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 C1 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.