ALIVE-LIO: Degeneracy-Aware Learning of Inertial Velocity for Enhancing ESKF-Based LiDAR-Inertial Odometry

Seongjun Kim; Daehan Lee; Junwoo Hong; Sanghyun Park; Hyunyoung Jo; Soohee Han

cs.ROApr 3, 2026

ALIVE-LIO: Degeneracy-Aware Learning of Inertial Velocity for Enhancing ESKF-Based LiDAR-Inertial Odometry

Authors: Seongjun Kim, Daehan Lee, Junwoo Hong, Sanghyun Park, Hyunyoung Jo, Soohee Han

Organizations: S. Kim is with the Department of Electrical Engineering, POSTECH, Pohang 37673, Republic of Korea · D. Lee, J. Hong, S. Park, and H. Jo are with the Department of Convergence IT Engineering, POSTECH, Pohang 37673, Republic of Korea · S. Han is with the Department of Electrical Engineering and Convergence IT Engineering, POSTECH, Pohang 37673, Republic of Korea

Abstract

Odometry estimation using light detection and ranging (LiDAR) and an inertial measurement unit (IMU), known as LiDAR-inertial odometry (LIO), often suffers from performance degradation in degenerate environments, such as long corridors or single-wall scenarios with narrow field-of-view LiDAR. To address this limitation, we propose ALIVE-LIO, a degeneracy-aware LiDAR-inertial odometry framework that explicitly enhances state estimation in degenerate directions. The key contribution of ALIVE-LIO is the strategic integration of a deep neural network into a classical error-state Kalman filter (ESKF) to compensate for the loss of LiDAR observability. Specifically, ALIVE-LIO employs a neural network to predict the body-frame velocity and selectively fuses this prediction into the ESKF only when degeneracy is detected, providing effective state updates along degenerate directions. This design enables ALIVE-LIO to utilize the probabilistic structure and consistency of the ESKF while benefiting from learning-based motion estimation. The proposed method was evaluated on publicly available datasets exhibiting degeneracy, as well as on our own collected data. Experimental results demonstrate that ALIVE-LIO substantially reduces pose drift in degenerate environments, yielding the top-ranked result in 22 out of 32 sequences. Our code is available at https://github.com/cocel-postech/alive-lio.

Figures & tables

Panel of Figure 1 — Fig. 1: Comparison of state update methods. The state $\mathbf{x}$ and its components, such as translation $\mathbf{t}$ , velocity $\mathbf{v}$ and rotation $\mathbf{R}$ , are denoted as $(\cdot)^{\text{LIO}}$ , $(\cdot)^{\text{NN}}$ , and $(\cdot)^{\text{NEW}}$ for the LIO state, the neural network state, and the newly updated state, respectively. (a) Degeneracy ratio-based weighted update, (b) Projection onto the degenerate space, (c) Our ESKF-based update. Note that, in contrast to (a) and (b), our approach performs a full state update by leveraging the system uncertainty $\mathbf{P}^{\text{LIO}}$ and the data-driven uncertainty $\bm{\Sigma}^{\text{NN}}$ , rather than updating only the velocity.

Notation	Description
${}^{W}(\cdot)\hskip 9.24994pt$	A vector $(\cdot)$ in the world frame
${}^{B}(\cdot)\ \$	A vector $(\cdot)$ in the body frame
$\ \ (\cdot)_{m}$	Measured raw sensor data
$\hskip 9.24994pt(\cdot)^{\text{NN}}$	Output of the neural network
$\ \widehat{\mathbf{x}}^{\kappa}$	$\kappa$ -th update of $\mathbf{x}$ in IESKF
$\delta\mathbf{x}$	Error state in IESKF

TABLE I: Notations used in this paper.

Panel of Figure 4 — Fig. 3: Comparison of motion updates between the well-conditioned TunnelingTunnel_1 and the ill-conditioned (degenerate) ShieldTunnel_1 sequences of the GEODE dataset [ 34 ] . (a) Box plot of the LiDAR-only translational change in well- and ill-conditioned (degenerate) scenarios. (b) Body-frame velocity in the degenerate scenario.

Fig. 4: Distribution of gravity

{}^{W}\mathbf{g}

, acceleration bias

\mathbf{b}_{a}

and gyro bias

\mathbf{b}_{g}

estimated by the LIO system. The

z

-component of gravity is shown after removing the well-known constant magnitude.

