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

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

cs.ROApr 6, 2026

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

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

Organizations: The authors are with the Service Robotics Laboratory, Universidad Pablo de Olavide, Seville, Spain.

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.

Figures & tables

Panel of Figure 1 — Fig. 1 : 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.

Panel of Figure 2 — Fig. 2 : 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.

Dataset	Distance Error (m)			Gradient $\\|\nabla\hat{d}\\|$
Dataset	MAE $\downarrow$	Med. $\downarrow$	Std $\downarrow$	Mean	Std $\downarrow$
New College	0.033	0.018	0.044	0.984	0.089
Snail	0.035	0.018	0.049	0.979	0.108

TABLE I : Quantitative results on reconstruction fidelity. Distance errors are in meters (

\downarrow

lower is better). Gradient magnitude (

\|\nabla\hat{d}\|

) indicates Eikonal consistency (

\approx 1.0

is ideal).

Panel of Figure 4 — Fig. 3 : 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).

Traj.	Method	Inertial $\downarrow$			No IMU $\downarrow$			Low $\downarrow$			High $\downarrow$
Traj.	Method	Pos	Rot	Time	Pos	Rot	Time	Pos	Rot	Time	Pos	Rot	Time
bc	Ours	0.084	1.133	76.9	0.215	1.204	95.2	0.084	1.133	107.3	0.118	1.207	118.5
	Fast-GICP	0.082	1.129	67.7	2.884	38.900	1366.9	0.122	1.179	78.7	0.261	1.452	134.6
	NDT	0.084	1.138	94.7	0.308	3.349	81.5	0.087	1.134	98.9	0.169	1.241	134.7
sl	Ours	0.157	1.049	61.8	0.217	0.985	63.3	0.158	1.048	70.6	0.192	1.089	83.9
	Fast-GICP	0.153	1.043	63.5	-	-	-	0.169	1.045	75.2	0.320	1.306	148.9

TABLE II : Robustness Study: Evaluation of G-EDF-Loc against Fast-GICP and NDT across trajectories (0.5 m resolution). Systems are tested under normal operation (Inertial), missing IMU, and degraded priors (Low/High Gaussian noise). Best and second-best results are bold and underlined [Pos: m, Rot: °, Time: ms].

Map-Based Localization

Map-Based Localization estimates a device or robot’s position and orientation by matching sensor observations to stored maps.

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May 6, 2026J/K move · Enter open · S save

ULF-Loc: Unbiased Landmark Feature for Robust Visual Localization with 3D Gaussian Splatting

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Wuhan University · University of Zaragoza · The First Surveying and Mapping Institute of Hunan Province+1

3D Gaussian Splatting Visual Place Recognition Map-Based Localization Robot Localization

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Visual localization is a core technology for augmented reality and autonomous navigation. Recent methods combine the efficient rendering of 3D Gaussian Splatting (3DGS) with feature-based localization. These methods rely on direct matching between 2D query features and the 3D Gaussian feature field, but this often results in mismatches due to an inherent bias in the learned Gaussian feature. We theoretically analyze the feature learning process in 3DGS, revealing that the widely adopted

α

-blending optimization inherently introduces bias into 3D point features. This bias stems from the entanglement between individual Gaussians and their neighboring Gaussians, making the learned features unsuitable for precise matching tasks. Motivated by these findings, we propose ULF-Loc, an unbiased landmark feature framework that replaces biased feature optimization with geometry-weighted feature fusion. We further introduce keypoint-consensus landmark sampling to select reliable Gaussians and local geometric consistency verification to reject mismatches caused by rendering artifacts. On the Cambridge Landmarks dataset, ULF-Loc reduces the mean median translation error by 17% compared to the state-of-the-art, while achieving superior efficiency with only 1/10 the training time and 1/6 the GPU memory of STDLoc.

Abstract

Map-Based Localization

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