D-LIO: 6DoF Direct LiDAR-Inertial Odometry based on Simultaneous Truncated Distance Field Mapping

Newer College Dataset — Reconstruction overview

Newer College Dataset — Reconstruction overview

Overview

D-LIO is a 6DoF Direct LiDAR-Inertial Odometry approach that simultaneously maps L1 truncated distance fields (Fast-TDF) on CPU. This continuous representation lets it work directly with raw 3D LiDAR data online — without LiDAR feature selection or tracking — casting point-cloud registration as a nonlinear optimization while updating the map at constant time, independently of its size. Benchmarked against state-of-the-art odometry methods, D-LIO matches or exceeds their accuracy.

Method

EKF-based Pose Estimation & TDF Mapping

The D-LIO algorithm incrementally estimates the system pose using an Extended Kalman Filter (EKF). It integrates inertial measurements for pose prediction and uses point cloud-to-map registration for pose updates.

The environment is mapped based on the Truncated Distance Field (TDF). This alignment is used to constrain the EKF's pose and velocity. Whenever the estimated pose variation exceeds a threshold, the TDF map is updated by incorporating new information.

Fast-TDF

The core of D-LIO is the Fast Truncated Distance Field (Fast-TDF). This method represents the environment as a 3D grid, but instead of just storing "occupied" or "free", it efficiently encodes the L1 distance to the nearest obstacle.

To achieve constant-time map updates, it uses a pre-calculated binary kernel. The distance in this kernel is represented as a bit-set mask, where each set bit accounts for the distance.

This encoding has a key advantage: the shortest distance from multiple overlapping kernels can be found with a single, highly efficient bitwise-AND operation. This avoids complex comparisons and makes the process parallelizable on the CPU.

Table 1 — Correspondence between bit-set masks and L1 distance.
Binary Mask (4-bit)	L1 Distance
0000	0 (Center)
0001	1
0011	2
0111	3
1111	4 (Max / Truncation)

Fast-TDF bitwise-AND operation — Figure 1 — The final distance map (center) is computed by applying the bitwise-AND operation to overlapping kernels (top/bottom).

Results

We benchmarked D-LIO on three challenging public datasets: VIRAL, Newer College, and VBR. These tests evaluate performance in diverse scenarios, including aerial (UAV) and ground platforms, against several state-of-the-art (SOTA) methods.

Trajectory Accuracy (ATE)

The Absolute Translation Error (ATE) [m] was measured on the VIRAL and Newer College datasets. As shown in the table, D-LIO achieves consistently high accuracy, ranking first or second in most sequences. It remains highly competitive even when compared to methods that utilize back-end optimization (like LIO-SAM or PIN-SLAM), which D-LIO does not.

Table 2 — ATE (m) on VIRAL and Newer College. Best (**bold**) and second-best (underline) odometry methods.
Sequence	D-LIO	A-LOAM	M-LOAM	KISS-ICP	FAST-LIO2	LIO-SAM	PIN-SLAM
eee₀₁	0.074	0.212	0.249	2.383	0.166	0.075	-
eee₀₂	0.073	0.199	0.168	1.586	0.100	0.069	2.056
eee₀₃	0.121	0.148	0.233	1.055	0.142	0.101	0.615
nya₀₁	0.080	0.077	0.123	0.359	0.127	0.076	0.086
nya₀₂	0.104	0.091	0.191	-	0.151	0.070	0.092
nya₀₃	0.065	0.108	0.226	1.389	0.130	0.137	0.455
sbs₀₁	0.085	0.103	0.173	1.353	0.130	0.089	0.205
sbs₀₂	0.067	0.091	0.147	1.435	0.144	0.083	0.528
sbs₀₃	0.098	0.367	0.153	1.037	0.126	0.140	0.708
q-easy	0.093	0.085	0.141	0.100	0.100	0.074	0.090

Scalability on Large Datasets

To evaluate performance in large-scale environments, we used the VBR dataset, featuring long trajectories (up to 2.5 km) in complex indoor/outdoor settings. D-LIO demonstrates robust scalability, maintaining low ATE (m) and Relative Pose Error (RPE) (%).

Table 3 — ATE (m) and RPE (%) on the VBR dataset.
Sequence	D-LIO	KISS-ICP	PIN-SLAM
diag	0.560 (0.72%)	1.397 (1.79%)	0.362 (0.47%)
pincio	7.390 (3.45%)	0.784 (0.49%)	0.647 (0.45%)

Mapping Quality

We also evaluated the 3D reconstruction quality on the Newer College (Quad-Easy) sequence using standard metrics: Accuracy, Completeness, Chamfer-L1 (C-L1), and F-Score. D-LIO produces highly competitive maps, achieving the best completeness and ranking second for C-L1 and F-Score among all tested odometry-driven methods.

Table 4 — Mapping metrics on Newer College. Best (**bold**) and second-best (underline) scores.
Method	Pose	Acc. (cm)	Comp. (cm)	C-L1 (cm)	F-Score (%)
VDB-Fusion	KissICP	14.03	25.46	19.75	69.50
SHINE	KissICP	14.87	20.02	17.45	68.85
NKSR	KissICP	15.67	36.87	26.67	58.57
PUMA	Odometry	15.30	71.91	43.60	57.27
SLAMesh	Odometry	19.21	48.83	34.02	45.24
NeRF-LOAM	Odometry	12.89	22.21	17.55	74.37
S²KAN-SLAM	Odometry	13.32	18.80	16.06	72.03
ImMesh	Odometry	15.05	19.80	17.42	66.87
PIN-SLAM	Odometry	11.55	15.25	13.40	82.08
KN-LIO	Odometry	8.18	11.65	9.92	91.01
D-LIO	Odometry	12.14	10.63	11.39	83.83

Runtime Analysis

The system's performance was analyzed on an Intel Core i7-13700H CPU without GPU acceleration. The map update step is the most computationally expensive, as its time strongly depends on point cloud density. However, optimization runs at the sensor rate (10 Hz) while updates are triggered less frequently, balancing the load.

Table 5 — Runtime analysis (mean ± std. dev) with no downsampling.
Dataset	Points (avg.)	Total (s)	Optimize (s)	Update (s)
eee	~20k	0.048 ± 0.055	0.046 ± 0.013	0.155 ± 0.009
nya	~20k	0.049 ± 0.034	0.042 ± 0.014	0.146 ± 0.016
sbs	~20k	0.051 ± 0.048	0.044 ± 0.016	0.142 ± 0.034
q-easy	~100k	0.479 ± 0.196	0.442 ± 0.158	0.470 ± 0.095
diag	~190k	0.603 ± 0.240	0.565 ± 0.194	0.315 ± 0.085
pincio	~140k	0.576 ± 0.256	0.505 ± 0.182	0.563 ± 0.146

Project Video

Qualitative results, 3D reconstructions, and estimated trajectories from the datasets.

Citation

If you use D-LIO in your research, please cite our paper:

BibTeX

@ARTICLE{11248856,
  author={Coto-Elena, L. and Maese, J.E. and Merino, L. and Caballero, F.},
  journal={IEEE Robotics and Automation Letters},
  title={D-LIO: 6DoF Direct LiDAR-Inertial Odometry Based on Simultaneous Truncated Distance Field Mapping},
  year={2026},
  volume={11},
  number={1},
  pages={169-176},
  keywords={Odometry;Laser radar;Point cloud compression;Accuracy;Feature extraction;Location awareness;Kernel;Simultaneous localization and mapping;Real-time systems;Three-dimensional displays;Mapping;odometry;simultaneous localization and mapping},
  doi={10.1109/LRA.2025.3632615}}