Sequence	GenZ- ICP [ 3 ]	CV w/ X-ICP [ 11 ]	FAST- LIO2 [ 33 ]	D-LIO [ 41 ]	PV-LIO [ 19 ]	PV-LIO w/ CO [ 13 ]	Ours w/o CO	Ours
Car
vehicle_highway_0	$\times$	$\times$	1085.34	943.08	$\times$	$\times$	377.58	375.75
vehicle_tunnel_0	510.43	$\times$	2378.02	$\times$	387.25	403.56	56.64	53.05
HK-CHTunnel	730.45	710.53	656.58	$\times$	$\times$	$\times$	153.59	100.85
HK-Whampoa	2.48	$\times$	5.63	6.99	5.22	5.59	4.23	3.87
Urban_Tunnel_1	$\times$	$\times$	$\times$	$\times$	$\times$	$\times$	$\times$	$\times$

TABLE II: Performance of LiDAR-Based Odometry on Degenerate Scenarios (ATE

\downarrow

[m]).

Panel of Figure 7 — Fig. 5: Vehicle motion: Estimated trajectory visualization under degenerate conditions (X–Y plane in meters). The symbols $\triangle$ and ☆ denote the start and end points, respectively, of each trajectory.

Sequence	GenZ- ICP [ 3 ]	CV w/ X-ICP [ 11 ]	FAST- LIO2 [ 33 ]	D-LIO [ 41 ]	PV-LIO [ 19 ]	PV-LIO w/ CO [ 13 ]	Ours w/o CO	Ours
degenerate_seq_0	$\times$	23.66	7.53	8.89	5.11	5.89	2.26	2.04
degenerate_seq_1	10.15	27.60	6.14	37.27	3.50	1.98	0.01	0.10
degenerate_seq_2	$\times$	11.36	19.32	$\times$	12.59	9.03	1.38	0.38
LiDAR_Degenerate	11.5	$\times$	6.09	6.03	0.02	2.07	0.01	0.64
Bright_Screen_Wall	$\times$	$\times$	0.02	$\times$	0.03	0.69	2.01	1.26
CBD_Building_2	17.66	$\times$	1.95	$\times$	0.01	1.66	0.02	0.01

TABLE III: Performance of LiDAR-Based Odometry on Degenerate Scenarios (End-to-End Error

\downarrow

[m]).

Panel of Figure 9 — Fig. 6: Handheld motion: Estimated trajectory and velocity visualization on degenerate cases. The left column shows the trajectory (X–Y plane in meters), and the right column presents the body-frame velocities (velocity in meters per second over time in seconds). The symbols $\triangle$ and ☆ denote the start and end points, respectively, of each trajectory.

Panel of Figure 10 — Fig. 7: Plots of the estimated trajectories, velocities, and acceleration biases for degenerate cases. The left column shows the trajectory (X–Y plane in meters), the center displays the body-frame velocities (velocity in meters per second over time in seconds), and the right column presents the estimated acceleration biases (m/s 2 over time). The symbols $\triangle$ and ☆ denote the start and end points, respectively, of each trajectory.

Sequence	Liao et al. [ 14 ]	ININ-LIO [ 15 ]	Ours
ShieldTunnel_1	101.99	22.58	12.67
ShieldTunnel_2	162.67	105.94	21.60
ShieldTunnel_3	58.97	14.34	12.68
ShieldTunnel_4	79.98	27.76	21.84
ShieldTunnel_5	41.12	$\times$	6.55
ShieldTunnel_6	74.93	10.86	6.40

TABLE IV: Comparison Between Odometry Updates (ATE

\downarrow

[m]).

Fig. 8: Performance comparison under abundant and sparse visual features in geometrically featureless environments: Plots of estimated trajectory and velocity visualization on degenerate cases from the private dataset. The left column shows a single frame from the sequence, the middle column presents the estimated trajectory (X–Y plane in meters), and the right column displays the body-frame velocities (velocity in meters per second over time in seconds).

Sequence	PV-LIO [ 19 ]	FAST- LIVO2 [ 7 ]	Ours
handheld_light	$\times$	0.72	12.65
handheld_dark	$\times$	205.35	30.07

TABLE V: Performance Evaluation on Private Datasets (End-to-End Error

\downarrow

[m]).

Sequence	Not Compensated		${}^{W}\mathbf{g},\ \mathbf{b}_{a},\ \mathbf{b}_{w}$ Compensated
Sequence	AVE	ATE	AVE	ATE
Car
vehicle_campus_1	0.09	4.75	0.07	4.54
vehicle_multilayer_0	0.06	3.81	0.04	3.96
Average	0.07	4.28	0.06	4.25
Others

TABLE VI: Effect of Input Representation Choices (AVE

\downarrow

[m/s], ATE

\downarrow

[m]).

