Maml Co-Initialization Achieves Faster Active Noise Control with 2-Phase Inner Loops

Active noise control faces a persistent challenge: adapting rapidly to fluctuating acoustic environments, as initial performance heavily relies on effective system setup. Ziyi Yang, Li Rao, and Zhengding Luo from the Smart Nation TRANS Lab at Nanyang Technological University, alongside Dongyuan Shi et al, present a novel meta-learning approach to overcome this limitation. Their research introduces a Model-Agnostic Meta-Learning (MAML) co-initialization technique that simultaneously optimises both the control filter and secondary-path model for feedforward ANC systems , crucially, without altering the core runtime algorithm. By pre-training this initializer on a limited dataset of measured acoustic paths, using a streamlined two-phase process, the team demonstrates significantly improved early-stage error reduction, faster target achievement, minimised auxiliary noise, and quicker recovery from environmental shifts , offering a simple yet powerful method for robust feedforward ANC in dynamic settings.

This breakthrough establishes a method for jointly setting these initial conditions, ensuring faster adaptation and improved noise reduction without altering the core runtime algorithm of the filtered-x LMS (FxLMS) framework. The team achieved this by pre-training an initializer on a limited set of measured acoustic paths, employing short, two-phase inner loops that simulate identification followed by residual-noise reduction.

The study reveals that this pre-trained initializer, applied simply by setting the learned initial coefficients, dramatically enhances the speed and stability of feedforward ANC systems. Experiments conducted within an online secondary path modeling FxLMS testbed demonstrate lower early-stage error, a shorter time-to-target, reduced auxiliary-noise energy, and faster recovery after abrupt changes in the acoustic path compared to a standard ANC system without re-initialization. This innovative approach circumvents the limitations of traditional methods that rely on auxiliary noise injection for secondary path identification, which often suffers from low signal-to-noise ratios and sluggish response times. The researchers prove that the diversity of training paths further enhances the initializer’s performance, with secondary-path diversity exerting the strongest positive effect.
This work opens new avenues for robust and efficient ANC systems in dynamic environments. The co-initialization method provides a ‘fast start’ for ANC, requiring only a small set of measured paths for pre-training, making it practical for real-world applications. The team’s findings demonstrate that the pre-trained initializer reaches the target error sooner, maintains lower early residuals, and requires less auxiliary-noise energy than conventional approaches. Furthermore, the system exhibits a markedly faster recovery after environmental shifts, crucial for applications like in-ear headphones and open-space noise cancellation. The main contributions of this research are a few-shot meta-learned co-initialization for FxLMS-based ANC, jointly learning the initial controller and secondary-path model from a small set of measured paths, and generalization to similar unseen acoustic conditions.

MAML for Fast ANC Co-initialization and Adaptation

Scientists pioneered a novel co-initialization technique for feedforward active noise control (ANC) systems, leveraging Model-Agnostic Meta-Learning (MAML) to simultaneously optimize both the control filter and the secondary-path model. This research directly addresses the slow start-up behaviour of FxLMS-based ANC when faced with changing acoustic environments, a limitation of conventional methods relying on zero or nominal initial values. The team engineered a pre-training procedure utilising a small set of measured acoustic paths, employing short two-phase inner loops designed to mimic identification followed immediately by residual-noise reduction. Experiments employed an online secondary path modeling (OSPM), FxLMS testbed, where the system harnessed measured in-ear headphone paths to evaluate performance.

Crucially, the initializer was deployed by simply setting the learned initial coefficients, leaving the runtime adaptive updates of the FxLMS algorithm entirely unchanged. This innovative approach achieves a fast start for feedforward ANC, requiring only a limited number of paths for effective pre-training. The study meticulously constructed the OSPM scheme, incorporating a lightweight error-jump detector to facilitate re-initialization when necessary, as depicted in Figure 1. Researchers defined the reference signal as x(n), the disturbance as d(n), and introduced a zero-mean white auxiliary noise, v(n), with its scaled output denoted as vm(n).

