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arxiv: 2604.02827 · v1 · submitted 2026-04-03 · 💻 cs.RO

Orientation Matters: Learning Radiation Patterns of Multi-Rotor UAVs In-Flight to Enhance Communication Availability Modeling

Martin Zoula , Daniel Bonilla Licea , Jan Faigl , V\'aclav Navr\'atil , Martin Saska This is my paper

Pith reviewed 2026-05-13 19:58 UTC · model grok-4.3

classification 💻 cs.RO
keywords UAV radiation patternsantenna calibrationin-flight learningspherical harmonicscommunication modelingquadrotor UAVspattern decouplingpath planning
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The pith

Radiation patterns of two heterogeneous UAVs can be learned and decoupled from joint calibration flight data using linear regression.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates a method to model and separate the antenna radiation patterns of two different quadrotor UAVs from data collected during one shared flight. Each pattern is represented either as a spherical harmonics series or as a weighted average over selected sample points. Linear regression on polynomial coefficients isolates the contribution from each UAV independently. The approach reaches 3.6 dB root-mean-square error on real measurements, which equals the level of measurement noise. This separation supports updated models of communication availability when UAV orientations or payloads change during operations.

Core claim

By flying both UAVs together along a joint trajectory in an open area, received signal strength measurements can be used to fit independent sets of polynomial coefficients for each vehicle's radiation pattern. The resulting models, expressed either through spherical harmonic expansions or weighted sums over inducing points, reconstruct the directional gain of each antenna separately.

What carries the argument

Joint calibration trajectory combined with linear regression on polynomial coefficients that decouples the two UAV radiation patterns modeled as spherical harmonics series or weighted averages over inducing samples.

If this is right

  • Enables rapid recalibration of models when payloads or antenna configurations change on either UAV.
  • Supports more accurate autonomous path planning that accounts for orientation effects on link quality.
  • Improves swarm control algorithms in settings where UAV setups are modified between missions.
  • Maintains communication availability predictions without separate calibration flights or dedicated test equipment.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The regression approach could extend to three or more UAVs by increasing the number of coefficient sets solved simultaneously.
  • Adding terms for known obstacles or multipath effects might allow the same decoupling in non-anechoic environments.
  • The technique could apply to learning orientation-dependent performance of other onboard systems such as cameras or sensors.

Load-bearing premise

A single joint calibration trajectory in an obstacle-free anechoic altitude supplies enough measurements to separate the two UAVs' radiation patterns through linear regression of their polynomial coefficients.

What would settle it

After learning the patterns from the calibration data, collect signal strength measurements on independent flights and check whether the prediction error remains at or below the original 3.6 dB noise level.

Figures

Figures reproduced from arXiv: 2604.02827 by Daniel Bonilla Licea, Jan Faigl, Martin Saska, Martin Zoula, V\'aclav Navr\'atil.

Figure 1
Figure 1. Figure 1: Illustration of our work. UAV A approaches UAV B four [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Radiation pattern geometry. Two UAVs see each other at indepen [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Learning trajectory: coordinates for both UAVs plotted in a common [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of the SH basis functions, l ∈ {0, 1, 2, 3}. Horizontal (x) axes denote azimuth, vertical (y) axes denote inclination. In the following paragraphs, we present the three consid￾ered radiation pattern models, the Spherical Harmonics (SH), Basis Grid (BG), and Polynomial (P). All of them are linear combinations of base functions, i.e., Ga, Gb ∼ X i pifi(α, β), i ∈ ϕ or ψ. Latent parameters p∗ are… view at source ↗
Figure 6
Figure 6. Figure 6: Illustration of the representative dataset. Plots Figs. 6a and 6b share [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A learnt radiation patterns selection. The sub-figures pairs depict both decoupled RPs [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Radiation patterns learnt by Spherical Harmonics (SH), order [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

The paper presents an approach for learning antenna Radiation Patterns (RPs) of a pair of heterogeneous quadrotor Uncrewed Aerial Vehicles (UAVs) by calibration flight data. RPs are modeled either as a Spherical Harmonics series or as a weighted average over inducing samples. Linear regression of polynomial coefficients simultaneously decouples the two independent UAVs' RPs. A joint calibration trajectory exploits available flight time in an obstacle-free anechoic altitude. Evaluation on a real-world dataset demonstrates the feasibility of learning both radiation patterns, achieving 3.6 dB RMS error, the measurement noise level. The proposed RP learning and decoupling can be exploited in rapid recalibration upon payload changes, thereby enabling precise autonomous path planning and swarm control in real-world applications where setup changes are expected.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that radiation patterns (RPs) of two heterogeneous quadrotor UAVs can be learned and decoupled from joint in-flight calibration measurements using linear regression on spherical-harmonics or inducing-point coefficients. A single obstacle-free anechoic-altitude trajectory is used to collect received-power data; the resulting model achieves 3.6 dB RMS error on real-world data, stated to equal the measurement noise floor. The learned RPs are positioned as enabling improved communication availability modeling for path planning and swarm control after payload changes.

