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Resilient Decentralized Radar-LiDAR-Inertial Odometry in Challenging Subterranean Environments
Moumita Mukherjee, Avijit Banerjee, Anton Koval, George Nikolakopoulos
TL;DR
GPS-denied subterranean localization is challenged by visibility loss that degrades LiDAR, while radar provides a complementary sensing modality. The paper combines LiDAR, radar, and inertial odometry in decentralized RETOIF fusion with adaptive residual thresholding. In smoke-free testing, RETOIF reduces localization RMSE relative to conventional centralized fusion, and experiments report maintained trajectory estimation under smoke degradation.
Problem
In GPS-denied subterranean environments, smoke, dust, and fog degrade LiDAR, while reliable localization must contend with complementary but imperfect sensor measurements.
Source: §1 · p. 2, §1.1.4 · p. 6Method
The decentralized RETOIF framework fuses LiDAR-inertial odometry with four heterogeneous radar-inertial sources and uses adaptive residual thresholding to detect temporal sensor degradation.
Source: §1.2 · p. 7Results
RETOIF achieves localization RMSE 2.1733 versus 2.9929 for conventional centralized fusion (CF-LRIO), a 27.4% reduction, and maintains trajectory estimation under smoke degradation.
Source: §6 · pp. 35–36Takeaways & Limitations
The experiments support decentralized fusion as a potential approach for resilient localization and mapping in challenging subterranean environments.
Source: §6 · p. 36The stacked covariance formulation assumes mutually uncorrelated estimation errors.
Source: §2 · p. 9
Abstract
from arXiv · showhide
Accurate localization in GPS-denied and visually degraded environments affected by smoke, dust, or fog remains a critical challenge for autonomous systems. While LiDAR provides high-resolution spatial perception, its performance deteriorates under particulate occlusion. In contrast, frequency-modulated continuous-wave (FMCW) radar offers robustness under such conditions but suffers from sparse measurements and outliers. This article presents a resilient decentralized LiDAR Radar Inertial Odometry (LRIO) framework that fuses the complementary strengths of LiDAR, radar, and inertial sensing to achieve robust pose estimation in challenging subterranean environments. At the core of the framework is an Adaptive Residual Thresholding (ART) mechanism that autonomously detects temporal sensor degradation and selectively adjusts the fusion process to minimize unreliable measurements. Building on this, a Robust Error-Tolerant Optimal Information Filter (RETOIF) is employed within a decentralized fusion architecture to integrate LiDAR-inertial and multiple radar-inertial odometry estimates in a fault-aware manner, enhancing resilience to environmental disturbances and intermittent sensor failures. The proposed framework is evaluated using real-world sensor data collected in GPS-denied subterranean tunnels under smoke-free and smoke-degraded conditions. In the smoke-free experiment, the proposed RETOIF framework achieves a root mean square localization error (RMSE) of 2.1733, compared with 2.9929 for the conventional centralized LRIO approach, corresponding to a 27.4\% reduction in RMSE. Experimental results further demonstrate the framework's ability to maintain pose estimation under smoke-induced sensor degradation, highlighting its potential for resilient autonomous navigation and mapping in challenging subterranean environments.
1. Introduction
Subterranean localization must contend with GPS denial and visibility loss, which degrade LiDAR while radar offers complementary robustness. The paper proposes decentralized LRIO with adaptive thresholding and RETOIF to select reliable estimates across sensor modalities.
1. Introduction
- LiDAR can degrade in smoke, dust, and fog, while FMCW radar offers a complementary modality for GPS-denied subterranean localization.The paper frames their complementary strengths as motivation for resilient odometry and mapping.Source: §1 · p. 2
1.1.1. Radar Inertial Odometry
- Radar measurements can be sparse and outlier-prone, making scan matching ineffective and causing substantial drift in challenging tunnel settings.Radar performance also depends on mounting geometry, field of view, and environmental conditions.Source: §1.1 · p. 3, §1.1.1 · p. 4
1.1.2. LiDAR Radar Inertial Odometry
- Prior LRIO approaches trade off latency, computational cost, initialization sensitivity, and adaptive handling of LiDAR degradation.The proposed RETOIF-based LRIO uses residual generation and adaptive thresholding to detect outliers for downstream fusion.Source: §1.1.2 · pp. 5–6
1.1.3. Centralized vs Decentralized Multi Sensor Fusion
- Decentralized fusion can adapt covariance to sensor reliability and handle transient failures, unlike centralized fusion’s limited response to short-term degradation.The passage attributes this distinction to centralized fusion’s limited ability to rapidly adjust covariance during localized, temporary LIO degradation.Source: §1.1.3 · p. 6
1.1.4. Autonomous Thresholding
- Fixed thresholds may not suit changing scenarios, while common covariance-based innovation metrics do not determine failure duration.ART evaluates residuals in real time without accumulated data, supporting online RETOIF operation without batch processing.Source: §1.1.4 · pp. 6–7
1.2. Contributions
- The decentralized RETOIF architecture fuses LiDAR-inertial odometry with four heterogeneous FMCW radars and uses adaptive residual thresholding to detect temporal degradation.The framework also transforms radar body-frame point clouds into a global reference frame to construct a global map.Source: §1.2 · pp. 7–8
- Evaluation uses a Pioneer 3-AT platform in GPS-denied subterranean terrain across no-smoke, mild-smoke, and dense-smoke scenarios on identical trajectories.The experiments compare the proposed decentralized approach with centralized fusion.Source: §1.2 · p. 8
2. Notation
The notation defines the state and sensor measurements, then expresses leave-one-out estimates, residuals, and the fusion covariance assumption.
