GLIO2: A GPU-Parallelized Tightly-Coupled LiDAR-Inertial-GNSS System for Robust and Real-Time Global Localization and Mapping

Qi Zhang; Xikun Liu; Qijun Qin; Xiangru Wang; Junzhe Wang; Naigui Xiao; Jianhao Jiao; Weisong Wen

Figure 1: GLIO2 in two challenging self-collected scenes, with the point-cloud map (colored by height) projected onto satellite imagery. Top : the

5.66

km Bridge , crossed at up to

96

km/h, where the straight bridge and the heavy moving traffic cause LiDAR degeneracy along the driving direction (front views A, B). Bottom : the

1.44

km dense-canyon Urban route, where high-rise buildings block and reflect the GNSS signals (location C, with fisheye sky view C1 and front view C2). In each scene GLIO2 keeps the global map continuous and aligned with the imagery despite the complementary LiDAR and GNSS degradation.

System	LiDAR Factor	GNSS	Coupling	RT
LIO-SAM [ 3 ]	S2M	GNSS Solution	loose FGO	✓
LIO-Fusion [ 37 ]	S2M	GNSS Solution	loose FGO	✓
He et al. [ 38 ]	S2M	GNSS Solution	loose FGO	$\times$
GIL [ 9 ]	S2M	PPP: PSR+CP	tight EKF	$\times$
P3-LINS [ 31 ]	S2M	PPP: PSR+CP+DOP	tight EKF	$\times$
Li et al. [ 45 ]	S2MS	PPP: PSR+CP	tight MSCKF	✓

Table 1: Summary of the Most Relevant Methods for LiDAR–Inertial–GNSS Integration Systems.

Figure 2: System overview of GLIO2. The front-end IMU-deskews each LiDAR scan and bootstraps by LIO initialization, where the IMU pre-integration and scan-to-multiscan (S2MS) voxelized-GICP (VGICP) LiDAR factors supply motion and local geometry; GNSS is then aligned to the LIO trajectory, and its double-differenced (DD) pseudorange and Doppler factors enter the graph. The sliding-window graph is solved on the CPU at the LiDAR rate with the dense per-point linearization on the GPU: at each linearization point

\mathbf{x}_{k}

, the points are re-associated against the hash-indexed keyframe voxel maps and the block Hessians returned, the CPU solves for the next

\mathbf{x}_{k}

until convergence, and the converged poses update the active keyframe set while out-of-window states are marginalized. The offline back-end reuses the cached relative factors, applies several rounds of GNSS fault detection and de-weighting (FDD), and batch-optimizes the whole trajectory.

Notations	Explanation
${}^{E}(\cdot),{}^{w}(\cdot),{}^{l}(\cdot)$	ECEF, local-world, and LiDAR coordinate frames
${}^{i}(\cdot),{}^{r}(\cdot)$	IMU and GNSS receiver coordinate frames
${}_{b}^{a}(\cdot)$	Variable of frame $b$ represented in frame $a$
$(\cdot)_{k}$	Physical quantity at discrete time step $k$
$\lfloor\cdot\rfloor_{\times},\;(\cdot)^{\wedge}$	Skew operator; hat map, $\mathbb{R}^{6}\!\to\!\mathfrak{se}(3)$
$\boxplus,\;\boxminus,\;\oplus$	Manifold plus/minus; orthogonal direct sum

Table 2: Nomenclature of Coordinates and System States

Figure 3: The five coordinate frames of GLIO2: the Earth-centered ECEF frame (

E

), the local-world frame (

w

), and the LiDAR (

l

), IMU (

i

), and GNSS-receiver (

r

) frames on the platform. The LiDAR and IMU share a fixed extrinsic; the local-world frame relates to ECEF through the estimated extrinsic

{}_{w}^{E}\mathbf{T}

.

Figure 4: Double-differenced pseudorange geometry among the rover

r

, base station

b

, master satellite

m

, and secondary satellite

i

. Double differencing cancels the error terms common to both receivers and both satellites, namely the clock offsets and atmospheric delays.

Figure 5: Block structure of the window information matrix (GNSS in red, LiDAR in blue), contrasting the two LiDAR factors; nodes

\mathbf{x}_{i},\mathbf{x}_{j_{1}},\mathbf{x}_{j_{2}},\mathbf{x}_{j_{3}}

are the current scan and three keyframes, and each cell is a

6\times 6

pose subblock. (a) Scan-to-map enters LiDAR as a unary absolute constraint on the diagonal blocks (red-boxed), acting on the same global degrees of freedom as GNSS. (b) Scan-to-multiscan enters LiDAR as relative constraints coupling

\mathbf{x}_{i}

to each keyframe (off-diagonal blocks), so

\mathcal{G}\subseteq\ker(\mathbf{H}^{\mathcal{L}})

.

