Localization-Uncertainty-Aware UAV Swarm Search for GNSS-Denied Maritime Surveillance

Siyuan Yang; Junning Lyu; Xiaoyu He; Lakmal Seneviratne; Shaoming He

cs.ROOct 26, 2026

Localization-Uncertainty-Aware UAV Swarm Search for GNSS-Denied Maritime Surveillance

Authors: Siyuan Yang, Junning Lyu, Xiaoyu He, Lakmal Seneviratne, Shaoming He

Organizations: School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China · Professor Emeritus with King’s College London, London WC2R 2LS, United Kingdom

Abstract

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	$\checkmark$	$\triangle$	$\triangle$	$\checkmark$
Cooperative localization	$\times$	$\checkmark$	$\times$	$\checkmark$
Cascading uncertainty propagation	$\times$	$\times$	$\times$	$\checkmark$
Robust connectivity maintenance	$\times$	$\triangle$	$\times$	$\checkmark$
Collision avoidance under uncertainty	$\times$	$\triangle$	$\triangle$	$\checkmark$
Forward-looking sensing	$\times$	$\times$	$\times$	$\checkmark$

TABLE I: Comparison of related works (

\checkmark

: addressed;

\triangle

: partially addressed;

\times

: not addressed).

Panel of Figure 3 — Fig. 2: (a) Top-down view of the front-sector sensing model; (b) 3D view of the sensing cone.

Fig. 3: The uncertainty radius $\epsilon_{i}$ (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	$\mathcal{R}_{i}^{\mathrm{CBF}}$	UAV	$\mathcal{R}_{i}^{\mathrm{CBF}}$
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

n_{1}=n_{2}=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 $\Omega$	$x\in[-1500,1500]$ m, $y\in[0,3000]$ 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): $(-120,10),\dots,(-180,130)$
	Squad 2 (UAV 8–14): $(120,10),\dots,(180,130)$

TABLE III: Numerical baseline configuration.

Parameter	Symbol	Value
Safe distance	$d_{\text{safe}}$	10 m
Localization range	$d_{\text{loc}}$	850 m
Detection radius	$r_{\text{det}}$	400 m
Horizontal field of view	$\theta_{\text{hfov}}$	120 ∘
Ranging noise std	$\sigma_{r}(d)$	$0.5(1+(d/850)^{2})$ m
Measurement availability	$p(d)$	$1/(1+(d/850)^{2})$

TABLE IV: Numerical baseline parameters.

Panel of Figure 10 — 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 $|p-\hat{p}|$ versus the uncertainty radius $\epsilon$ with marginal distributions.

Fig. 10: Uncertainty radius $\epsilon_{i}=3\sqrt{\lambda_{\max}(\boldsymbol{\Sigma}_{i})}$ of the EKF for UAVs 1, 3, 5, and 7 (Squad 1).

Fig. 11: True distances of the fixed localization links versus $d_{\text{loc}}$ (dashed: bUAV links).

Fig. 12: Minimum inter-UAV distance over time with the prescribed safe separation $d_{\text{safe}}$ .

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)	$305.7\pm 7.9$ ( $301.0$ – $330.0$ )
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)

Panel of Figure 20 — 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.

Panel of Figure 23 — 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: $\|p_{i}-\hat{p}_{i}\|$ versus $\epsilon_{i}$ with marginal histograms.

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AUSLUN: A Fixed-Hover UAV--USV System for GNSS-Denied Maritime Search and Navigation

Siyuan Yang, Zikai Jia, Hailiang Kuang, Xiaoyu He+3

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

Robot Navigation GNSS-Denied Localization Cooperative Localization Unmanned Surface Vehicle Maritime Navigation

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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.

Abstract

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