💻 computer science

Mitigation of multi-path propagation artefacts in acoustic targets with adaptive cepstral filtering

This paper proposes an adaptive cepstral filtering method that effectively mitigates multi-path propagation artefacts in acoustic targets, thereby improving signal-to-noise ratios and ship-type classification accuracy in underwater environments.

Original authors: Lucas C. F. Domingos, Russell S. A. Brinkworth, Paulo E. Santos, Karl Sammut

Published 2026-01-23

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Lucas C. F. Domingos, Russell S. A. Brinkworth, Paulo E. Santos, Karl Sammut

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 listen to a friend talking to you across a large, empty canyon. You hear their voice clearly, but you also hear a loud, confusing echo bouncing off the canyon walls. This echo mixes with their voice, making it hard to understand exactly what they are saying or where they are coming from.

In the world of sound, this is called multi-path propagation. It happens when sound waves travel from a source (like a ship or an airplane) to a listener (a microphone) via two paths: the direct path and a path where the sound bounces off a surface (like the ocean floor or the ground) first. This creates a messy "echo" that distorts the original sound, much like that canyon echo.

This paper introduces a clever new way to clean up that messy sound so we can hear the "true" voice of the target.

The Problem: The "Ghost" in the Machine

When a ship or plane moves, the sound it makes gets complicated. The direct sound and the reflected sound interfere with each other, creating a pattern called the Lloyd's Mirror Effect. Think of this like looking at a reflection in a puddle while walking; the image of the object and its reflection merge, making it hard to tell where the real object is or what it looks like.

For computers trying to identify these ships or planes, this "ghost reflection" is a nightmare. It hides the unique features of the engine or propeller, making it harder for the computer to say, "That's a tugboat," or "That's a cargo ship."

The Solution: The "Echo-Eraser" Glasses

The authors propose a new method to fix this, which they call Adaptive Cepstral Filtering. Here is how it works, using a simple analogy:

The Spectrogram (The Map): First, they turn the sound into a visual map called a spectrogram. This shows the sound's frequency (pitch) over time.
The Cepstrum (The "Echo-Map"): They then transform this map into something called a cepstrum. Imagine this as a special "echo-map." In this map, the original sound and the echoes are separated into different lanes. The echoes show up as specific, repeating patterns (peaks) that are easy to spot.
The Adaptive Filter (The Smart Eraser): This is the magic part. Usually, people use a fixed eraser to wipe out these echo patterns. But the authors realized that echoes aren't always the same strength; sometimes they are loud, sometimes faint.
- Their new filter is like a smart, shape-shifting eraser. If the echo is loud, the eraser gets bigger and wider to wipe it out completely. If the echo is quiet, the eraser gets smaller so it doesn't accidentally wipe out the friend's voice.
- It constantly adjusts its size based on how strong the "echo signal" is at that exact moment.

What They Tested

The researchers tested this "smart eraser" in two ways:

The Simulation (The Practice Run): They took recordings of airplanes sitting still and artificially added "echoes" and movement to them using a computer. They then ran their filter on these fake sounds.
- Result: The filter successfully cleaned up the sound, making it look much more like the original, clean airplane noise. It reduced the "distortion" (the messiness) significantly, especially when the plane was moving fast.
The Real World (The Shipyard Test): They used real underwater recordings of ships. These recordings were naturally full of echoes from the ocean floor. They tried to classify the ships (e.g., distinguishing a tugboat from a tanker) using a computer program.
- The Twist: They found that if they only used the cleaned-up sound, the computer actually got worse at identifying the ships. Why? Because the "echo" actually contained useful clues about the ship's size and depth!
- The Winning Strategy: The best result came from a team-up approach. They fed the computer both the original messy sound (with the useful echo clues) and the cleaned-up sound (with the clear engine noise) at the same time.
- Result: This combination improved the computer's ability to correctly identify the ship type by about 2.3% to 2.6% compared to using the messy sound alone.

The Bottom Line

This paper shows that we can use a "smart eraser" to remove confusing echoes from sound recordings. While removing the echoes entirely isn't always the best idea (because the echoes sometimes hold useful secrets), using this filter to clean up the sound and then combining it with the original sound helps computers understand moving targets like ships and planes much better.

It's like giving a detective two clues: one that is a bit blurry but has the full picture, and one that is crystal clear but missing some background details. Putting them together solves the mystery faster and more accurately.

Technical Summary: Mitigation of Multi-Path Propagation Artefacts in Acoustic Targets with Adaptive Cepstral Filtering

Problem Statement
Passive acoustic sensing is a cost-effective method for monitoring moving targets such as vessels and aircraft. However, its performance is significantly hindered by complex propagation effects, specifically multi-path reflections and motion-induced artefacts like the Lloyd's Mirror Effect (LME). In bounded media, sound waves reflect off surfaces (e.g., the sea surface or ground), creating interference patterns with direct paths. While these patterns encode physical information (velocity, distance, depth), they introduce spectral ambiguity that obscures the true source signature, complicating tasks such as target classification and time-delay estimation. Existing filtering techniques often fail to account for environmental variability or the specific characteristics of the target's motion, limiting their ability to separate source signals from reflections effectively.

