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Robust Odometry and Mapping for Multi-LiDAR Systems with Online Extrinsic Calibration

Jianhao Jiao, Haoyang Ye, Yilong Zhu, Ming Liu

arXiv:2010.14294v2cs.ROcs.CV

TL;DR

LiDAR-based SLAM can be limited by sparse measurements and uncertain map points, while multi-LiDAR systems also need extrinsic calibration. M-LOAM combines calibration initialization and convergence monitoring with multi-LiDAR odometry and mapping; the authors report better performance than state-of-the-art LiDAR methods and centimeter/deci-degree calibration accuracy. They describe it as a complete calibration-and-SLAM system evaluated across platforms and environments.

  • Problem

    LiDAR SLAM faces sparse measurements and limited vertical field of view, while uncertain global-map points can limit accuracy and multi-LiDAR systems require extrinsic calibration.

    Source: A. Motivation · p. 1, 2) Low Pose Drift · p. 1

  • Method

    M-LOAM initializes multi-LiDAR extrinsics from aligned motion sequences, monitors calibration convergence using the information matrix's smallest eigenvalue, and refines calibration during odometry.

    Source: B. Calibration of Multi-LiDAR System · p. 6, D. Monitoring the Convergence of… · p. 8

  • Results

    M-LOAM outperforms state-of-the-art LiDAR-based methods and achieves centimeter-level translation and deci-degree rotation accuracy for extrinsic calibration.

    Source: C. Contributions · p. 2

  • Takeaways & Limitations

    The authors present M-LOAM as a complete multi-LiDAR calibration and SLAM system evaluated on handheld devices and autonomous vehicles across indoor and outdoor scenarios.

    Source: C. Contributions · p. 2

    Calibration accuracy is not sufficient for applications such as HD map construction; calibration errors can propagate into and deteriorate map quality, and high-frequency robot motion can challenge tracking.

    Source: B. Limitations · p. 17

Abstract

from arXiv · show

Combining multiple LiDARs enables a robot to maximize its perceptual awareness of environments and obtain sufficient measurements, which is promising for simultaneous localization and mapping (SLAM). This paper proposes a system to achieve robust and simultaneous extrinsic calibration, odometry, and mapping for multiple LiDARs. Our approach starts with measurement preprocessing to extract edge and planar features from raw measurements. After a motion and extrinsic initialization procedure, a sliding window-based multi-LiDAR odometry runs onboard to estimate poses with online calibration refinement and convergence identification. We further develop a mapping algorithm to construct a global map and optimize poses with sufficient features together with a method to model and reduce data uncertainty. We validate our approach's performance with extensive experiments on ten sequences (4.60km total length) for the calibration and SLAM and compare them against the state-of-the-art. We demonstrate that the proposed work is a complete, robust, and extensible system for various multi-LiDAR setups. The source code, datasets, and demonstrations are available at https://ram-lab.com/file/site/m-loam.

I. INTRODUCTION

M-LOAM targets multi-LiDAR SLAM, where broader sensing can address LiDAR sparsity and blind spots but calibration and pose drift remain challenges. It combines automatic initialization, online calibration, tightly coupled odometry, and uncertainty-aware mapping; the introduction also positions these choices against prior SLAM and preprocessing approaches.

A. Motivation S

  • Multi-LiDAR sensing increases measurement range and density, helping address LiDAR sparsity and limited vertical field of view, including vehicle blind spots.The introduction identifies narrow corridors and stairs as examples where sparse scans can cause state-estimation degeneracy.Source: A. Motivation · p. 1

1) Precise and Flexible Extrinsic Calibration:

  • Online calibration needs convergence identification because insufficiently observable motion or environments can yield suboptimal or unreliable extrinsics.The authors also identify centimeter-level calibration error and unexpected extrinsic changes over time as reasons to model extrinsic perturbation.Source: 1) Precise and Flexible Extrinsic… · p. 1

2) Low Pose Drift:

  • Uncertain points in a global map can limit accuracy, motivating multi-LiDAR odometry that uses local-window measurements to reduce degeneracy and frame-to-frame registration failure.The introduction describes mapping as a lower-frequency stage with more feature points and iterations, but notes that uncertain map points still need to be captured and rejected.Source: 2) Low Pose Drift · p. 1

C. Contributions

  • M-LOAM combines automatic initialization, online extrinsic calibration with convergence identification, sliding-window multi-LiDAR odometry, and uncertainty-aware mapping.The system starts from uncalibrated LiDARs and aims to provide poses and a globally consistent map.Source: C. Contributions · p. 2

