Reflection-Based Relative Localization for Cooperative UAV Teams Using Active Markers

Tim Lakemann; Daniel Bonilla Licea; Viktor Walter; Martin Saska

cs.RONov 21, 2025

Reflection-Based Relative Localization for Cooperative UAV Teams Using Active Markers

Authors: Tim Lakemann, Daniel Bonilla Licea, Viktor Walter, Martin Saska

Organizations: Multi-Robot Systems Group, Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, Prague, Czech Republic · Mohammed VI Polytechnic University, Morocco

Abstract

Reflections of active markers in the environment are a common source of ambiguity in onboard visual relative localization. This work presents a novel approach that exploits these typically unwanted reflections for onboard relative localization in heterogeneous multi-UAV teams operating over specular, near-planar surfaces such as calm water and flat indoor floors. Using only a camera, active markers, and a single-beam rangefinder, the method requires no prior knowledge of robot size, marker configuration, or surface reflectance properties, and propagates the uncertainty introduced by surface irregularities, including those of dynamic water surfaces. We further characterize, analytically and experimentally, how surface tilt biases the estimate, and identify the slope range over which the level-surface assumption holds. Indoor multi-UAV and outdoor experiments validate the localization accuracy, demonstrating reliable operation across varying lighting conditions and greater effective range than state-of-the-art vision-based active-marker methods, with higher accuracy beyond 30 m. The project website with the video is available under the following link: https://timlakemann.github.io/reflection-based-relative-localization/.

Figures & tables

Panel of Figure 1 — Fig. 1 : Outdoor (left) and indoor dark (right) experiments: A UAV estimates the relative position by using surface reflections from active markers attached to a team member UAV . Blue boxes: the UAV with active markers attached. Red boxes: Surface reflections of the light emitted by the UAV .

Panel of Figure 2 — Fig. 2 : Excerpt from an outdoor experiment showing active markers attached to the UAV (blue) and their diffuse reflections on the water surface (red), captured onboard the UAV .

Panel of Figure 3 — Fig. 3 : One UAV equipped with a camera (yellow) constructs an elliptical cone based on the diffuse reflections of light emitted by the transmitting UAV (top left). (a) Side view of our approach, showing the potential location of the transmitting UAV determined by the intersection of two elliptical cones (gray area). (b) Top-down view of the observer UAV with the ellipse around the diffuse reflection.

Fig. 4 : Indoor experiments on different floor types ( PVC , top left; tiles, top right) and under dark conditions (top center). Bottom: heterogeneous multi- UAV experiment.

Panel of Figure 5 — Fig. 5 : Relative position estimates obtained using our approach (blue) compared to the relative position ground truth from UWB (black) during indoor experiments 1–4 (from top to bottom).

Experiment	$n$	$n_{p}$	$\alpha_{r}^{\max}$	$\alpha_{d}^{\max}$	$\upsilon_{d}^{\max}$	$x_{m}$	$z_{m}$	$\sigma$	$t_{\text{exp}}$
			[ ∘ ]	[ ∘ ]	[ ∘ ]	[m]	[m]		[ms]
Indoor 1–4	500	1500	3	3	3	15	2.5	30	20
Multi–UAV	500	1500	3	3	3	10	2.5	30	10
Outdoor 1–3	1000	1000	4	3	3	30–40	10	40	2–3

TABLE I : Parameters for indoor and outdoor experiments.

Panel of Figure 7 — Fig. 6 : Relative position estimates obtained using our approach (blue) and the ground truth from UWB (black) for the UAV (top) and MAV (bottom) during the multi- UAV experiment.