Figure 6: Factor graph of the global batch optimization (Sec. 4-4.9 ): the whole trajectory is re-optimized jointly over all states

\mathbf{x}_{0},\dots,\mathbf{x}_{k}

under IMU pre-integration factors, the scan-to-multiscan LiDAR between-factors, and the raw double-differenced pseudorange and Doppler factors.

Dataset (carrier)	LiDAR	IMU	GNSS receiver	Reference	Sequences (scenario)
UrbanNav [ 10 ]	Velodyne HDL-32E, 10 Hz	Xsens MTi-10, 400 Hz	u-blox ZED-F9P, 1 Hz	NovAtel SPAN-CPT	Hong Kong Tst, Whampoa (deep-canyon NLOS)
MARS-LVIG [ 11 ]	Livox Avia, 10 Hz	BMI088, 200 Hz	u-blox ZED-F9P, 10 Hz	DJI RTK-fixed	HKisland1, HKairport1 (aerial, LiDAR degeneracy)
M3DGR [ 12 ]	Livox Mid-360, 10 Hz	ICM40609, 200 Hz	CUAV C-RTK 9Ps, 10 Hz	Fixed RTK + ArUco	Gra1, Out1, Den1 (induced degradation, GNSS-denied)
Ours (UAV)	Livox Mid-360, 10 Hz	ICM40609, 200 Hz	u-blox ZED-F9P, 10 Hz	u-blox ZED-F9P RTK-fixed	Switch (indoor/outdoor), Plain (flat, LiDAR degeneracy)
Ours (Vehicle)	Velodyne VLP-32E, 10 Hz	Xsens MTi-30, 400 Hz	u-blox ZED-F9P, 1 Hz	NovAtel SPAN-CPT	Urban (urban canyon), Bridge (LiDAR degeneracy)
Ours (Vehicle)	Hesai XT-32, 10 Hz	Xsens MTi-30, 400 Hz	u-blox ZED-F9P, 1 Hz	NovAtel SPAN-CPT	Urban (urban canyon), Bridge (LiDAR degeneracy)

Table 3: Overview of the public and self-collected datasets: platform, sensor suite, reference (ground-truth) source, and the evaluated sequences with their dominant degradation scenario.

Figure 7: Self-collected platforms: (a) , (b) the two UAVs; (c) the ground vehicle (top) and its roof-mounted sensor suite (bottom). Per-platform sensor models and reference sources are listed in Tab. 3 .

Figure 8: Per-sequence GNSS noise and LiDAR registration degeneracy along each timeline, colored green/yellow/red for low/moderate/high severity. The two modalities degrade in complementary sequences: GNSS in Urban and Switch , LiDAR on Bridge and Plain .

Sequence	GLIO2(Online)		GLIO2(Batch)		GLIO(Online) [ 7 ]		GLIO(Batch)		LIGO [ 8 ]		LIO-SAM-GPS [ 3 ]		RTKLIB [ 49 ]
Sequence	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D
UrbanNav-Tst	2.153	3.539	1.064	2.583	5.164	19.559	1.516	3.748	5.935	8.051	8.061	18.930	6.965	11.801
UrbanNav-Whampoa	2.834	7.756	1.955	2.987	7.358	16.627	2.070	5.967	8.506	16.800	10.460	22.710	21.230	41.762
MARS-LVIG-HKairport1	2.545	3.207	0.899	1.701	$\times$	$\times$	$\times$	$\times$	7.002	10.472	42.980	45.355	2.194	9.672
MARS-LVIG-HKisland1	2.260	3.877	2.134	2.473	$\times$	$\times$	$\times$	$\times$	6.999	9.317	13.111	15.530	2.772	13.038
M3DGR-Gra1	0.527	0.534	0.318	0.346	–	–	–	–	0.690	1.334	4.967	9.912	7.974	12.945

Table 4: Horizontal (2D) and 3D ATE RMSE (m) on the public sequences (UrbanNav, MARS-LVIG, M3DGR).

Sequence	GLIO2(Online)		GLIO2(Batch)		GLIO(Online) [ 7 ]		GLIO(Batch)		LIGO [ 8 ]		LIO-SAM-GPS [ 3 ]		RTKLIB [ 49 ]		FAST-LIO2 [ 1 ]
Sequence	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D	Hor.	3D
Urban	1.127	1.978	0.919	1.327	3.529	12.377	1.589	4.492	3.663	12.935	10.468	13.212	15.945	38.877	6.035	14.604
Switch	0.425	0.636	0.213	0.301	2.727	3.303	0.654	0.881	0.734	0.865	1.334	1.442	3.890	11.212	0.564	0.580
Bridge	1.625	3.586	1.438	2.552	$\times$	$\times$	$\times$	$\times$	$\times$	$\times$	$\times$	$\times$	5.634	11.367	$\times$	$\times$
Plain	0.596	0.663	0.142	0.162	$\times$	$\times$	$\times$	$\times$	9.881	9.882	17.580	18.378	0.150	0.289	$\times$	$\times$

Table 5: Horizontal (2D) and 3D ATE RMSE (m) on the self-collected sequences.