D. Organization

  • The paper is organized from related work and problem formulation through system modules, experiments, discussion, and conclusion; Fig. 1 depicts preprocessing, calibration, odometry, and mapping outputs.The figure caption says the mapping trajectory is more accurate than the odometry trajectory.Source: D. Organization · p. 2, Figure 1 · p. 2

A. LiDAR-Based SLAM

  • Prior LiDAR SLAM methods build on ICP and add preprocessing, degeneracy prediction, or sensor fusion; dense pixel matching can require GPU hardware for real-time operation.The paper contrasts these dense methods with sparse approaches, including LOAM, which selects edge and planar features.Source: A. LiDAR-Based SLAM · p. 2, 1) Measurement Preprocessing · pp. 2–3

1) Measurement Preprocessing:

  • M-LOAM extracts sparse edge and planar features after denoising and represents their residuals in a concise, unified way to limit computation as LiDAR count grows.This design follows the sparse-feature approach of LOAM.Source: 1) Measurement Preprocessing · p. 3

2) Degeneracy in State Estimation:

This section frames multi-LiDAR estimation as a state-estimation problem whose observability, sensor fusion, calibration, and measurement uncertainty shape the optimization. It introduces the MLE formulation and representations used for poses, features, and uncertainty.

2) Degeneracy in State Estimation:

  • Solution remapping updates states in well-conditioned directions, while the smallest eigenvalue of the information matrix serves as a degeneracy factor for online extrinsic calibration.The paper adopts solution remapping because its problem linearizes the objective as in Zhang et al..Source: 2) Degeneracy in State Estimation · p. 3

3) Multi-Sensor Fusion:

  • Tightly coupled estimation jointly exploits sensor measurements, and M-LOAM optimizes multiple LiDAR states in a sliding window to use their combined constraints.The paper contrasts this with loosely coupled fusion, where each sensor's pose is estimated independently.Source: 3) Multi-Sensor Fusion · p. 3

B. Multi-Sensor Calibration

  • M-LOAM focuses on online multi-LiDAR extrinsic calibration, monitors convergence, and models extrinsic perturbation to reduce its negative effect in long-term navigation.The system assumes hardware-based external-clock synchronization rather than estimating temporal offsets.Source: B. Multi-Sensor Calibration · p. 3

A. Notations and Definitions

  • The notation uses a primary LiDAR as the base frame, auxiliary LiDAR frames, 3D points for features, and translation-quaternion states, with rotation matrices and SE(3) transformations for poses.The feature set contains features extracted from raw LiDAR measurements.Source: A. Notations and Definitions · pp. 3–4

B. Maximum Likelihood Estimation

  • The paper formulates pose and extrinsic estimation as maximum likelihood estimation, yielding nonlinear least squares under a Gaussian measurement-noise assumption.The objective uses a robust Huber loss for outliers and covariance-weighted residuals; iterative solvers locally linearize it.Source: B. Maximum Likelihood Estimation · p. 4

C. Uncertainty Representation

  • A noisy LiDAR point is represented as a noise-free point plus a small zero-mean Gaussian perturbation, while a noisy pose is represented by a mean transformation and a small perturbation with covariance.The measurement covariance is set as a constant matrix, with depth-noise standard deviations taken from LiDAR manuals.Source: C. Uncertainty Representation · p. 4
  • The paper identifies sensor noise, degenerate pose estimation, and extrinsic perturbation as sources of landmark uncertainty that should inform mapping.Degenerate environments can make poses uncertain along poorly constrained directions; calibration errors can also perturb multi-sensor measurements.Source: C. Uncertainty Representation · p. 4

D. MLE with Approximate Gaussian Noise in M-LOAM

M-LOAM uses approximate Gaussian-noise models to balance real-time odometry against more uncertainty-aware mapping. Its system preprocesses features, initializes states, refines calibration during sliding-window odometry, and branches to pure odometry after calibration converges.

D. MLE with Approximate Gaussian Noise in M-LOAM

  • Real-time odometry approximates residual covariance with sensor-noise covariance, omitting pose-uncertainty propagation because it can take around 10–20 ms with more LiDARs and sliding windows.Mapping has more time, so it accounts for sensor noise, degenerate pose estimation, and extrinsic perturbation when propagating uncertainty.Source: D. MLE with Approximate Gaussian Noise… · pp. 4–5

IV. SYSTEM OVERVIEW

  • After preprocessing and initialization, sliding-window multi-LiDAR odometry refines poses and extrinsics; once calibration converges, the system skips extrinsic initialization and refinement and proceeds with pure odometry and mapping.The odometry and mapping modules run concurrently in separate threads, and mapping constructs a global map to reduce odometry drift.Source: §IV · p. 5, Figure 2 · p. 5

V. MEASUREMENT PREPROCESSING

  • Preprocessing segments point clouds to remove noisy objects, extracts edge and planar features, and matches features between consecutive frames, handling each LiDAR independently.Source: §V · p. 5

A. Segmentation for Noise Removal

The system removes small noisy clusters, selects edge and planar features, and matches them across frames. It initializes motion and estimates scan-to-scan motion from feature residuals, correcting for rolling-scan skew.

