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Coupled Meta-Adaptive Filtering for Active Noise Control Under Time-Varying Acoustic Paths

Boxiang Wang, Zhengding Luo, Ziyi Yang, Dongyuan Shi, Xuexian Liu, Woon-Seng Gan

arXiv:2609.30945v1eess.AS

TL;DR

Meta-AF-based ANC relies on a fixed secondary-path model and lacks online path tracking for time-varying environments. CoMeta-AF-ANC jointly learns control-filter adaptation and acoustic-path tracking in a coupled framework. It maintains stable operation across 90 unseen head-movement scenarios and restores more than 20 dB of noise reduction within approximately 1 s after sudden path changes.

  • Problem

    Meta-AF-based ANC relies on a fixed secondary-path model and lacks online path tracking in time-varying acoustic environments.

    Source: §1 · pp. 3–4

  • Method

    CoMeta-AF-ANC couples meta-learned control-filter adaptation with online acoustic-path tracking in a unified framework.

    Source: §5 · p. 27

  • Results

    Across 90 unseen head-movement scenarios, CoMeta-AF-ANC maintains stable operation and restores more than 20 dB of noise reduction within approximately 1 s after sudden path changes.

    Source: §5 · p. 27

  • Takeaways & Limitations

    The paper concludes that coupled meta-adaptive filtering addresses ANC under time-varying acoustic paths.

    Source: §5 · p. 27

    The cited Meta-AF-based ANC method uses a fixed secondary-path model and lacks online path tracking in time-varying environments.

    Source: §1 · p. 4

Abstract

from arXiv · show

Meta-adaptive filtering (Meta-AF) provides a data-driven alternative to hand-crafted adaptive filter updates by employing a learned optimizer throughout online adaptation. However, when Meta-AF is used for active noise control (ANC), time-varying acoustic paths remain a major challenge. In particular, the physics-informed optimizer features are constructed using a secondary path estimate and become mismatched when the physical path changes, leading to inaccurate filter updates and degraded noise reduction. To address this problem, this paper proposes a Coupled Meta-Adaptive Filtering Active Noise Control (CoMeta-AF-ANC) method, which applies meta-learning to jointly learn the control filter adaptation and acoustic path tracking within a closed-loop framework. The proposed Meta-Gated Joint Path Identifier (MG-JPI) simultaneously tracks the primary and secondary paths from the available ANC signals without auxiliary noise, while the updated secondary path estimate is fed back to reconstruct the Meta-AF controller features. A delayless dual-rate realization performs learned adaptation at the frame rate while generating the control signal at the sampling rate in the time domain. Evaluation using measured headrest acoustic paths shows that CoMeta-AF-ANC outperforms representative ANC algorithms in tracking time-varying acoustic paths, while maintaining higher stability across unseen head movement scenarios. It also generalizes well to real-world noises not encountered during training.

1. Introduction

Meta-AF learns filter updates but depends on secondary-path-informed features that can become mismatched as acoustic paths change. CoMeta-AF-ANC couples controller adaptation with online path tracking, and the introduction reports experiments validating its effectiveness and generalization against representative ANC baselines.

1. Introduction

  • Meta-AF learns a signal-feature-to-filter-increment mapping and keeps its learned optimizer active online, reducing reliance on hand-crafted update rules and empirical tuning.Prior audio adaptive-filtering tasks showed faster convergence than conventional algorithms.Source: §1 · p. 4
  • When acoustic paths vary, secondary-path mismatch can distort Meta-AF features and produce inaccurate control-filter updates, degrading noise reduction and tracking.The introduction identifies device repositioning, listener motion, and environmental changes as sources of path variation; the existing Meta-AF-based ANC method lacks online path tracking.Source: §1 · p. 4
  • Existing path-tracking alternatives trade off probing noise, control-signal identifiability, or added device complexity and potential privacy concerns.Auxiliary-noise methods add residual noise, while noise-free methods depend on control-signal spectral richness; sensor-conditioned approaches may require cameras.Source: §1 · p. 4
  • CoMeta-AF-ANC couples meta-learned control adaptation with MG-JPI, which tracks primary and secondary paths using available ANC signals without auxiliary noise.The two processes are mutually dependent within the framework.Source: §1 · pp. 4–5
  • The controller output excites path identification, while the updated secondary-path estimate reconstructs physics-informed features for subsequent controller adaptation.The controller and path optimizers are jointly trained through the same closed-loop recursion.Source: §1 · p. 5
  • A delayless dual-rate realization generates control sample by sample while learned adaptation runs at frame rate, avoiding block-processing delay in the control path.The introduction also describes experiments across time-varying conditions as validating the method’s effectiveness and generalization.Source: §1 · p. 5
  • Experiments using measured acoustic paths and diverse noises validate CoMeta-AF-ANC’s effectiveness and generalization against representative ANC baselines under time-varying conditions.The introduction does not report specific comparative values.Source: §1 · p. 5

2. Preliminaries

This section reviews conventional FxLMS adaptation and a Meta-AF extension for feedforward ANC. It motivates the proposed approach by describing how fixed secondary-path estimates and blockwise frequency-domain generation limit Meta-AF under changing paths.