All finite impulse response (FIR) filters were implemented as causal column vectors, with xw(n) representing the reference signal stack of length Lw, xs(n) the secondary signal stack of length Ls, and u(n) the auxiliary input stack. The true secondary path is defined as s ∈ RLs, its estimate as s, the control filter as w ∈ RLw, and the auxiliary canceller as h ∈ RLs, driven by a delayed stack xh(n). The control output, u(n) = w⊤xw(n), provides the last Ls samples forming uw(n). The resulting microphone residual, calculated as e(n) = d(n) + s⊤uw(n) + s⊤u(n), and the cleaned error, demonstrate a significant improvement in performance. Data analysis revealed that the diversity of training paths enhances the initializer’s effectiveness, with secondary-path diversity exerting the stronger influence, ultimately enabling faster adaptation to environment changes and reduced auxiliary-noise energy. This method delivers a lower early-stage error, a shorter time-to-target, and faster recovery after path changes compared to a baseline system without re-initialization.

Meta-learning boosts rapid ANC adaptation performance significantly

Scientists have achieved a breakthrough in active noise control (ANC) by developing a co-initialization method based on meta-learning, significantly improving early-stage performance and adaptation to changing acoustic environments. The research team addressed the challenge of slow adaptation in ANC systems by jointly optimising the control filter and secondary-path model using a Model-Agnostic Meta-Learning (MAML) approach, all while maintaining the existing runtime algorithm unchanged. This innovative initializer is pre-trained on a limited set of measured acoustic paths, employing short two-phase inner loops that simulate identification followed by residual-noise reduction, a process that allows for rapid deployment by simply setting the learned initial coefficients. Experiments conducted within an online secondary-path modeling (OSPM), FxLMS testbed revealed substantial improvements in ANC performance.

The pre-trained initializer demonstrably reduces early-stage error, achieving a faster time-to-target and minimising auxiliary-noise energy compared to a baseline system without re-initialization. Crucially, tests confirm a quicker recovery after abrupt changes in the acoustic path, demonstrating the robustness of the method. Measurements show the system adapts more effectively to dynamic environments, maintaining lower residual errors and requiring less auxiliary noise for optimal performance. Data studies further illuminate the effectiveness of the approach, revealing that the diversity of training paths enhances the initializer’s performance, with secondary-path diversity proving particularly impactful.

The team measured the canceller norm, Jh(n), monitoring changes over a look-back window M with a threshold γh; a significant jump in Jh(n), defined as ∆Jh(n) = Jh(n) − Jh(n −M) γh, triggers an instantaneous reset of the auxiliary canceller h to zero, and the secondary path and control filters (s, w) to their meta-initializations (Ψ, Φ). The core of this work lies in the few-shot meta-learned co-initialization for FxLMS-based ANC, where the controller and secondary-path model are jointly learned from a small set of measured paths. Inner-loop adaptation utilises short segments of input data, xc and dc, with Phase A dedicated to secondary-path updates over TA steps and Phase B focusing on control filter updates over TB steps. Validation errors, e†s(k) and e†(k), are then used to compute meta-gradients (∆Ψ and ∆Φ) with forgetting factors λs and λw applied to the most recent validation samples, a process that ensures robust and efficient adaptation to unseen acoustic conditions.

Co-initialization speeds adaptive noise control systems significantly

Scientists have developed a meta-learned co-initialization technique for feedforward filtered-x least mean squares (FxLMS) active noise control (ANC) systems, improving performance in dynamic acoustic environments. This method pre-trains both the control filter and the secondary-path model using a small dataset of acoustic paths, employing short, two-phase inner loops that simulate identification followed by residual-noise reduction. The initializer is implemented simply by setting initial coefficients, leaving the runtime adaptive algorithm unchanged. Testing on an online secondary path modeling FxLMS testbed demonstrated that this co-initialization yields lower early-stage error, a shorter time.

This research offers a straightforward method for accelerating the performance of feedforward ANC systems when faced with environmental shifts, requiring only a modest collection of acoustic paths for pre-training. Future work could explore extending this approach to more complex ANC scenarios or investigating the potential for incorporating unsupervised learning techniques to further enhance the adaptability of the system. The findings contribute to the field by improving the initialisation stage of classical FxLMS-based ANC, without altering the core adaptive update rules.