	1. PVC (d)	2. PVC (n)	3. Tiles (n)	4. Tiles (n)
MAE $(x)$ [m]	$1.29\pm 0.67$	$2.12\pm 0.70$	$1.30\pm 0.61$	$1.22\pm 0.60$
MAE $(y)$ [m]	$0.65\pm 0.52$	$1.09\pm 0.74$	$0.68\pm 0.42$	$0.61\pm 0.41$
MAE $(z)$ [m]	$0.12\pm 0.09$	$0.08\pm 0.12$	$0.10\pm 0.09$	$0.08\pm 0.09$

TABLE II : MAE ( MAE ) in the

x

y

-, and

z

-axes for indoor experiments conducted under daylight (d) and nighttime (n) conditions on different floor types. Values are reported as MAE

\pm

one standard deviation.

Panel of Figure 9 — Fig. 7 : Outdoor experiment: (Left) Observing UAV (white), transmitting UAV with active markers (blue), and surface reflections (red). (Right) Onboard UV -filtered image showing the detected marker centroid (blue) and reflection ellipse (red).

		X			Y			Z
		MAE [m]	p -value	$95\text{\,}\mathrm{\%}$ CI	MAE [m]	p -value	$95\text{\,}\mathrm{\%}$ CI	MAE [m]	p -value	$95\text{\,}\mathrm{\%}$ CI
1. Outdoor	Ours	$3.50\pm 1.86$	$1.9\text{\times}{10}^{-8}$	$[-2.62,-1.61]$	$1.18\pm 0.80$	$0.015$	$[-0.26,-0.07]$	$1.04\pm 1.57$	$0.917$	$[0.15,0.42]$
1. Outdoor	UVDAR	$5.58\pm 5.77$	$1.9\text{\times}{10}^{-8}$	$[-2.62,-1.61]$	$1.37\pm 1.09$	$0.015$	$[-0.26,-0.07]$	$0.78\pm 0.83$	$0.917$	$[0.15,0.42]$
2. Outdoor	Ours	$2.42\pm 1.50$	$2.0\text{\times}{10}^{-5}$	$[-0.75,-0.29]$	$1.73\pm 0.95$	$0.071$	$[-0.16,0.02]$	$0.70\pm 0.47$	$0.009$	$[-0.01,0.07]$
2. Outdoor	UVDAR	$2.97\pm 2.14$	$2.0\text{\times}{10}^{-5}$	$[-0.75,-0.29]$	$1.76\pm 0.97$	$0.071$	$[-0.16,0.02]$	$0.67\pm 0.44$	$0.009$	$[-0.01,0.07]$
3. Outdoor	Ours	$5.01\pm 4.15$	$2.2\text{\times}{10}^{-11}$	$[-1.95,-1.18]$	$3.29\pm 1.58$	$0.000$	$[-4.89,-4.19]$	$0.98\pm 0.85$	$0.793$	$[-0.04,0.11]$

TABLE III : MAE ( MAE ) and one standard deviation along the

x

y

-, and

z

-axes, together with the Wilcoxon p-values and

95\text{\,}\mathrm{\%}

CI ( CI ) of the paired differences, comparing our method with UVDAR in outdoor experiments.

	$x$		$y$		$z$
	$-15\text{\,}\mathrm{\%}$	$+$ $15\text{\,}\mathrm{\%}$	$-15\text{\,}\mathrm{\%}$	$+$ $15\text{\,}\mathrm{\%}$	$-15\text{\,}\mathrm{\%}$	$+$ $15\text{\,}\mathrm{\%}$
1. Outdoor	$+0.33$	$-0.23$	$-0.03$	$-0.01$	$+0.02$	$-0.04$
2. Outdoor	$+0.07$	$+0.14$	$+0.39$	$-0.16$	$-0.05$	$+0.09$
3. Outdoor	$+0.92$	$+1.22$	$+0.10$	$-0.55$	$+0.30$	$+0.15$

TABLE IV : Sensitivity analysis: change in MAE [m] under systematic bias in the height measurement of the observer UAV , relative to the unbiased results in Tab. III .