A. Segmentation for Noise Removal

  • Small range-image clusters are discarded as potentially unreliable constraints, while breadth-first traversal segments points using neighboring-beam geometry.The method assumes neighboring points belong to the same object when their connected line is roughly perpendicular (> 60deg) to the laser beam.Source: A. Segmentation for Noise Removal · p. 5

B. Feature Extraction and Matching

  • Curvature selects representative high-curvature edge and low-curvature planar features, matched across consecutive frames using two edge neighbors or three planar neighbors.The three planar correspondences are selected to form a plane.Source: B. Feature Extraction and Matching · pp. 5–6

VI. INITIALIZATION

  • Initialization estimates motion and extrinsics without requiring prior mechanical configuration or manual effort.Source: §VI · p. 6

A. Scan-Based Motion Estimation

  • Scan motion is estimated by minimizing residuals from edge and planar correspondences; edge residuals combine two plane residuals and provide vector-valued constraints.The planar residual is a point-to-plane distance; the edge formulation permits a 3 × 3 covariance matrix.Source: A. Scan-Based Motion Estimation · p. 6
  • After estimating incremental motion, the system corrects rolling-scan skew by transforming each point into the last frame using its capture time.Source: A. Scan-Based Motion Estimation · p. 6

B. Calibration of Multi-LiDAR System

The system initializes multi-LiDAR extrinsics by aligning sensor motion sequences. Rotation and translation are solved separately, with observability checks and a planar-motion boundary for translation.

B. Calibration of Multi-LiDAR System

1) Rotation Initialization:

  • Quaternion equations form an overdetermined rotation system solved by SVD; sufficient motion excitation is checked through the second-smallest singular value.A priority queue stores up to K = 300 historical constraints, removing constraints with small rotation to bound computation.Source: 1) Rotation Initialization · pp. 6–7

2) Translation Initialization:

  • Translation is estimated by least squares, but planar robot motion leaves z-translation unobservable, so it is set to zero initially and recovered during refinement.Unlike, the method cannot initialize z-translation by leveraging ground planes.Source: 2) Translation Initialization · p. 7

VII. TIGHTLY COUPLED MULTI-LIDAR ODOMETRY WITH CALIBRATION REFINEMENT

M-LO jointly optimizes multi-LiDAR states in a sliding window, using local maps for feature correspondences. Its online-calibration stage refines poses and extrinsics through map-based measurements.

VII. TIGHTLY COUPLED MULTI-LIDAR ODOMETRY WITH CALIBRATION REFINEMENT

  • Starting from initialized values, tightly coupled M-LO optimizes the states of multiple LiDARs within a sliding window.Source: §VII · p. 7

A. Formulation

  • The window groups primary-sensor poses and auxiliary-LiDAR extrinsics; local maps assembled from earlier window features provide data association for joint state optimization.Online calibration treats extrinsics as variables, whereas pure odometry fixes them after convergence.Source: A. Formulation · pp. 7–8

B. Optimization With Online Calibration

  • Online calibration refines poses and extrinsics using map-based correspondences: primary-sensor features constrain poses, while auxiliary-LiDAR features constrain extrinsics.Nearest-neighbor searches in local edge and planar maps establish the correspondences.Source: B. Optimization With Online Calibration · p. 8

C. Optimization With Pure Odometry

After calibration convergence, pure odometry fixes extrinsics and uses map measurements from all LiDARs. A convergence monitor determines when calibration ends, while marginalization carries historical constraints forward.

C. Optimization With Pure Odometry

  • Once calibration converges, pure odometry fixes extrinsics and uses all available map-based measurements to improve single-LiDAR odometry.The cost incorporates constraints between features from all LiDARs and local maps.Source: C. Optimization With Pure Odometry · p. 8

D. Monitoring the Convergence of Calibration

E. Marginalization

  • Marginalization removes the oldest window state and applies the Schur complement to retain historical constraints as a prior for consistent odometry and calibration.Source: E. Marginalization · p. 8

VIII. UNCERTAINTY-AWARE MULTI-LIDAR MAPPING

The mapping module uses prior odometry and map-based residuals to place current features in a global map, where uncertain poses can make landmarks noisy. It propagates point and pose uncertainty to model map points as Gaussian variables and support uncertainty-aware mapping.