Significance. If the decoupling result is robust, the work would provide a practical, data-driven route to accurate per-UAV antenna models without separate anechoic-chamber campaigns. Reaching noise-limited error on real flights is a concrete strength that directly supports downstream uses in autonomous UAV communication planning.

major comments (2)
  1. [Methods / Regression formulation] The central decoupling step (linear regression of the joint coefficient vector) is load-bearing for the claim that both RPs are recovered independently. No rank, condition-number, or singular-value analysis of the design matrix formed from the two UAVs' basis functions along the chosen trajectory is reported; limited relative yaw or insufficient angular diversity could render the matrix rank-deficient, making the recovered patterns non-unique even when RMS error appears low.
  2. [Experimental evaluation] The evaluation reports 3.6 dB RMS error matching measurement noise, yet provides no description of data-exclusion criteria, train/validation/test splits, or propagation of measurement uncertainty into the fitted coefficients. Without these, it is impossible to judge whether the noise-limited result generalizes or is an artifact of the particular trajectory and preprocessing.
minor comments (2)
  1. [Notation / Model] Notation for the two UAVs' coefficient vectors and the combined design matrix should be introduced with explicit dimensions and a short matrix-equation example to clarify how the simultaneous regression is constructed.
  2. [Abstract] The phrase 'anechoic altitude' in the abstract is unclear; clarify whether an open-sky outdoor site or a controlled chamber is intended.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We provide point-by-point responses to the major comments below.

read point-by-point responses

  1. Referee: [Methods / Regression formulation] The central decoupling step (linear regression of the joint coefficient vector) is load-bearing for the claim that both RPs are recovered independently. No rank, condition-number, or singular-value analysis of the design matrix formed from the two UAVs' basis functions along the chosen trajectory is reported; limited relative yaw or insufficient angular diversity could render the matrix rank-deficient, making the recovered patterns non-unique even when RMS error appears low.

    Authors: We agree that an explicit analysis of the design matrix is necessary to confirm that the decoupling is unique. In the revised manuscript we will add the rank, condition number, and singular-value spectrum of the joint design matrix constructed from the two UAVs' basis functions evaluated along the calibration trajectory. This will be placed in the Methods section and will demonstrate that the matrix is full rank and numerically stable, thereby supporting the claim that both radiation patterns are independently recoverable. revision: yes

  2. Referee: [Experimental evaluation] The evaluation reports 3.6 dB RMS error matching measurement noise, yet provides no description of data-exclusion criteria, train/validation/test splits, or propagation of measurement uncertainty into the fitted coefficients. Without these, it is impossible to judge whether the noise-limited result generalizes or is an artifact of the particular trajectory and preprocessing.

    Authors: We acknowledge that additional experimental details are required for reproducibility and to rule out artifacts. In the revised manuscript we will expand the Experimental Evaluation section to describe the data-exclusion criteria applied, the train/validation/test partitioning of the flight data, and the procedure used to propagate measurement uncertainty into the estimated coefficients. These additions will allow readers to assess whether the reported 3.6 dB RMS error is robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper fits radiation pattern coefficients for two UAVs via simultaneous linear regression on received-power measurements collected along a joint calibration trajectory, then reports RMS error on the real-world dataset as 3.6 dB matching the independently observed measurement noise floor. This evaluation step compares the residual directly to external noise statistics rather than to any quantity defined by the fitted coefficients themselves. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the derivation; the central claim remains independently falsifiable against the noise benchmark and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions about antenna pattern representability and the sufficiency of the chosen trajectory for decoupling; no new entities are postulated.

free parameters (1)
  • Spherical harmonics polynomial coefficients
    Coefficients are learned via linear regression from calibration flight data for each UAV.
axioms (1)
  • domain assumption Antenna radiation patterns can be modeled as a Spherical Harmonics series or as a weighted average over inducing samples
    This representation choice enables the linear regression decoupling step described in the abstract.

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Reference graph

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