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Classification and detection of multiple UAVs using rational Gaussian wavelet neural networks

This paper proposes a cost-effective, interpretable machine learning system that uses rational Gaussian wavelet neural networks to detect and classify both single unmanned aerial vehicles (UAVs) and drone swarms based on acoustic signals, demonstrating superior performance over traditional methods in various environments.

Original authors: Ungvári Gergő, Ferenc Braun, Attila Ámon, Péter Kackstädter, János Volk, Péter Kovács, Tamás Dózsa

Published 2026-05-27

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CC BY 4.0

Original authors: Ungvári Gergő, Ferenc Braun, Attila Ámon, Péter Kackstädter, János Volk, Péter Kovács, Tamás Dózsa

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to identify a specific bird chirping in a very noisy forest. You can't see the bird, and there are cars, wind, and other animals making noise. Most security systems try to solve this by using "super-hearing" microphones and then running the sound through a massive, black-box computer brain (Deep Learning) that guesses what the sound is. While these black boxes are often very good at guessing, they don't tell you why they made that guess, and they need expensive, powerful computers to run.

This paper proposes a different, smarter, and cheaper way to listen for drones (UAVs). Here is the breakdown of their approach:

1. The Problem: The "Needle in a Haystack"

Drones are becoming common, but they are also used for bad things like spying or smuggling. To stop them, we need to hear them. But drones are small, fly low, and their sound is easily drowned out by wind, traffic, or other noise. Furthermore, sometimes a single drone is flying, and other times a whole "swarm" (a group) is flying together. Distinguishing between one drone and a group, or telling a "Mavic" drone from a "Mini" drone, is like trying to tell the difference between a violin and a flute when someone is playing them both while a truck drives by.

2. The Solution: A "Tunable Ear" instead of a "Black Box"

The authors built a system that acts like a tunable ear rather than a black box.

The Old Way (Static Filters): Imagine trying to listen to a specific bird with a pair of headphones that have a fixed filter. If the bird changes its song or the wind picks up, your headphones can't adjust, and you miss the bird. Previous methods used these "fixed" filters.
The New Way (Adaptive Filters): The authors created a special tool called a Rational Gaussian Wavelet (RGW). Think of this as a shapeshifting ear.
- It starts with a basic shape (like a generic ear).
- As it listens to the drone, it learns to change its shape to perfectly match the specific "hum" of that drone.
- It can stretch, shrink, and twist to fit the sound signature of a tiny drone or a large industrial one, even if the wind is blowing.

3. How It Works: The "Musical Score"

The system takes the raw sound and runs it through this shapeshifting ear.

The Wavelet: Instead of just looking at the volume of the sound, it breaks the sound down into a "time-scale" map (like a musical score that shows when a note happens and how high or low it is).
The Learning: The system doesn't just memorize the sound; it learns the shape of the sound's signature. It figures out exactly which "notes" (frequencies) belong to a drone and which belong to the wind.
The Decision: Once the sound is broken down into these clear, physical features, a small, simple computer brain (a small neural network) looks at the score and says, "That's a Mavic Pro," or "That's a swarm of three drones," or "That's just the wind."

4. Why This is Special

It's Explainable: Because the system uses these "shapeshifting ears" (wavelets) that have a clear mathematical shape, we can look at the results and understand what the system heard. We aren't just trusting a mysterious computer; we can see the physical features it found.
It's Lightweight: Because the system is smart about how it listens, it doesn't need a massive supercomputer. It can run on small, cheap hardware (like the microphones in a phone).
It Handles Swarms: It can tell the difference between one drone and a group of them, which is a very hard task for other systems.

5. The Results: Winning the Noise

The authors tested this in two places:

A Quiet Studio: Where they could hear the drones perfectly.
A Noisy Outdoors: Where helicopters, traffic, and wind were screaming in the background.

The Outcome:

In the quiet studio, their system was nearly perfect (99% accuracy) at telling different drone models apart, beating almost every other method tested.
In the noisy outdoors, it was still the best at detecting if a drone was there at all, outperforming even complex, heavy-duty computer models.
Crucially, it did all this while being interpretable (we know how it works) and cost-effective (it doesn't need expensive hardware).

In a nutshell: They replaced a giant, mysterious computer brain with a clever, adaptable "shapeshifting ear" that can hear a drone's specific song even in a hurricane, and it can explain exactly what it heard.

Technical Summary: Classification and Detection of Multiple UAVs Using Rational Gaussian Wavelet Neural Networks

Problem Statement

The detection and classification of Unmanned Aerial Vehicles (UAVs) is a critical challenge for protecting civilian and military infrastructure against threats ranging from smuggling to surveillance. While various detection modalities exist (radar, vision, RF), sound-based detection offers distinct advantages: it is cost-effective, deployable without line-of-sight, and capable of classifying UAV types and estimating positions. However, acoustic detection faces significant hurdles, including background noise, wind interference, and the non-stationary, non-periodic nature of drone audio signals.

Existing sound-based approaches often rely on static feature extraction (e.g., Short-Time Fourier Transform) followed by traditional machine learning models. While interpretable, these static methods fail to adapt to varying UAV types, maneuvers, and environmental conditions. Conversely, deep learning models achieve high performance but often lack physical interpretability and require specialized hardware, posing risks for safety-critical applications. The authors identify a gap for a system that is both highly accurate and physically interpretable, capable of distinguishing single UAVs from swarms in noisy environments.