VIII. UNCERTAINTY-AWARE MULTI-LIDAR MAPPING

  • Current features are transformed into the world frame and added to a global map, whose quality affects pose-optimization precision.The map is downsampled with a voxel grid filter to reduce computational and memory complexity.Source: §VIII · p. 9
  • Sensor noise, degenerate pose estimates, and extrinsic perturbations are identified as sources of noisy map points.The method propagates point and pose uncertainty so that each map point is modeled as an i.i.d. Gaussian variable.Source: §VIII · p. 9

A. Uncertainty Propagation

  • Pose uncertainty is obtained by inverting the information matrix, while extrinsic covariance is scaled according to calibration recency and possible drift.The covariance scaling parameter is larger when a system has been used for a long time without recalibration; it also relates to time, external impact, and temperature drift.Source: A. Uncertainty Propagation · p. 9
  • The method compounds uncertain poses using a fourth-order approximation, then propagates point uncertainty through a noisy transformation using first-order terms.The transformed landmark is represented by a mean and covariance.Source: A. Uncertainty Propagation · p. 9

B. Uncertainty-Aware Operation

Uncertainty-aware operation modifies mapping to account for pose and extrinsic uncertainty, filter uncertain points, and sample map voxels probabilistically. Experiments cover simulated, handheld, and vehicle platforms with different multi-LiDAR configurations.

B. Uncertainty-Aware Operation

  • Mapping incorporates propagated covariance into its cost, weights points near the origin more highly, and assigns the primary LiDAR greater confidence than auxiliary LiDARs.Pose uncertainty and extrinsic perturbation are both included.Source: B. Uncertainty-Aware Operation · p. 9
  • Points whose covariance trace exceeds a threshold are filtered, and the voxel filter samples points according to their covariances.The sampling weight is normalized as w − tr(Σ_i).Source: B. Uncertainty-Aware Operation · pp. 9–10

IX. EXPERIMENT

  • Experiments assess calibration, SLAM across indoor and outdoor scenarios, sensitivity to extrinsic perturbations, and performance and computation time across LiDAR combinations.The study uses three platforms: a simulated robot, a handheld device, and a vehicle.Source: §IX · p. 10, A. Implementation Details · p. 10

A. Implementation Details

  • The simulated robot and handheld device use two LiDARs, while the vehicle carries four RS-LiDAR-16s for urban-road tests.The simulated robot moves at 0.5 m/s, the handheld device at 2 m/s, and the vehicle at 3 m/s.Source: A. Implementation Details · p. 10

B. Performance of Calibration

M-LOAM outperforms other methods in most SLAM cases, and its calibration refinement outperforms Auto-Calib and is comparable to PS-Calib on the reported metrics. The section also defines calibration metrics and reports initialization limits under planar motion.

1) Evaluation Metrics:

  • EGT measures rotation and translation error against ground truth, while MME measures point-cloud compactness and can be used without ground truth.MME is averaged over 10 consecutive point-cloud frames containing many planes; the real-world EGT reference is PS-Calib.Source: 1) Evaluation Metrics · pp. 10–11

2) Calibration Results:

  • Online refinement outperforms Auto-Calib and is comparable to PS-Calib [12] in EGT (< 3deg and < 0.07m) and MME.On the RHD, MME is better than Auto-Calib for both r = 0.3m and r = 0.4m.Source: 2) Calibration Results · pp. 11–12
  • Initialization estimates rotational offsets below 9deg in all cases but fails to recover translation offsets above 0.3m on the simulated robot and vehicle.Planar movement makes x- and y-translation recovery poor and leaves z-translation unobservable; the RHD can be moved in 6-DoF to gather richer constraints.Source: 2) Calibration Results · p. 12

C. Performance of SLAM

  • At 40m, the median RPE pairs were (0.62deg, 0.06m) for M-LOAM, (0.87deg, 0.07m) for M-LOAM-wo-ua, and (1.26deg, 0.22m) for A-LOAM.The figure reports results over 10 trials on SR05.Source: Figure 13 · p. 13
  • Across sequences, M-LOAM outperforms other methods in most cases, while M-LO exceeds A-LO by around 4–10 orders of magnitude.The paper attributes mapping gains to refinement of odometry and notes calibration error and poor pose priors as factors in competing methods’ errors.Source: C. Performance of SLAM · p. 13

1) Simulated Experiment:

Across simulated, indoor, and outdoor experiments, M-LOAM is compared with other LiDAR methods, with results also examining uncertainty-aware mapping and sensitivity to extrinsic perturbations.

