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G-EDF-Loc: 3D Continuous Gaussian Distance Field for Robust Gradient-Based 6DoF Localization

José E. Maese, Lucía Coto-Elena, Luis Merino, Fernando Caballero

Abstract

This paper presents a robust 6-DoF localization framework based on a direct, CPU-based scan-to-map registration pipeline. The system leverages G-EDF, a novel continuous and memory-efficient 3D distance field representation. The approach models the Euclidean Distance Field (EDF) using a Block-Sparse Gaussian Mixture Model with adaptive spatial partitioning, ensuring $C^1$ continuity across block transitions and mitigating boundary artifacts. By leveraging the analytical gradients of this continuous map, which maintain Eikonal consistency, the proposed method achieves high-fidelity spatial reconstruction and real-time localization. Experimental results on large-scale datasets demonstrate that G-EDF-Loc performs competitively against state-of-the-art methods, exhibiting exceptional resilience even under severe odometry degradation or in the complete absence of IMU priors.

G-EDF-Loc: 3D Continuous Gaussian Distance Field for Robust Gradient-Based 6DoF Localization

Abstract

This paper presents a robust 6-DoF localization framework based on a direct, CPU-based scan-to-map registration pipeline. The system leverages G-EDF, a novel continuous and memory-efficient 3D distance field representation. The approach models the Euclidean Distance Field (EDF) using a Block-Sparse Gaussian Mixture Model with adaptive spatial partitioning, ensuring continuity across block transitions and mitigating boundary artifacts. By leveraging the analytical gradients of this continuous map, which maintain Eikonal consistency, the proposed method achieves high-fidelity spatial reconstruction and real-time localization. Experimental results on large-scale datasets demonstrate that G-EDF-Loc performs competitively against state-of-the-art methods, exhibiting exceptional resilience even under severe odometry degradation or in the complete absence of IMU priors.

Paper Structure

This paper contains 20 sections, 8 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Map Representations
  4. Point Cloud Registration and Localization
  5. Continuous Distance Field Representation
  6. Mathematical Formulation
  7. Optimization and Training
  8. Block-Sparse Architecture
  9. Local Ground Truth Generation
  10. Adaptive Complexity
  11. Reconstruction and Continuity
  12. Map Serialization and Implementation
  13. Direct Gradient-Based Localization
  14. Prior Guess - Error State Kalman Filter
  15. Point Cloud Registration and Optimization
  16. ...and 5 more sections

Figures (3)

  • Figure A1: Overview of the Snail dataset environment reconstruction. Top: detailed perspectives of the large-scale outdoor structures and local elevation changes. Bottom: a top-down view showing the full $900 \times 610 \times 120$ m extent of the environment.
  • Figure C1: Cross-section analysis on a local subset of the New College dataset ($z=3.0$ m). Parameters: $1.0$ m$^3$ blocks with $\delta=0.25$ m overlap. Left column (a, c): Discontinuities in the distance field and gradient without blending. Right column (b, d): The proposed G-EDF representation, ensuring global $C^1$ continuity.
  • Figure E1: Qualitative 2D trajectory comparison featuring the full bc sequence (top row) and a zoomed-in detail of the park sequence (bottom row). Trajectories are depicted as follows: ground truth (black), the proposed G-EDF-Loc (red), Fast-GICP (blue), and NDT (green).