2.1. FxLMS-Based Control Filter Adaptation

  • FxLMS updates the control filter using the error signal and a reference filtered by the estimated secondary path.The step size scales this filtered-reference update.Source: §2.1 · p. 6
  • CoMeta-AF-ANC replaces the hand-crafted FxLMS update with a control-filter update rule learned directly from data.FxLMS can converge slowly, track poorly, or diverge when its step size is unsuitable.Source: §2.1 · p. 7

2.2. Meta-AF-Based Control Filter Adaptation

  • Meta-AF predicts control-filter increments from signal features rather than applying a hand-crafted update rule.This ANC extension follows the original Meta-AF framework and predicts the increment directly.Source: §2.2 · pp. 7–8
  • When the physical secondary path changes but its estimate stays fixed, Meta-AF features become mismatched and produce inaccurate control-filter updates.The frequency-domain blockwise control-signal generation also introduces processing delay.Source: §2.2 · p. 8
  • These limitations motivate delayless realization and online secondary-path tracking in the proposed method.The extension generates control signals in the frequency domain using a fixed secondary-path estimate.Source: §2.2 · pp. 7–8

3. The Proposed CoMeta-AF-ANC Method

The proposed CoMeta-AF-ANC method couples control-filter adaptation with online acoustic-path tracking in a closed-loop framework, using updated secondary-path estimates to refresh controller features. It combines frame-rate learned adaptation and sample-rate control generation with joint training based on multi-frame measured-error losses.

3.1. Delayless Meta-AF Control Filter Adaptation

  • The delayless control filter generates the control signal sample by sample while holding its coefficients over each hop and adapting at the frame rate.Meta-AF operates in the frequency domain, and its controller features use the latest online secondary-path estimate.Source: §3.1 · pp. 9–10

3.2. Meta-Gated Joint Path Identifier

  • MG-JPI jointly tracks the primary and secondary paths from reference, control, and error signals without auxiliary noise, using learned frequency-dependent gates to scale normalized path updates.The continuously adapting controller provides temporal variation that helps separate the two path contributions despite correlated excitations.Source: §3.2 · pp. 10, 12

3.3. Coupled Online Recursion

  • Within each frame, the controller output excites MG-JPI, whose updated secondary-path estimate reconstructs controller features before the next filter update.The frame-m error spectrum is used only for updates from frame m+1, preserving causality.Source: §3.3 · p. 13

3.4. Network Architecture

  • The meta-optimizers use independent complex-valued recurrent networks with parameters shared across frequency bins; stacked GRU layers retain optimizer memory across frames.The control optimizer produces filter increments, while the path optimizers produce bounded gates.Source: §3.4 · pp. 13–14
  • Median inference takes 4.04 ms per frame, below the 64 ms hop interval, for an approximate real-time factor of 0.063 on one CPU thread.The evaluation used an AMD Ryzen Threadripper PRO 5975WX.Source: §3.4 · p. 15
  • A co-processor can offload learned-optimizer computation while preserving sample-rate control-signal generation.Source: §3.4 · p. 15

3.5. Joint Closed-Loop Training

  • The three meta-optimizers are jointly trained through an M-frame closed-loop recursion, with updates evaluated on subsequent states rather than one-step error alone.Source: §3.5 · pp. 15–16
  • Measured-error noise-control loss enables unsupervised training without labels; secondary-path loss uses the true path only in training, while the primary estimate is optimized indirectly.No direct primary-path modeling loss is imposed.Source: §3.5 · p. 16
  • After each segment, training detaches the computation graph but carries online filters, path estimates, recurrent states, and signal histories forward without resetting them.This implements truncated backpropagation through time.Source: §3.5 · pp. 16–17
  • During deployment, optimizer parameters remain fixed while adaptive and recurrent states continue to evolve online.Source: §3.5 · p. 17

4. Experimental Evaluation

The experiments evaluate CoMeta-AF-ANC on measured acoustic paths against representative ANC methods. They examine tracking under time-varying paths, generalization to unseen real-world noises, MG-JPI ablations, and acoustic path modeling.