1) Simulated Experiment:

2) Indoor Experiment:

  • In the narrow corridor, uncertainty-aware mapping captures and discards uncertain points, producing a map with a better signal-to-noise ratio than M-LOAM-wo-ua.Source: 2) Indoor Experiment · p. 14
  • After two loops in RHD02lab, M-LOAM is almost drift-free, while M-LOAM-wo-ua and A-LOAM accumulate significant drift in all three directions.Source: 2) Indoor Experiment · p. 14
  • M-LOAM-wo-ua and M-LOAM are more accurate and consistent than A-LOAM on RHD04, while both variants have similar accuracy on well-conditioned RHD03 and RHD04.Source: 2) Indoor Experiment · p. 14, Table V · p. 15

3) Outdoor Experiment:

  • On the 3.23-km RV sequence, M-LOAM and M-LOAM-wo-ua perform competitively with LEGO-LOAM, while A-LOAM has the highest errors.Source: 3) Outdoor Experiment · p. 15

D. Sensitivity to Noisy Extrinsics

  • All methods degrade as extrinsic perturbations increase, but M-LOAM-wo-ua and M-LOAM have smaller errors; M-LOAM is much more robust under the largest perturbation.Source: D. Sensitivity to Noisy Extrinsics · p. 15

E. Single LiDAR v.s. Multiple LiDARs

Using more LiDARs improves odometry, with mapping gains most noticeable in high-speed tests where the global map is sparser. The paper also presents M-LOAM’s design advantages, limitations, and future directions.

E. Single LiDAR v.s. Multiple LiDARs

  • Around 8deg relative rotation error and 3.5% translation error, Four-LiDAR-Odom median values are smaller than One-LiDAR-Odom in high-speed tests.Mapping improvement is small at normal speed but noticeable at high speed, and the Four-LiDAR setup has smaller variance than the others.Source: Figure 22 · p. 16, E. Single LiDAR v.s. Multiple LiDARs · p. 16
  • Odometry time increases with more LiDARs, preprocessing time does not because it is parallelized, and mapping time does not grow linearly because voxel filtering bounds map complexity.Table VII reports average feature counts and running times for different LiDAR setups on the RV sequence.Source: Table VII · p. 16, E. Single LiDAR v.s. Multiple LiDARs · p. 16

A. Main Advantages

  • Processing each LiDAR separately allows parallelized segmentation and feature extraction, preserves scan-model range images without data loss, and supports modeling extrinsic perturbations.Source: A. Main Advantages · p. 17
  • M-LOAM combines tightly coupled sliding-window multi-LiDAR odometry with uncertainty-aware mapping, which improves robustness to degeneracy and extreme extrinsic perturbation despite approximate covariances.The paper also describes the system as extensible to different LiDAR combinations.Source: A. Main Advantages · pp. 16–17

B. Limitations

  • Calibration uses experimentally selected thresholds and is not sufficiently accurate for applications such as HD map construction; errors should be below 0.01m and 1deg to avoid proportional map-quality degradation.Modeling extrinsic perturbation does not entirely eliminate this effect.Source: B. Limitations · p. 17
  • Low-frequency LiDAR data can make registration initialization difficult during rapid motion, and linear pose interpolation cannot represent smooth or fast motion well.The paper suggests higher-order curves such as B-splines as a possible alternative.Source: B. Limitations · p. 17
  • Edge and planar features constrain only perpendicular directions, so M-LOAM may fail in long tunnels with mostly parallel planes and has limited matching power across large viewpoint changes.The paper also notes these features are less useful than surfel-based or visual features for place recognition and relocalization.Source: B. Limitations · p. 17

XI. CONCLUSION AND FUTURE WORK

  • Future directions include adding loop closure to correct accumulated drift and exploring object-centric SLAM and calibration or uncertainty modeling for other sensor modalities.Source: §XI · p. 17

APPENDIX

The appendix derives Jacobians for residuals used in state optimization and explains how marginalization preserves information about retained states in the sliding window.

A. Jacobians of Residuals

B. Marginalization

  • Marginalization uses the Schur complement to remove marginalized states while retaining a prior residual that encodes their dependencies and supports consistency of the remaining states.The information matrix is factorized to express the prior residual for the next optimization.Source: B. Marginalization · p. 18
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