled real-world data. To examine our proposed neural-aided adaptive invariant Kalman filter, we focus on the challenging real-world scenario of autonomous underwater navigation. Experimental results demonstrate superior performance compared to existing methods in terms of position root mean square error. These results validate our sim2real pipeline and further confirm that geometric invariance significantly enhances learning-based adaptation and that adaptive noise estimation in the tangent Lie space offers a powerful mechanism for improving navigation accuracy in nonlinear autonomous platforms.

Neural Aided Adaptive Innovation-Based Invariant Kalman Filter

Abstract

Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are applied. To cope with real-world scenarios, adaptive noise estimation methods have been developed primarily for classical Euclidean formulations. However, these methods remain largely unexplored in the tangent Lie space, despite it provides a principled geometric framework with favorable error dynamics on Lie groups. To fill this gap, we combine invariant filtering theory with neural-aided adaptive noise estimation in real-world settings. To this end, we derive a novel theoretical extension of classical innovation-based process noise adaptation formulated directly within the Lie-group framework. We further propose a lightweight neural network that estimates the process noise covariance parameters directly from raw inertial data. Trained entirely in a sim2real framework via domain adaptation, the network captures motion-dependent and sensor-dependent noise characteristics without requiring labeled real-world data. To examine our proposed neural-aided adaptive invariant Kalman filter, we focus on the challenging real-world scenario of autonomous underwater navigation. Experimental results demonstrate superior performance compared to existing methods in terms of position root mean square error. These results validate our sim2real pipeline and further confirm that geometric invariance significantly enhances learning-based adaptation and that adaptive noise estimation in the tangent Lie space offers a powerful mechanism for improving navigation accuracy in nonlinear autonomous platforms.

Paper Structure

This paper contains 23 sections, 68 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Inertial Navigation
  4. Invariant Kalman Filter Formulation
  5. Measurement Model for IKF
  6. Right-Invariant Kalman Filter
  7. Propagation (Prediction)
  8. Update (Correction)
  9. Proposed approach
  10. Adaptive Hybrid Invariant Kalman Filter
  11. Neural Network Architecture
  12. Justification of the adaptive approach in the invariant setting
  13. Sim-to-Real Training Perspective
  14. Training
  15. Analysis and Results
  16. ...and 8 more sections

Figures (2)

  • Figure 1: Block diagram of the proposed neural-aided adaptive innovation-based IKF for inertial/DVL fusion.
  • Figure 2: Modeling the innovation as a Gaussian distribution in the Lie algebra results in a warped, banana-shaped distribution on the Lie group manifold. On the left, the Lie group representation displays the prior estimated state ($\hat{x}_t$, green) and the posterior estimated state ($x_t$, purple). On the right, the corresponding Lie algebra representation illustrates the same prior and posterior states, where the 68% and 95% uncertainty contours form standard concentric circles.