Panel of Figure 15 — Fig. S1: Evaluation of deep learning-based inertial odometry on multiple datasets. The left column shows the trajectory (X–Y plane in meters), while the right column presents the body-frame velocities along the $x$ , $y$ , and $z$ axes (velocity in m/s over time in seconds). The symbols $\triangle$ and ☆ denote the start and end points of each trajectory, respectively.

Seq.	AVE	ATE	RTE
Car
vehicle_campus_1	0.07	4.54	0.43
vehicle_multilayer_0	0.04	3.96	0.10
Avg.	0.06	4.25	0.26
Others
hku_campus_seq_3	0.14	2.52	0.35

TABLE S1: Quantitative Results of Neural Network (AVE

\downarrow

[m/s], ATE

\downarrow

[m], RTE

\downarrow

[m]).

Panel of Figure 17 — Fig. S2: Distribution of the body-frame velocity for the automotive and portable handheld platforms ( $x$ -axis: ${}^{B}\mathbf{v}_{x}$ , $y$ -axis: ${}^{B}\mathbf{v}_{y}$ [m/s]).

Platform	Dataset	Sequence
		Train	Evaluation	Degeneracy (Deployment)
Car	FusionPortableV2 [ 46 ]	vehicle_campus_0	vehicle_campus_1	vehicle_highway_0
		vehicle_highway_1	vehicle_multilayer_0	vehicle_tunnel_0
		vehicle_street_0
	UrbanNav [ 38 , 39 ]	HK-TST		HK-CHTunnel
	UrbanNav [ 38 , 39 ]	HK-Mongkok		HK-Whampoa

TABLE S2: Dataset split for training, evaluation, and degeneracy sequences.

Processor	$N=500$	$N=1000$	$N=2000$
Desktop (CPU)	1.40	3.14	3.10
Desktop (GPU)	1.93	2.25	3.10
OnBoard (CPU)	–	4.68	–
“–” denotes a case that was not measured.

TABLE S3: The network inference time (ms

\downarrow

Sequence	Mean	Max
ShieldTunnel_1	41.24	89.75
Urban_Tunnel_2	42.80	80.30
HIT_Graffiti_Wall_2	28.08	92.49

TABLE S4: End-to-end per-frame runtime [ms] of the proposed system on representative degenerate sequences.

Sequence	Scaling factor $\sigma_{v}$
Sequence	$0.001$	$0.01$	$0.1$	$1$
ShieldTunnel_1	12.81	12.69	11.25	39.87
ShieldTunnel_5	10.75	8.73	7.34	7.85
vehicle_tunnel_0	56.73	53.05	71.01	148.17

TABLE S5: Sensitivity of the ATE (m

\downarrow

) to the scaling factor

\sigma_{v}

, evaluated on a logarithmic scale over representative sequences spanning different motions and platforms. We adopt

\sigma_{v}=0.01

Fig. S3: Estimated trajectory on vehicle_tunnel_0 for

\sigma_{v}=1

and

\sigma_{v}=0.01

(X–Y plane in meters). The symbols

\triangle

and ☆ denote the start and end points, respectively.

Dataset	Sequence	ATE	RTE	$\\|\Delta\mathbf{t}\\|_{2}$
FusionPortableV2	vehicle_campus_0	10.27	1.29	0.02
	vehicle_highway_1	28.81	3.17	0.08
	vehicle_street_0	37.74	1.73	0.02
	vehicle_campus_1	6.33	1.32	0.02
	vehicle_multilayer_0	0.31	0.01	0.01
UrbanNav	HK-TST	8.06	6.51	0.24

TABLE S6: Reliability of the PV-LIO pseudo-ground-truth labels, evaluated against the dataset ground truth on the well-conditioned training and evaluation sequences (ATE [m], RTE [m], and the average

\|\Delta\mathbf{t}\|_{2}

[m]).

Panel of Figure 24 — Fig. S4: PV-LIO estimate on vehicle_highway_1 , which has a long trajectory and exhibits pronounced drift along the $z$ -axis. The trajectory is shown in the X–Y plane (in meters), where $\triangle$ and ☆ denote the start and end points, respectively.

Panel of Figure 25 — Fig. S5: Neural-velocity reliability versus the rotation rate $\omega$ . (a) Network-reported uncertainty $\|\mathbf{\Sigma}^{\text{NN}}_{v,M}\|_{2}$ pooled over all frames ( $r=0.71$ ). (b) Per-sequence mean $\omega$ versus mean $\|\mathbf{\Sigma}^{\text{NN}}_{v,M}\|_{2}$ (red: rotation-vulnerable, blue: smooth). (c) Neural speed error $|\,\|{}^{B}\mathbf{v}^{\text{NN}}_{M}\|_{2}-\|{}^{B}\mathbf{v}^{\text{ref}}\|_{2}\,|$ within sequences with a reliable reference, where the reference is public GT when available and otherwise FAST-LIVO2 or PV-LIO.

