SE(3)-LIO: Smooth IMU Propagation With Jointly Distributed Poses on SE(3) Manifold for Accurate and Robust LiDAR-Inertial Odometry

Gunhee Shin; Seungjae Lee; Jei Kong; Youngwoo Seo; Hyun Myung

cs.ROMar 17, 2026

SE(3)-LIO: Smooth IMU Propagation With Jointly Distributed Poses on SE(3) Manifold for Accurate and Robust LiDAR-Inertial Odometry

Authors: Gunhee Shin, Seungjae Lee, Jei Kong, Youngwoo Seo, Hyun Myung

Organizations: School of Electrical Engineering, KAIST (Korea Advanced Institute of Science and Technology), Daejeon, 34141, South Korea · Hanwha Aerospace, 6, Pangyo-ro 319 beon-gil, Bundang-gu, Seongnam-si, Gyeonggi-do, South Korea.

Abstract

In estimating odometry accurately, an inertial measurement unit (IMU) is widely used owing to its high-rate measurements, which can be utilized to obtain motion information through IMU propagation. In this paper, we address the limitations of existing IMU propagation methods in terms of motion prediction and motion compensation. In motion prediction, the existing methods typically represent a 6-DoF pose by separating rotation and translation and propagate them on their respective manifold, so that the rotational variation is not effectively incorporated into translation propagation. During motion compensation, the relative transformation between predicted poses is used to compensate motion-induced distortion in other measurements, while inherent errors in the predicted poses introduce uncertainty in the relative transformation. To tackle these challenges, we represent and propagate the pose on SE(3) manifold, where propagated translation properly accounts for rotational variation. Furthermore, we precisely characterize the relative transformation uncertainty by considering the correlation between predicted poses, and incorporate this uncertainty into the measurement noise during motion compensation. To this end, we propose a LiDAR-inertial odometry (LIO), referred to as SE(3)-LIO, that integrates the proposed IMU propagation and uncertainty-aware motion compensation (UAMC). We validate the effectiveness of SE(3)-LIO on diverse datasets. Our source code and additional material are available at: https://se3-lio.github.io/.

Figures & tables

Figure 1: Overview of the proposed IMU propagation and LiDAR–inertial odometry (LIO), referred to as $\mathrm{SE}(3)$ -LIO. The IMU propagation is performed on $\mathrm{SE}(3)$ manifold to yield a smooth trajectory and accurate prior. The joint distribution of predicted poses is derived to characterize the relative transformation uncertainty by considering their correlation, which is incorporated into the measurement noise during motion compensation to construct a probabilistic undistorted point cloud. Finally, $\mathrm{SE}(3)$ -LIO optimizes both the prior and the measurement distribution, improving the performance of odometry estimation.

Figure 2: Illustration of the difference between the conventional [ 6 ] and the proposed IMU propagation method, which are denoted as

\mathrm{SO}(3)\times\mathbb{R}^{3}

and

\mathrm{SE}(3)

, respectively. The twist,

\boldsymbol{\zeta}(t)\doteq[\mathbf{v}(t)\;\boldsymbol{\omega}(t)]

, is defined as a variable to simulate aggressive motion [ 4 ] and generate the ground-truth trajectory with a sufficiently small time step,

\Delta t_{gt}=10^{-4}

(black dashed line). Both methods are performed with 10 IMU inputs, each computed from adjacent twist values, and an interval of

\Delta t=10^{-2}

. The outputs of the proposed method (green dots) yield a smoother trajectory and follow the ground truth (black dashed line) more closely compared with the outputs of the conventional method (red crosses). The highlighted box shows that the proposed method properly addresses rotational changes while propagating translation, whereas the conventional method does not.