Methodology
The paper proposes a temporal filtering pipeline applied to the cepstral domain to separate target signals from their reflections. The methodology consists of four stages:

Cepstral Representation: The Short-Time Fourier Transform (STFT) or Constant Q Transform (CQT) is used to generate a spectrogram. The cepstrum is then derived by applying the Inverse Discrete Fourier Transform (IDFT) to the log-magnitude of the spectrum ( $q(\tau) = \text{IDFT}[\log |X(f)|]$ ). This representation separates the signal and its reflections additively, where reflections appear as periodic structures (quefrency peaks).
Quefrency Selection: The method identifies a specific band of quefrencies affected by LME. Quefrencies near zero are ignored as they are source-dependent, and very high quefrencies are excluded as they exceed the maximum delay produced by the LME geometry. The central band, corresponding to the reflection delays, is targeted for processing.
Adaptive Band-Stop Filtering: Instead of using a fixed-frequency band-stop filter, the authors propose an adaptive approach. The filter dynamically adjusts its bandwidth based on the relative intensity of the quefrency components.
- A low-pass filter is applied to the signal to estimate the adaptation state.
- A tone-mapping operation (Naka-Rushton transform) converts the signal amplitude into a relative intensity value ( $I_{nr,t}$ ).
- This intensity value modulates the corner frequencies ( $f_{m1}$ and $f_{m2}$ ) of the band-stop filter. Stronger multi-path components (higher amplitude) trigger a wider filter bandwidth, while weaker components result in a narrower bandwidth.
Signal Reconstruction: The filtered cepstral representation is transformed back into the spectral domain using the exponential of the Discrete Fourier Transform (DFT) to recover the spectrogram.

Key Contributions

Adaptive Temporal Filtering: The paper introduces an innovative temporal filtering method for cepstral representations that utilizes an adaptive band-stop filter. Unlike static methods, this filter adjusts its strength based on the intensity of individual quefrency components, allowing for more effective suppression of reflections while preserving target-specific harmonic features.
Robust Evaluation: The method is rigorously evaluated in two distinct scenarios:
- Simulated Data: Attenuation of movement artefacts in aircraft noise with simulated motion across velocities of 10–100 m/s.
- Real-World Classification: Application to underwater ship-type classification using the DeepShip and VTUAD v2 datasets, where LME is present.

Results

Synthetic Data (Aircraft Noise): The adaptive filtering successfully improved the Log-Spectral Distance (LSD) across all tested velocities, indicating a recovery of the spectral shape and improved perceptual quality. In scenarios involving multi-path reflections (LME), the method also improved the Signal-to-Noise Ratio (SNR). The adaptive filter outperformed a fixed band-stop filter, showing 4–8% greater improvement in LSD metrics in multi-path scenarios.
Underwater Classification: When applied to ship classification tasks, using the filtered spectrogram alone did not improve performance and sometimes degraded it, as the filtering removed depth-related information valuable for classification. However, a parallel classification pipeline—which fed both the unprocessed and filtered spectrograms into the model—yielded significant gains.
- For the DeepShip dataset, the parallel adaptive approach improved the Matthews Correlation Coefficient (MCC) by 2.28 percentage points (SAS task) and 1.35 percentage points (FAS task) over the baseline.
- For the VTUAD v2 dataset, improvements were 2.62 percentage points (SAS) and 0.85 percentage points (FAS).
- The Sequential Audio Sampling (SAS) task benefited most from the parallel approach, suggesting that the complementary information provided by the filtered signal helps the model generalize across time-varying segments.

Significance and Claims
The authors claim that the proposed pipeline demonstrates the potential to improve acoustic target classification and time-delay estimation in multi-path environments. The study highlights that while complete removal of LME is not always desirable (as it contains depth information), adaptive cepstral filtering can effectively separate reflection components to enhance the underlying harmonic structure of the source.

The paper concludes that the method is particularly effective in environments with changing conditions (e.g., varying target speeds or medium properties) due to its adaptive nature. However, the authors modestly note limitations: the filtering process can alter signal amplitude (affecting SNR in non-reflection scenarios), and the adaptive strategy introduces computational overhead compared to fixed filters. Future work is identified as focusing on amplitude preservation and extending the method to multi-sensor and towed array applications.

The Problem: The "Ghost" in the Machine

The Solution: The "Echo-Eraser" Glasses

What They Tested

The Bottom Line

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