4. Experimental Evaluation

  • The evaluation tests CoMeta-AF-ANC on measured acoustic paths through comparisons with representative ANC methods.The experiments assess tracking, noise generalization, MG-JPI ablations, and path modeling.Source: §4 · p. 17
  • Tracking performance is examined under time-varying acoustic paths.This is the first evaluation stage.Source: §4 · p. 17
  • Generalization to unseen real-world noises is assessed alongside comparison with an initialization-based meta-learning method.Source: §4 · p. 17
  • The evaluation concludes with an MG-JPI ablation study and assessment of acoustic path modeling performance.Source: §4 · p. 17

4.1. Experimental Setup

The evaluation uses measured headrest acoustic paths and simulated head movement, with training and test sets designed to differ in noise recordings and head positions. It compares CoMeta-AF-ANC with reference and adaptive ANC methods using noise reduction and instability metrics.

4.1. Experimental Setup

  • The headrest setup measures primary–secondary path pairs at 60 positions to represent acoustic changes caused by head movement.The left-side channel uses one reference microphone, one secondary loudspeaker, and one error microphone.Source: §4.1 · p. 17

4.1.1. Dataset Construction

  • Training, validation, and test datasets combine noise signals with time-varying acoustic paths derived from measured head-rest responses, using both synthesized and real-world noises.Synthesized noises are band-limited white noise with random bandwidths within 100–2000 Hz; real-world noises come from UrbanSound8K.Source: §4.1.1 · pp. 18–19

4.1.2. Network Training

  • The three learned optimizers are jointly updated with one Adam optimizer, and model selection uses held-out validation scenarios containing synthesized and real-world noise.The online processing settings are summarized in Table 4.Source: Table 4 · p. 18, §4.1.2 · p. 19

4.1.3. Compared Methods

  • Comparisons include a known-path Wiener reference, fixed-secondary-path FxLMS and delayless FD-FxNLMS, two OSPM methods, and Co-initial MAML.Zhang’s OSPM uses auxiliary probing noise, Hu’s OSPM does not, and Co-initial MAML jointly meta-initializes the control filter and secondary-path estimate.Source: §4.1.3 · p. 19

4.1.4. Evaluation Metrics

  • The evaluation reports averaged noise reduction in dB and instability rate, counting a scenario as unstable if values are non-finite or final post-change steady-state NR falls below 0 dB.Frame-wise values for time-varying NR curves are smoothed with a six-frame moving average.Source: §4.1.4 · p. 20

4.2. Performance Under Time-Varying Acoustic Paths

Across 90 held-out head-movement scenarios, CoMeta-AF-ANC remains stable and converges faster after path changes than the baselines. It also maintains noise reduction across sudden and gradual transitions, recovering rapidly after each change.

4.2. Performance Under Time-Varying Acoustic Paths

  • More than 20 dB of noise reduction is restored within 1 s after each sudden path change, while FxLMS and delayless FD-FxNLMS diverge and both OSPM methods recover relatively slowly.CoMeta-AF-ANC has only a brief transient; Fig. 6 compares sudden and gradual transitions lasting 1, 5, and 10 s.Source: §4.2 · pp. 20–22, Figure 6 · p. 21
  • 0% instability and 7.9 ± 3.5 dB first-3-s NR characterize CoMeta-AF-ANC across 90 unseen scenarios; baseline instability rates are 53.3% for FxLMS, 65.6% for delayless FD-FxNLMS, 6.7% for Zhang’s OSPM, and 20.0% for Hu’s OSPM.The NR measure is averaged over the first 3 s after each path change in stable scenarios.Source: Table 5 · p. 22, §4.2 · p. 22
  • Across gradual transition durations, CoMeta-AF-ANC remains stable, maintains higher NR, and shows smaller transient residual-noise increases while tracking the evolving paths.The authors report robust tracking over a wide range of transition durations.Source: §4.2 · p. 22

4.3. Real-World Noise Cancellation

On five real-world noise recordings unseen during training, CoMeta-AF-ANC maintains low residual energy and restores attenuation rapidly after path changes. The reported results are consistent across the recordings’ varied temporal and spectral characteristics.

4.3. Real-World Noise Cancellation

  • For five unseen stationary real-world noise recordings—drilling, jackhammer, air-conditioner, engine-idling, and vacuum-cleaner—CoMeta-AF-ANC maintains low residual energy across the target 100–2000 Hz band and rapidly restores effective attenuation.Source: §4.3 · p. 23
  • Compared methods show stronger, longer-lasting residual noise and less uniform frequency attenuation, while CoMeta-AF-ANC’s results remain consistent across all five noises.The authors conclude that it generalizes to nonstationary real-world noise while maintaining fast tracking under acoustic path changes.Source: §4.3 · p. 24

4.4. Comparison with Initialization-Based Meta-Learning

Co-initial MAML meta-learns starting values for the control filter and secondary-path estimate, whereas CoMeta-AF-ANC learns and continues applying the update mechanism. In the reported comparison, CoMeta-AF-ANC recovers faster after path changes and achieves higher later NR.

