Organizations: School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China · Professor Emeritus with King’s College London, London WC2R 2LS, United Kingdom
This paper studies UAV swarm search in GNSS-denied maritime environments, where inter-UAV ranging drives cooperative localization and uncertainty propagates along the multi-hop reference chain, affecting connectivity, collision avoidance, and search effectiveness. We propose an uncertainty-aware control barrier function (CBF) framework approximating cascading localization covariance through Fisher information matrices. First, the cascading covariance model captures how ranging noise and neighbor uncertainty accumulate along the localization chain. Second, uncertainty-tightened CBFs incorporate the covariance model and its rate into margins for connectivity maintenance and collision avoidance, with conditional invariance and graceful-degradation bounds. Third, a hierarchical Voronoi-target strategy with formation keeping supports efficient forward-looking coverage. The distributed controller is validated with a standard unbiased extended Kalman filter in the loop. The framework is demonstrated on several polygon shapes and swarm sizes from 6 to 30 sUAVs. An estimator-in-the-loop run completes the search in 302.5 s, 20 Monte Carlo deployments confirm repeatable completion with all local QPs feasible and containment in at least 98.97% of UAV-frames, and six MBZIRC runs provide estimator-in-the-loop evidence. The source code is publicly available.
Figures & tables
Fig. 1: The uGdMS scenario: sUAVs search a GNSS-denied region with forward-sector sensing while coastal bUAVs provide localization anchors.
Feature
Prior GdMS [ 3 ]
Cooperative Localization Works
Uncertainty-aware Coverage Works
This paper
GNSS-denied maritime search
✓
△
△
✓
Cooperative localization
×
✓
×
✓
Cascading uncertainty propagation
×
×
×
✓
Robust connectivity maintenance
×
△
×
✓
Collision avoidance under uncertainty
×
△
△
✓
Forward-looking sensing
×
×
×
✓
TABLE I: Comparison of related works ( ✓ : addressed; △ : partially addressed; × : not addressed).
Fig. 2: (a) Top-down view of the front-sector sensing model; (b) 3D view of the sensing cone.
Fig. 3: The uncertainty radius ϵi (circle) contains the Mahalanobis-radius-3 ellipse of the position covariance.
Fig. 4: Fixed triangular-ladder CBF references with M=3 bUAVs and N=6 sUAVs; range-visible references can enter the FIM without adding CBF edges.
Squad 1
Squad 2
UAV
RiCBF
UAV
RiCBF
1
{15,16}
8
{16,17}
2
{1,16}
9
{8,16}
3
{2,1}
10
{9,8}
4
{3,2}
11
{10,9}
5
{4,3}
12
{11,10}
TABLE II: Assigned CBF references for the triangular ladder ( s=2 , n1=n2=7 ); global indices.
Fig. 5: Target points for 14 sUAVs and 3 bUAVs in 2 squads: leaders (7, 14) partition via Voronoi cells; followers form the triangular ladder.
Item
Value
Search region Ω
x∈[−1500,1500] m, y∈[0,3000] m
Swarm configuration
N=14 sUAVs, M=3 bUAVs, s=2 squads
Formation
Triangular ladder
Coverage grid
10 m resolution
Initial positions (m)
Squad 1 (UAV 1–7): (−120,10),…,(−180,130)
Squad 2 (UAV 8–14): (120,10),…,(180,130)
TABLE III: Numerical baseline configuration.
Parameter
Symbol
Value
Safe distance
dsafe
10 m
Localization range
dloc
850 m
Detection radius
rdet
400 m
Horizontal field of view
θhfov
120 ∘
Ranging noise std
σr(d)
0.5(1+(d/850)2) m
Measurement availability
p(d)
1/(1+(d/850)2)
TABLE IV: Numerical baseline parameters.
Fig. 6: Swarm search progression with uncertainty radii, Voronoi boundaries, CVT targets, and dependency chains.
Fig. 7: Search coverage progress with the estimator in the control loop.
Fig. 8: FIM-approximated versus EKF-reported uncertainty radius on the representative run (median ratio 0.82 , 95 th percentile 2.25 ).
Fig. 9: Localization error of the estimator-in-the-loop run: scatter of ∣p−p^∣ versus the uncertainty radius ϵ with marginal distributions.
Fig. 10: Uncertainty radius ϵi=3λmax(Σi) of the EKF for UAVs 1, 3, 5, and 7 (Squad 1).
Fig. 11: True distances of the fixed localization links versus dloc (dashed: bUAV links).
Fig. 12: Minimum inter-UAV distance over time with the prescribed safe separation dsafe .
Fig. 13: Search performance of the estimator-in-the-loop variants.
Variant
Time (s)
Coverage (%)
Status
Pure CVT
24
20.0
Loc. violation
Conventional CBF
118
47.3
Loc. violation
CVT+Formation
350
42.4
Partial
uGdMS
302.5
100
Success
TABLE V: Component analysis: performance of different algorithm variants.
Metric
Value
Completion time (s)
305.7±7.9 ( 301.0 – 330.0 )
Coefficient of variation (%)
2.6
Completion rate (%)
100% (20/20 runs)
QP feasibility
100% ( 196,000/196,000 ; 27 re-solves)
Containment per run (%)
98.97 – 100% (median 100% )
Localization error (m)
0.82/2.81/9.57 (median/p95/max)
TABLE VI: Monte Carlo estimator-in-the-loop results (20 runs)
Fig. 14: Algorithm capabilities: triangular, trapezoidal, hexagonal, and rectangular regions with 6–30 sUAVs and M=3 bUAVs.
Fig. 15: Search performance across the cases of Fig. 14 ; the 6-sUAV case (dashed) cannot reach the farthest region.
