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

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.