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

arXiv: https://arxiv.org/abs/2604.04525 · HTML: https://mlsanity.com/paper/2604.04525/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Builds on (most cited first, 12 of 12)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [FAST-LIO2: Fast Direct LiDAR-inertial Odometry](https://mlsanity.com/paper/2107.06829/) (2021)
- [Voxblox: Incremental 3D Euclidean Signed Distance Fields for On-Board MAV Planning](https://mlsanity.com/paper/1611.03631/) (2016)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [SHINE-Mapping: Large-Scale 3D Mapping Using Sparse Hierarchical Implicit Neural Representations](https://mlsanity.com/paper/2210.02299/) (2022)
- [FIESTA: Fast Incremental Euclidean Distance Fields for Online Motion Planning of Aerial Robots](https://mlsanity.com/paper/1903.02144/) (2019)
- [Multi-Camera LiDAR Inertial Extension to the Newer College Dataset](https://mlsanity.com/paper/2112.08854/) (2021)
- [VDB-GPDF: Online Gaussian Process Distance Field with VDB Structure](https://mlsanity.com/paper/2407.09649/) (2024)
- [SNAIL Radar: A large-scale diverse benchmark for evaluating 4D-radar-based SLAM](https://mlsanity.com/paper/2407.11705/) (2024)
- [DLL: Direct LIDAR Localization. A map-based localization approach for aerial robots](https://mlsanity.com/paper/2103.06112/) (2021)
- [DB-TSDF: Directional Bitmask-based Truncated Signed Distance Fields for Efficient Volumetric Mapping](https://mlsanity.com/paper/2509.20081/) (2025)

## Abstract (arXiv)

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.