2. Notation
- The system state and its estimate at time k are denoted X_k and ˆX_k, respectively, in R^ns.The process model maps R^ns to R^ns.Source: §2 · p. 8
- The measurement set y contains n sensor measurements, and each leave-one-out estimator ˆX_bi uses all measurements except sensor i.The centralized estimator uses all n measurements; residuals compare it with each leave-one-out estimate.Source: §2 · pp. 8–9
- The stacked covariance Σ_k is block diagonal, assuming mutually uncorrelated estimation errors.The optimal stacked fusion-weight matrix is denoted W_k.Source: §2 · p. 9
3. Problem Formulation
The formulation motivates multi-radar sensing for subterranean coverage and introduces selective fusion to handle sensor limitations.
3. Problem Formulation
- Four radars cover the robot’s front, left, rear, and right, while two additional radars tilt upward to capture cave ceilings.The arrangement is intended to provide 360-degree horizontal coverage.Source: §3 · p. 9
- A single radar may provide sparse or unreliable measurements when its field of view faces open space, making complementary configurations useful.Radar point measurements depend on relative motion.Source: §3 · p. 9
- The proposed decentralized framework selectively integrates LiDAR and multiple radar modalities and excludes modalities when temporal anomalies are detected.It uses an IMU drift-tolerant RIO backbone before applying adaptive threshold-based modality selection.Source: §3 · p. 10
4. Generic Algorithm for Robust Error-Tolerant Optimal Information Filter (RETOIF)
RETOIF uses adaptive residual thresholding to select admissible estimates and optimally fuse them in a decentralized architecture. Its filter bank compares estimates made with different sensor combinations against an all-sensor estimate.
4. Generic Algorithm for Robust Error-Tolerant Optimal Information Filter (RETOIF)
- RETOIF integrates LiDAR-inertial and multiple radar-inertial estimates through a decentralized, adaptive-threshold fusion process.The framework treats the IMU as an external source of control inputs rather than one of the n primary sensors.Source: §4 · p. 10
4.1. Derivation of likelihood functions
- Each likelihood estimator uses a different combination of n sensor measurements, omitting one sensor, while an additional tightly coupled EKF uses all n inputs.The estimators are EKFs that estimate the same state vector.Source: §4.1 · pp. 12–13
4.2. Residue Generation
- Residuals compare each filter-bank estimate with the centralized all-sensor estimate, and their L2 norms provide scalar test statistics for thresholding.Each residual represents the deviation associated with excluding a sensor measurement.Source: §4.2 · pp. 13–14
4.4. Hypothesis test for adaptive threshold and Ultimate Layer for MLE Synthesis
- Residual magnitudes inside the adaptive region are retained as admissible estimators; those outside it are excluded from the ultimate-layer fusion.The thresholding decision is binary, and the retained pose estimates are fused using weights chosen to minimize covariance trace under constraints.Source: §4.2 · p. 14, §4.4 · pp. 18, 20, 23
4.3. Adaptive Threshold Region
- The adaptive threshold region is based on residual mean and standard deviation, with positive gain K tuning its bounds.The residuals are assumed to follow a normal distribution with non-zero mean.Source: §4.3 · pp. 14–16, Figure 4 · p. 15
4.4. Hypothesis test for adaptive threshold and Ultimate Layer for MLE Synthesis
- The evaluated fusion scheme combines four radar configurations and LIO into five redundant pose estimates, using a filter bank to generate residuals for selection.The radar configurations yield distinct fields of view, while LIO supplies an additional independent pose source.Source: §4.4 · pp. 21–22, Figure 6 · p. 22
5. Experimental Evaluations
The tunnel experiments evaluate decentralized LRIO across clear and smoke-degraded conditions, using adaptive residual selection and final fusion to combine sensor estimates. RETOIF lowers smoke-free RMSE relative to centralized LRIO and produces trajectory estimates in both smoke cases.