Panel of Figure 26 — Fig. S6: Body-frame velocity error versus the rotation rate $\omega$ . (a) Body-frame velocity vector error $\|{}^{B}\mathbf{v}^{\text{NN}}_{M}-{}^{B}\mathbf{v}^{\text{ref}}\|_{2}$ . (b) Per-axis error root-mean-square (RMS) along the forward ( $x$ ), lateral ( $y$ ), and up ( $z$ ) axes for sequences sharing the IMU frame with their reference; the lateral axis dominates.

Fig. S7: Per-scan degeneracy decision over time on the five sequences of Table S7 . Blue denotes scans classified as degenerate and gray denotes well-conditioned scans.

Fig. S8: Distribution of the consecutive degenerate interval duration, pooled over all evaluated sequences and binned at 1 s. The vertical axis is the share of intervals on a logarithmic scale, and the number above each bar is the corresponding interval count. Short intervals dominate the interval count, although they account for

12.7\%

of the total degenerate time.

Fig. S9: Neural speed

\|{}^{B}\mathbf{v}^{\text{NN}}_{M}\|_{2}

(dashed) and the speed of the state (solid) on ShieldTunnel_1 (top) and ShieldTunnel_5 (bottom). The shaded regions denote the scans classified as degenerate.

Sequence	Dur.	Duty	Switch.	Degenerate interval [s]
Sequence	[s]	[%]	[min -1 ]	Med.	$\bm{p_{90}}$	Max
HIT_Graffiti_Wall_1	487.1	9.0	19.95	0.3	1.2	4.6
ShieldTunnel_1	542.1	70.8	10.63	0.3	5.2	162.0
ShieldTunnel_5	251.3	86.4	7.88	0.2	6.5	195.2
vehicle_highway_0	694.6	5.2	13.65	0.2	0.7	6.8
vehicle_tunnel_0	668.6	24.7	61.20	0.3	1.0	11.1

TABLE S7: Temporal stability of the binary degeneracy decision on five representative sequences spanning different platforms and environments. Duty denotes the fraction of scans classified as degenerate, and the switching rate counts the degenerate

\leftrightarrow

well-conditioned transitions. Med.,

p_{90}

, and Max denote the median, the 90th percentile, and the maximum duration of a consecutive degenerate interval, respectively.

Panel of Figure 31 — Fig. S10: Confidence-interval coverage of the network-predicted velocity covariance along the degenerate directions, evaluated on representative sequences. The horizontal axis is the nominal coverage and the vertical axis is the empirical coverage, so the dashed diagonal denotes a correctly calibrated prediction. A curve above the diagonal indicates that the predicted covariance is too wide ( under-confident ), and a curve below the diagonal indicates that it is too narrow ( over-confident ). The value $\sigma_{v}=1$ corresponds to the raw network output and $\sigma_{v}=0.01$ to the value used in the update.

Model	Notation	Value
Neural Network	$\lambda_{C}$	0.002
	$\delta_{\text{car}}$	0.5
	$\delta_{\text{Livox}}$	0.05
Degeneracy	$\theta_{w}$	$45^{\circ}$
	$\theta_{s}$	$80^{\circ}$
	$\tau_{w}$	180

TABLE S8: System Parameter Settings.

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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Inertial Odometry Robot Localization Adaptive Lidar-Inertial Odometry Multimodal Sensor Fusion

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Light detection and ranging (LiDAR)-inertial-visual odometry fuses geometric depth with visual measurements, but its sensors fail independently: LiDAR in under-constrained geometry, vision under poor illumination or texture. Weak information is harmless, since the filter then relies on the other sensor or the inertial prediction; over-confident information is not. Existing countermeasures act on weak information or switch vision by hand-set thresholds. This article presents SA-LIVO, which fuses vision through explicit, online-estimated error models. A frame-level noise scale, estimated by covariance matching, absorbs whole-image errors, and Schmidt filtering carries the correlation of reused observations. Subspace-aware information fusion models the error shared by a frame's observations as a pose offset capping the visual information per direction; the exact fusion attenuates vision only above that cap and reduces to the information sum when the visual model is consistent. LiDAR and visual residuals share one invariant extended Kalman filter loop. On 24 handheld and aerial sequences, SA-LIVO is the most accurate or tied on 22 and stays bounded where others diverge; on the HILTI 2022 benchmark it needs 13.4 ms per frame on a laptop processor and 2.0-6.2x less memory than FAST-LIVO2, R3LIVE, and SR-LIVO.

Abstract

LiDAR Odometry

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