Figure 3: Uncertainty characterization of predicted poses from IMU propagation and relative transformations for motion compensation. (a) IMU propagation is performed using 100 IMU inputs computed same as Fig. 2 , with a process noise covariance $\mathbf{Q}$ . Initial pose is set to origin with covariance $\mathbf{\Sigma}_{0}$ . (b) Relative transformation uncertainty is computed with respect to the last predicted pose $\mathbf{T}_{k}$ , either by neglecting cross terms and assuming independence [ 9 ] (red ellipses) or by considering the correlation between poses as the proposed method (purple ellipses). The uncertainties are illustrated as 95% confidence regions and validated using Monte Carlo simulation with 100 samples (black dots). The proposed method provides a more accurate characterization, while the independence assumption leads to overestimation. Results are shown every 20 IMU inputs for clarity.

Panel of Figure 4 — Figure 4: Resultant noise of the undistorted point cloud after applying uncertainty-aware motion compensation (UAMC). (a) Points are acquired clockwise over time. (b) The noise of raw measurements increases with distance from the center. (c) The point cloud is undistorted through UAMC. As highlighted, points acquired at the beginning exhibit larger noise than those acquired later because earlier points are transformed using relative transformations with higher uncertainty.

Figure 5: Pipeline of $\mathrm{SE}(3)$ -LIO that integrates the proposed IMU propagation and uncertainty-aware motion compensation (UAMC). Assume the pose at $t_{k-1}$ has been estimated, and a new LiDAR point cloud is acquired at $t_{k}$ . (a) IMU propagation is performed on $\mathrm{SE}(3)$ manifold using IMU measurements acquired over $[t_{k-1},t_{k}]$ , providing a prior distribution for the state update. (b) Relative transformations, along with their uncertainties, are computed from the reference pose at $t_{k}$ to poses at each point acquisition time. (c) These relative transformations are used to compensate for motion distortion in the raw point cloud, while their uncertainties are incorporated into the noise of each point, resulting in a probabilistic undistorted point cloud. (d) The undistorted point cloud is transformed into the world frame and used to construct residuals with the local map, for which we adopt VoxelMap [ 28 ] to obtain a measurement distribution. (e) Finally, the prior and measurement distributions are optimized through the update step, yielding an updated pose estimate at $t_{k}$ .

Figure 6: Description of our dataset, including CW (blue), CCW (gray), and mid (orange) sequences. (a) A ground vehicle equipped with a 128-channel LiDAR (Ouster OS2-128), an IMU (Xsens MTi-300), and a RTK-GNSS receiver (Emlid Reach RS). (b)–(c) Data were collected in large-scale rough terrain, including dense forest and wide open areas.

Dataset	NTU-VIRAL [ 18 ]						Newer-College [ 22 ]				Our dataset
Sequence	eee	nya	rtp	sbs	tnp	spms	quad-D	quad-M	quad-H	math-H	CW	CCW	mid
FAST-LIO2 [ 25 ]	0.250	0.256	0.276	0.27	0.244	3.12	0.356	0.064	0.084	0.084	14.07	17.08	2.50
PV-LIO	0.579	0.404	1.71	0.753	0.74	-	0.135	0.093	0.107	0.082	13.47	21.62	2.00
DLIO [ 3 ]	0.254	0.269	0.231	0.286	0.258	0.423	0.150	0.076	2.66	0.116	12.34	43.04	3.77
LIO-EKF [ 24 ]	0.772	0.479	1.04	0.308	0.365	2.45	2.48	0.314	2.95	1.21	-	40.35	-
MA-LIO [ 9 ]	0.252	0.256	2.32	0.268	0.248	0.464	0.156	0.060	0.307	0.102	76.82	27.77	3.09

Table 1: The root mean square error (RMSE) of absolute trajectory error (ATE) (m) on the NTU, Newer-College, and our datasets. Bold value denotes the best performance, underline value denotes the second-best performance and ‘-’ denotes that the odometry has diverged.

Figure 7: Qualitative comparison in spms sequence of the NTU-VIRAL [ 18 ] dataset (upper) and CW sequence of our dataset (lower). Baselines including (A) Fast-LIO2 [ 25 ] , (B) DLIO [ 3 ] , and (C) MA-LIO [ 9 ] are compared with (D) $\mathrm{SE}(3)$ -LIO (ours). Point clouds are colored by time, where brown and gray indicate the beginning and the end of the sequence, respectively. Highlighted boxes indicate the top-down view of the corresponding areas, showing the drift in estimated trajectory. Resultant point clouds are captured by identical viewpoints for fair comparison.