	Ours	UVDAR [ 9 ]	CREPES [ 3 ]	Swarm-LIO2 [ 4 ]	CNN [ 6 ]
Hardware	Cam, LED, Rng	Cam, LED	Cam, LED, UWB , IMU	LIDAR , IMU	Cam, GPU
Mass / power [g / W] 1	$62$ / $6.5$	$40$ / $5.9$	$130^{\star}$ / $\leq\!4^{\star}$	$265$ / $6.5$	$200^{\star}$ / $17^{\star}$
Output rate [Hz]	$10$	$60$	$100$	$30$	$5$
Error @ range [m] 2	MAE x $2.4$ – $5.0$ @ $\leq\!40$	MAE x $3.0$ – $7.0$ @ $\leq\!40$	P25–P75 $0.10$ – $0.16$ @ $\leq\!27.5$	std. $0.05$	P25–P75 $0.3$ – $0.7$ @ $6$
Approx. cost [$]	$570$	$450$	$500^{\star}$	$700^{\star}$	$500^{\star}$
Direct ID	✓	✓	✓	✗	✗

TABLE V : Comparison of onboard relative localization approaches. Symbols: ✓ yes, ◐ partial, ✗ no. 1 Sensing hardware only, onboard compute excluded. 2 Position error as reported in the original publications, following the convention of each work. MAE x : mean absolute error along the optical axis, P25–P75: interquartile range, std.: swarm-state consistency standard deviation reported by the authors, as mutual-distance ground truth was unavailable. The metrics are not directly comparable. ⋆ Estimated from datasheets or manufacturer specifications.

Panel of Figure 13 — Fig. 8 : Relative position estimates obtained using our approach (blue), UVDAR (orange), and the ground truth from RTK (black) for outdoor experiments 1–3 (from top to bottom).

Fig. 9 : Euclidean localization error vs. range for surface tilt angles $15^{\circ}$ , $10^{\circ}$ , $5^{\circ}$ , $-5^{\circ}$ , $-10^{\circ}$ , $-15^{\circ}$ . Solid lines show the theoretical prediction, dashed lines the measured moving average. No measurement is shown for $\tau=-15^{\circ}$ , where the geometry is singular within the evaluated range and the method produced no output.

Relative Pose Estimation

Relative pose estimation recovers the rotation and translation between cameras, objects, or robots from visual and other sensor measurements.

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AMR-Pose: An Active LED Marker-Based Relative Pose Estimation Framework With Probabilistic Switching PnP for Cooperative AUVs

Zeyu Sha, Xiaorui Wang, Mingyang Yang, Feitian Zhang

Robotics and Control Laboratory, School of Advanced Manufacturing and Robotics, and the State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing, 100871, China

Relative Pose Estimation Camera Pose Estimation Cooperative Localization Underwater Robotics

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Reliable relative pose estimation between autonomous underwater vehicles (AUVs) is critical for cooperative ocean exploration, sampling, and multi-robot coordination. However, achieving robust vision-based relative localization in underwater environments remains challenging due to severe optical degradation, including turbidity, illumination variations, reflections, and intermittent feature occlusions. This paper presents AMR-Pose, an active LED marker-based relative pose estimation framework for cooperative AUVs. A compact marker module consisting of one red central LED and three blue peripheral LEDs is developed and integrated onto the leader AUV to provide distinctive visual features under complex underwater conditions. Building upon the detected marker observations, a probabilistic switching Perspective-n-Point estimator (PSwPnP) is developed by combining Lie-group pose propagation on

SE(3)

, probabilistic marker association, and visibility-adaptive measurement fusion for robust six-degree-of-freedom relative pose estimation. The proposed framework dynamically adapts the estimation process according to marker visibility, maintaining geometric consistency and temporal stability during partial observations and visibility transitions. Extensive water-tank experiments with motion-capture ground truth validate that AMR-Pose achieves accurate, smooth, and robust relative pose estimation under challenging underwater conditions. Closed-loop leader-follower experiments further demonstrate its feasibility for real-time relative pose feedback in cooperative underwater robotics.

Abstract

Relative Pose Estimation

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