4.4. Comparison with Initialization-Based Meta-Learning

  • Co-initial MAML and Zhang’s OSPM share online adaptation parameters, but Co-initial MAML is reinitialized to its meta-learned control filter and secondary-path estimate after each path change.This comparison isolates the benefit of meta-learned initialization.Source: §4.4 · p. 24
  • CoMeta-AF-ANC restores more than 20 dB of noise reduction within approximately 1 s after each change, while Co-initial MAML remains about 2–4 dB lower after 10 s.Co-initial MAML converges faster than Zhang’s OSPM at startup and after changes, but the methods eventually reach similar NR levels.Source: §4.4 · p. 24
  • The authors characterize initialization-based meta-learning as improving the starting point, while CoMeta-AF-ANC learns the update mechanism itself and keeps it active online to respond to path variations.They associate the latter approach with faster response and higher subsequent NR.Source: §4.4 · p. 25

4.5. Ablation Study

The ablation results attribute MG-JPI’s performance gain to both learned path adaptation and joint primary-secondary path modeling. After acoustic-path changes, the complete method tracks faster than the compared alternatives.

4.5. Ablation Study

  • All four methods achieve comparable noise reduction while the acoustic paths are initially matched, but fixed-path Meta-AF-ANC degrades substantially after path changes.Adding Hu’s OSPM improves robustness through online secondary-path modeling.Source: §4.5 · p. 25
  • After path changes, CoMeta-AF-ANC tracks faster than Meta-AF-ANC with Hu’s OSPM, whose online secondary-path modeling improves robustness over fixed-path Meta-AF-ANC.The OSPM update tracks more slowly than CoMeta-AF-ANC.Source: §4.5 · pp. 25–26
  • Removing primary-path modeling makes CoMeta-AF-ANC converge more slowly than the complete method.The joint model better separates primary- and secondary-path contributions in the residual and facilitates secondary-path adaptation.Source: §4.5 · p. 26
  • MG-JPI’s gains arise from both its learned path-adaptation mechanism and its joint path-modeling strategy.The joint model separates primary- and secondary-path contributions in the residual, facilitating secondary-path adaptation.Source: §4.5 · p. 26

4.6. Acoustic Path Modeling Performance

After adaptation to position 4 from nominal position 1, estimated primary and secondary paths reproduce the dominant impulse-response structures and follow the true frequency responses well. The secondary-path estimate represents current path characteristics for the controller, while the primary-path estimate also agrees well despite no direct modeling loss.

4.6. Acoustic Path Modeling Performance

  • At position 4 after adaptation from nominal position 1, both estimated paths reproduce dominant impulse-response structures and follow the true frequency responses well.The comparison covers time and frequency domains over the 100–2000 Hz control band.Source: §4.6 · p. 26
  • The secondary-path estimate gives the Meta-AF controller an accurate representation of current path characteristics.The primary-path estimate also agrees well with the true response despite no direct primary-path modeling loss.Source: §4.6 · p. 26

5. Conclusion

CoMeta-AF-ANC jointly learns control-filter adaptation and acoustic-path tracking, with MG-JPI estimating primary and secondary paths without auxiliary noise. On measured headrest paths, it adapts to path changes, remains stable across unseen head movements, and generalizes to unseen real-world noise.

5. Conclusion

  • CoMeta-AF-ANC couples control-filter adaptation with online acoustic-path tracking, and MG-JPI jointly tracks primary and secondary paths without auxiliary noise.A delayless dual-rate realization adapts at the frame rate while generating the control signal at the sampling rate in the time domain.Source: §5 · p. 27
  • Following sudden path changes, CoMeta-AF-ANC restores more than 20 dB of noise reduction within approximately 1 s.The conclusion also reports fast, robust adaptation under sudden and gradual path variations and stable operation across 90 unseen head-movement scenarios.Source: §5 · p. 27
  • Comparisons with representative ANC algorithms show that learning the online update mechanism provides a sustained adaptation advantage over initialization-based meta-learning.MG-JPI is reported to play a critical role in maintaining effective control under secondary-path variations.Source: §5 · p. 27
  • CoMeta-AF-ANC generalizes to nonstationary real-world noise unseen during training.The conclusion reports evaluation using measured headrest acoustic paths.Source: §5 · p. 27
  • Future work will investigate real-time implementation and evaluation under continuous path variations.The conclusion’s evaluation reports sudden and gradual path variations.Source: §5 · p. 27
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