Sequences	eee	nya	rtp	sbs	tnp	spms
$\mathrm{SO}(3)\times\mathbb{R}^{3}$ (baseline)	0.548	0.469	2.64	0.750	0.693	0.638
$\mathrm{SE}(3)$ w/o UAMC	0.324	0.259	0.268	0.258	0.216	0.241
$\mathrm{SE}(3)$ w/ UAMC	0.321	0.246	0.269	0.253	0.204	0.238

Table 2: Ablation study on NTU-VIRAL [ 18 ] dataset. RMSE of ATE (m) is reported. Bold denotes the best performance.

Sequences	eee	nya	sbs	rtp	tnp	spms	avg
FAST-LIO2 [ 25 ]	16.02	14.15	18.44	14.24	14.80	17.74	15.90
PV-LIO [ 22 ]	51.84	38.92	46.49	49.79	36.48	44.87	44.73
DLIO [ 3 ]	99.08	98.60	100.21	98.89	99.78	100.44	99.50
MA-LIO [ 9 ]	23.97	23.77	28.52	23.33	24.22	26.38	25.03
$\mathrm{SE}(3)$ -LIO (ours)	26.66	13.95	25.03	19.15	11.32	26.66	20.46

Table 3: Comparison of average computation time (ms) of baselines and ours in NTU-VIRAL [ 18 ] dataset. Bold denotes the lowest computation time, and underline denotes the second-lowest computation time.

Figure 8: Time usage for each module of the proposed LIO framework in NTU-VIRAL [ 18 ] dataset.

LiDAR Odometry

LiDAR odometry (light detection and ranging) estimates a robot’s motion by aligning successive laser scans, often with inertial data.

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Jul 15, 2026J/K move · Enter open · S save

WNOJ-LIO: A White-Noise-on-Jerk Motion-Prior EKF for High-Dynamic LiDAR-IMU Fusion

Junning Lyu, Qizhi Guo, Xia Ning, Tao Song+1

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

Inertial Odometry LiDAR Odometry Robot State Estimation Multimodal Sensor Fusion Extended Kalman Filtering

Open paper AskPDF arXiv

LiDAR-inertial odometry (LIO) is a key component of autonomous navigation, but high-dynamic driving exposes two coupled challenges: intra-scan motion distortion and vibration-contaminated inertial measurements. Most real-time LiDAR-inertial pipelines propagate the system state by integrating raw IMU measurements and then use the propagated trajectory for point cloud de-distortion, thereby propagating inertial noise into both the corrected scan and the subsequent scan-to-map registration. This paper presents WNOJ-LIO, a LiDAR-IMU fusion framework based on a White-Noise-on-Jerk (WNOJ) Extended Kalman Filter (EKF). WNOJ-LIO employs a decoupled WNOJ prior on

\R^3 \times \SO(3)

for state prediction and treats the IMU as a high-frequency measurement source rather than the driver of state propagation. The resulting posterior state history is then used for LiDAR scan de-distortion and subsequent point-to-plane LiDAR updates. The decoupled process model enables closed-form covariance propagation, thereby bridging the gap between batch WNOJ Gaussian process (GP) trajectory priors and recursive filtering. Simulation results demonstrate improvements in acceleration and angular-velocity denoising, scan de-distortion, and localization accuracy over a FAST-LIO-style baseline. Real-world experiments were conducted using an autonomous racing car on four driving segments with maximum speeds ranging from 53 to 208~km/h, covering a wide range of vehicle vibration levels. The experiments further validate the proposed method and provide a comprehensive evaluation of its performance in estimating acceleration, angular velocity, body-frame linear velocity, attitude, and position under highly dynamic driving. The source code of WNOJ-LIO is publicly available at https://github.com/LvJohny/wnoj-ekf-lio.git.

Abstract

LiDAR Odometry

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