Figure 9: Urban sequence: the GLIO2 point-cloud map built online over the full vehicle route ( Start to End ). The four callouts A – D pair each onboard camera view with the local map at a representative location of strong GNSS NLOS and occlusion. The global map stays consistent across the route despite the persistent multipath.

Figure 10: Urban sequence: estimated trajectory (top-down and vertical) against the SPAN-CPT reference, with the inset magnifying the vertical drift over the final GNSS-degraded span (

250

–

310

s).

Figure 11: Comparison of GLIO2-Tight and GLIO2-Loose on Switch (top) and Urban (bottom). GLIO2-Tight (a, c) keeps a clean, continuous map, whereas GLIO2-Loose (b, d) injects trajectory jumps that tear the map: at the outdoor-to-indoor transition (b) and under tree-shaded GNSS dropouts (d) .

Variant	Switch		Urban
Variant	Hor.	3D	Hor.	3D
GLIO2-Tight	0.425	0.636	1.127	1.978
w/o tight GNSS (Loose)	diverges		10.884	12.705
w/o GPU (CPU)	1.570	2.608	2.569	4.064

Table 6: GNSS-coupling and GPU ablation: horizontal and 3D ATE RMSE (m) on Switch and Urban .

Figure 12: Architecture ablation on the Bridge : per-axis position error and the estimator’s reported

1\sigma

for the scan-to-map and S2MS variants in the body frame (lateral

x

; forward

y

, the driving direction; vertical

z

), on a log scale; the shaded band marks the LiDAR-degenerate span. Within it the scan-to-map along-track (

y

) error grows by orders of magnitude while its reported

1\sigma

stays millimeter-level, whereas the S2MS fusion keeps the along-track error at the meter level.

Sequence	LiDAR factor	ATE RMSE (m)	2D $1\sigma$ (cm)	3D $1\sigma$ (cm)	Outcome
Bridge	Scan-to-map	$669.6$	$0.50$	$0.51$	diverges
Bridge	S2MS (ours)	$\mathbf{3.586}$	$1.45$	$3.31$	bounded
Urban	Scan-to-map	$11.46$	$0.22$	$0.25$	drifts
Urban	S2MS (ours)	$\mathbf{1.978}$	$0.86$	$1.01$	bounded

Table 7: Architecture ablation on the degenerate Bridge and the well-conditioned Urban sequence.

Figure 13: Per-scan runtime distributions across the three LiDAR types on (a) the Jetson Orin NX edge platform and (b) the desktop platform. The dashed line marks the

100

ms real-time budget at the

10

Hz LiDAR rate; for LIGO on the Velodyne in (a) , readouts above

300

ms (

8.1\%

of scans) are excluded. In each box the center line is the median and the white diamond (

\Diamond

) is the mean, the whiskers span the

1.5\times

IQR range, and “+” marks outliers.

Jetson Orin NX
	Per-scan total (ms)			GLIO2 breakdown (ms)
LiDAR	LIGO	FAST-LIO2	GLIO2	Preproc.	Opt. upd.	Residual
Hesai	152.19	73.56	55.54	15.26	32.06	8.21
Velodyne	185.60	77.72	54.02	11.36	35.24	7.42
Mid-360	123.96	23.28	39.60	5.27	28.04	6.28
Desktop

Table 8: Per-scan runtime (ms) on the Jetson Orin NX and desktop platforms: per-scan total of LIGO, FAST-LIO2, and GLIO2, with the GLIO2 stage breakdown. Fastest total per row in bold.

Figure 14: Back-end batch optimization over the three sequences:

3

D ATE RMSE versus full optimization time (log scale), with bubble size the number of optimized nodes. GLIO2 reaches lower error in far less time while optimizing a larger graph.

Figure 15: Autonomous facade-cleaning UAV. (a) Close view of the UAV holding a

1

–

2.5

m standoff from the glass curtain wall (annotated distances are UAV-to-wall). (b) Online GLIO2 LiDAR point-cloud map of the repetitive facade, whose self-similar planar structure causes LiDAR degeneracy along the wall, with the estimated UAV pose. (c) The

110

m high-rise during the cleaning operation, with the UAV working along the facade.

Figure 16: Guide-dog navigation for the visually impaired. (a) Online GLIO2 point-cloud map. (b) Route on Google Maps imagery. (a1) Point cloud and (a2) real-world view of the LiDAR-degenerate section; (a3) real-world view and (a4) point cloud of the GNSS-denied section.

GLIO2: A GPU-Parallelized Tightly-Coupled LiDAR-Inertial-GNSS System for Robust and Real-Time Global Localization and Mapping

Abstract

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