5. Experimental Evaluations
- Experiments evaluated odometry in a GPS-denied subterranean tunnel under smoke-free and smoke-filled conditions; LiDAR SLAM provided the smoke-free ground truth, while measuring-tape measurements served as ground truth in smoke.Source: §5 · pp. 24–25
5.1. Experimental Results for Environment-1
- Five first-layer likelihood filters fused four of five sensor configurations apiece, then adaptive residual bounds selected estimates for final integration.The bound varies by sample; estimates inside it are retained, and the resulting selection decisions determine which estimates are forwarded to fusion.Source: §5.1 · pp. 27–29
- 0.008225 s per update was required for the filter bank, residual generation, MLE selection, and final integration; the complete four-RIO framework required 0.0658 s per update.The authors describe the decentralized framework as suitable for real-time operation.Source: §5.1 · p. 30
5.2. Quantitative Localization Error Analysis
- 2.1733 RMSE for RETOIF versus 2.9929 for centralized CF (LRIO), a 27.4% reduction in the smoke-free experiment.RETOIF also lowers mean error from 2.1851 to 1.6393 and standard error from 2.0453 to 1.4270; 1-RIO and 2-RIO have lower absolute RMSEs in this experiment.Source: §5.2 · p. 31, Table 3 · p. 31
5.3. Experimental Evaluation in Environment-2
- In dense smoke, the radar-only LF-3 residual remained within threshold and was treated as the MLE; the selected estimates were integrated into final trajectories for both smoke cases.The resulting trajectories were compared with measuring-tape ground truth on straight and curved segments; the paper reports accurate trajectory estimation in both cases.Source: §5.3 · pp. 33–34
6. Conclusion
The conclusion presents RETOIF as a decentralized LiDAR-radar-inertial framework for resilient subterranean localization. It reports lower smoke-free localization RMSE than conventional centralized fusion and trajectory estimation under smoke-related LiDAR degradation.
6. Conclusion
- A 27.4% reduction in localization error: RETOIF achieves RMSE 2.1733 versus 2.9929 for conventional centralized fusion (CF-LRIO).The conclusion also reports mean localization error declining from 2.1851 to 1.6393 and standard error from 2.0453 to 1.4270.Source: §6 · p. 35
- RETOIF combines LiDAR, radar, and inertial sensing through adaptive residual thresholding, likelihood-based consistency evaluation, and selective sensor fusion.The framework is described as decentralized and intended to address inconsistent measurements and temporary sensor degradation.Source: §6 · p. 35
- Figure 17 evaluates LF-1 and LF-2 under smoke conditions using estimated trajectories, residual bounds, and delta variations.The caption identifies the setting as Case-1.Source: Figure 17 · p. 36
- Under light and dense smoke, the framework maintains trajectory estimation despite substantial degradation of LiDAR-inertial odometry.The conclusion attributes identification and exclusion of inconsistent estimates to adaptive residual thresholding and describes multiple radar configurations as providing complementary environmental coverage.Source: §6 · p. 36
- Over the short 26 m trajectory, 1-RIO and 2-RIO have lower RMSE values of 0.9704 and 1.0297, respectively.The conclusion contrasts these individual configurations with RETOIF's heterogeneous fusion strategy, which adaptively selects reliable pose estimates.Source: §6 · p. 36
- Figure 18 presents trajectory estimates, residual bounds, and delta variations for LF-3 and LF-4 under smoke conditions.The caption identifies the setting as Case-1.Source: Figure 18 · p. 37
7. Declarations
The declarations report no conflicts of interest, identify funding sources and author contributions, and state that data are available on reasonable request.
7.1. Conflicts of Interest
- The authors report no conflicts of interest or competing interests with related parties.Source: §7.1 · p. 37
7.2. Funding
- The work received partial support from the European Union’s Horizon Europe Programme and the SP14 autonomous underground mining project.The stated funding includes Grant Agreement No. 101138451 PERSEPHONE; SP14 is jointly financed by LKAB and the Swedish Energy Agency.Source: §7.2 · p. 37
- Figure 19 shows residual and delta evaluation for LF-5 alongside first-layer filter trajectory performance under smoke conditions.The caption specifies Case-1.Source: Figure 19 · p. 38
7.3. CRediT authorship contribution statement
- Mukherjee is credited with conceptualisation, methodology, software, validation, investigation, data curation, formal analysis, drafting, review, and visualisation.The statement also credits Banerjee, Koval, and Nikolakopoulos with specified analysis, investigation, supervision, project, or funding roles.Source: §7.3 · p. 38
7.4. Data Availability
- Data will be made available on reasonable request.Source: §7.4 · p. 38
- Figure 20 compares all RIO configurations with LIO in a smoke-filled tunnel across Case-1 and Case-2 scenarios.Source: Figure 20 · p. 39