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

2026-04-06

AI Summary

This work addresses the challenge of robust real-time 6-DoF pose estimation in scenarios lacking reliable odometry or IMU priors by proposing a CPU-based direct point-cloud-to-map registration framework. The method introduces a block-sparse Gaussian mixture model to construct a C¹-continuous 3D Gaussian Euclidean Distance Field (G-EDF), which eliminates block-boundary artifacts through adaptive spatial partitioning and rigorously enforces Eikonal consistency to enable analytical gradient computation. By integrating continuous distance field modeling with direct scan-to-map optimization, the system achieves high-precision reconstruction and localization in large-scale environments, significantly outperforming existing approaches even under severely degraded odometry or in the complete absence of IMU measurements.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• 6DoF localization
• robust localization
• scan-to-map registration
• Euclidean Distance Field
• odometry degradation

Innovation

• Gaussian Mixture Model
• Euclidean Distance Field
• C1 Continuity
• Gradient-Based Localization
• Scan-to-Map Registration