Methodology

The paper proposes a Model-Driven Machine Learning (MDML) approach utilizing a Rational Gaussian Wavelet (RGW) Convolutional Neural Network. This architecture integrates signal processing directly into the learning process to ensure physical interpretability.

1. Signal Processing and Data Acquisition

Data Sources: Experiments utilized audio data from both a controlled indoor studio (192 kHz sampling) and a noisy outdoor environment (8 kHz sampling).
Preprocessing: Audio signals were segmented into 100 ms non-overlapping windows (19,200 samples at 192 kHz) and normalized to zero mean and unit variance.
UAV Diversity: The dataset included various commercial multirotor UAVs (e.g., DJI Mavic series, Avata 2, Matrice 30T) with differing masses, rotor configurations, and RPM ranges to cover a broad acoustic spectrum.

2. Rational Gaussian Wavelet (RGW) Kernels

The core innovation is the use of RGW kernels, a class of admissible wavelets defined by a parameter vector $\eta$ containing polynomial zeros ( $t_k$ ) and poles ( $z_j$ ). The mother wavelet $\psi_\eta(t)$ is defined as:
$\psi_\eta(t) = C(\eta) P_\eta(t) v_\eta(t) e^{-t^2/2}$
Unlike traditional wavelets with fixed shapes, RGWs allow the morphology of the mother wavelet to be optimized through learnable parameters. This enables the network to adaptively learn the optimal wavelet shape for specific UAV signatures.

3. Network Architecture

The proposed network consists of:

RGW Convolution Layer: Applies discrete convolutions of the input signal with RGW kernels at multiple scales ( $\lambda_k$ ). The layer learns the dilation parameters ( $\lambda$ ) and the morphology parameters ( $\eta$ ).
Pooling Layer: A unique pooling mechanism that retains only the top $Q$ maximum absolute wavelet coefficients for each scale. This acts as a 1D filter, extracting the dominant frequency components (pseudo-frequencies) while discarding noise.
Classification Head: Followed by fully connected layers with ReLU activation. The output uses a Sigmoid activation for binary tasks (detection) or Softmax for multi-class tasks (classification).

The model is designed to be lightweight, suitable for real-time deployment on limited hardware, and fully differentiable, allowing end-to-end training.

Key Contributions

Novel RGW Convolution Layer: The authors introduce a new convolutional layer using RGW kernels that learns both the optimal mother wavelet morphology and the relevant scales. This allows the system to extract physically meaningful features from non-periodic, non-stationary signals.
Swarm Detection Capability: The study demonstrates that the proposed method can effectively distinguish between single UAV intrusions and coordinated drone swarms, a task that complicates many defense strategies.
Interpretability and Performance: The approach bridges the gap between traditional interpretable signal processing and deep learning. The wavelet coefficients carry physical meaning (similarity to specific wavelet shapes at specific scales), unlike the opaque parameters of standard deep neural networks.
Cost-Effective System: By utilizing MEMS microphones and a lightweight neural network, the authors propose a system that avoids the high costs and complexity of radar or vision-based systems while maintaining high accuracy.

Experimental Results

The authors evaluated the model across three scenarios using 5-fold cross-validation, comparing it against Random Forest (RF), SVM (Linear and RBF), Naive Bayes (NB), Fully Connected NN (FCNN), and standard Convolutional NN (CNN).

Scenario 1: Swarm Detection (Indoor)
- Task: Distinguish between background noise, a single UAV, and multiple UAVs.
- Result: The proposed RGW model achieved a mean accuracy of 92.52%, outperforming the standard CNN (90.57%) and significantly surpassing traditional ML methods (e.g., RF at 78.94%).
Scenario 2: UAV Classification (Indoor)
- Task: Classify specific UAV models (Mavic Pro, Mavic Pro 2, Mavic Mini).
- Result: The RGW model achieved 99.20% mean accuracy, comparable to the CNN (99.97%) but with fewer parameters and higher interpretability.
Scenario 3: Detection in Noisy Outdoor Environment
- Task: Binary detection of a single UAV amidst heavy background noise (traffic, wind, helicopters).
- Result: The RGW model achieved 90.55% mean accuracy, outperforming the CNN (89.60%) and all baseline methods. The authors note that interpretability was crucial here to verify the model's validity in such a difficult setting.

Significance and Claims

The paper claims that the proposed method offers a physically interpretable machine learning algorithm that outperforms traditional machine learning approaches and matches or exceeds state-of-the-art deep learning performance in UAV detection tasks.

Key claims regarding significance include:

Adaptability: Unlike static feature extractors, the RGW layer adapts to different UAV types and environmental conditions.
Safety-Critical Suitability: The interpretability of the features addresses concerns regarding the "black box" nature of deep learning in safety-critical defense applications.
Efficiency: The model achieves high accuracy with a small number of parameters, making it suitable for deployment on resource-constrained hardware.
Reproducibility: The authors emphasize that their implementation is publicly available, ensuring the reproducibility of their results.

The authors conclude that while their current generic model is effective, future work will focus on specialized models for specific tasks and real-time deployment. They do not claim to solve all drone detection challenges but present a robust, interpretable, and cost-effective solution for acoustic-based detection and classification.