Run
Time (s)
Max (m)
QPs
Run
Time (s)
Max (m)
QPs
1
467.5
849.14
13,580
4
465.0
848.82
13,566
2
465.5
847.68
13,580
5
468.5
847.56
13,580
3
466.0
848.01
13,594
6
465.5
848.03
13,594
Mean: 466.3 s, 848.21 m, 13,582 optimal QPs/run (81,494 total)
TABLE VII: Summary of six independent MBZIRC runs.
Fig. 16: Cooperative search in the MBZIRC environment: Gazebo views (top) and coverage progression (bottom).
Fig. 17: Search progress over time in the MBZIRC simulation.
Fig. 18: Distances of the assigned localization links in the MBZIRC simulation.
Fig. 19: Localization error of the MBZIRC estimator-in-the-loop run: ∥pi−p^i∥ versus ϵi with marginal histograms.
Global navigation satellite system (GNSS) denial can prevent an unmanned surface vehicle (USV) from both finding a distant vessel and maintaining a globally referenced approach. This paper presents AUSLUN (Automatic UAV Search, Localization, and USV Navigation), a fixed-hover aerial-surface system that uses a coastal unmanned aerial vehicle (UAV), which estimates its own pose through visual-inertial odometry (VIO), as a long-range sensing and navigation anchor. The central design shifts sensing motion from UAV translation to a zoom pod and closes the loop through three coupled elements: polygon-aware annular pod scanning, modality-aware bearing-range localization, and target-relative USV guidance with visual-loss recovery. The same gated recursive estimator uses laser range for the non-cooperative target and datalink range for the cooperative USV. Search-planning simulations show that the adaptive yaw bounds reduce scan time and redundant coverage relative to a matched fixed-sector scan, and GPS-referenced field data show that the gated recursive estimator outperforms non-recursive baselines in localization accuracy. An integrated maritime mission further demonstrates the complete search-to-navigation sequence, including a deliberately triggered visual-loss recovery. These results establish the feasibility and operating boundary of fixed-hover UAV assistance for stationary-target approach in coastal GNSS-denied environments. The source code and a video demonstration are publicly available at https://github.com/xirhxq/pod_search and https://youtu.be/S-5RkJs35JI.
Siyuan Yang, Zikai Jia, Hailiang Kuang +4
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China · Khalifa University Center for Autonomous Robotic Systems (KUCARS), Khalifa University, Abu Dhabi 127788, United Arab Emirates
Reliable real-time 3D localization is essential for multi-UAV navigation, collision avoidance, and coordinated flight, yet onboard estimates can degrade under GNSS multipath, non-line-of-sight reception, vertical drift, and intentional interference. This paper presents a decentralized, lightweight 3D position-refinement layer that improves robustness by fusing each Unmanned Aerial Vehicle (UAV)'s local estimate with neighbor-shared state summaries and inter-UAV range or proximity constraints. The method performs uncertainty-aware neighborhood fusion by weighting each UAV's prior according to its reported covariance and weighting neighbor constraints according to link quality, ranging uncertainty, and a learned trust score. To support practical deployment, the framework explicitly handles cold start and temporary localization loss by inflating or substituting weak priors, allowing trusted neighborhood constraints to bootstrap and stabilize estimates until absolute sensing recovers. To mitigate the impact of faulty or malicious participants, each UAV applies a local range-consistency check, smoothed over time, to down-weight or exclude neighbors whose reported positions are incompatible with observed inter-UAV distances. Simulation experiments with 10 UAVs in a 3D volume show that the proposed refinement substantially reduces mean localization error during cold start, remains competitive after local estimators stabilize, and maintains lower error as the fraction of malicious nodes increases compared with fusion without trust. These results suggest that the approach can serve as a practical resilience layer for swarm operation in challenging environments.
Hosam Alamleh, Damir Pulatov
Computer Science University of North Carolina Wilmington Wilmington, North Carolina, USA
Cooperative UAV-swarm defenses commonly cross-check GNSS positions against measured inter-drone geometry. We show that this relative-geometry channel has a structural blind spot: a common, slowly varying translation (a rigid-covert shift, RigidShift) preserves all pairwise distances and is therefore unobservable to any relative-only detector (a gauge-freedom argument). We validate this blindness on distance-verification and semidefinite-feasibility baselines, while explicitly distinguishing it from onboard inertial/GNSS monitors that can raise a bare alarm but cannot recover the swarm's true position. To quantify when an external reference restores observability, we derive the drift-dependent detection floor 2γ/(1−ts/T) for a calibrated anchor-residual detector and empirically identify an additional detector-specific noise floor (measured slope 2.66 vs. predicted 2.67). We then present a centralized anchor-rooted recovery pipeline that reconstructs swarm geometry from inter-drone ranges, aligns it to a trusted-anchor subset with Byzantine-robust fitting, and recovers the absolute positions of non-anchored drones. A segmented estimator jointly estimates anchor drift, attack rate, and onset when no clean-epoch label is available. Across statistical simulations, ArduPilot software-in-the-loop experiments, and Gazebo experiments with rendered vision anchors, the method recovers the positions of non-anchored drones to a median error of 0.39 m (20 seeds) under approximately 10.1 m of GNSS drift, and to 7.1 cm (5 seeds) in the rendered-vision multi-SITL setting. We also characterize the explicit limits imposed by non-collinear anchor geometry, anchor coverage, τ→0 drift-attack aliasing, and majority anchor compromise. All evaluations are simulation-based and use no RF spoofing hardware or physical swarm.
Minseok Park, Joon Soo Yoo
Jeonbuk National University · Dept. of Electronic Engineering · Jeonju, Republic of Korea +1