A Bayesian inverse-problem framework for deriving uncertainty-aware adaptive algorithms in active noise control

This paper presents an inverse problem approach to analysis and design of adaptive active noise control algorithms. The proposed methodology employs Bayesian uncertainty quantification to guide and continuously optimize control algorithms in real time. By formulating the control problem as a Bayesian inverse problem, we develop an explicit probabilistic model that enhances the adaptability of the system. Building on this model, we introduce an uncertainty-aware adaptation strategy that quantifies uncertainty in real time and incorporates it directly into control updates. A key contribution of this work is the insight that uncertainty estimation provides a powerful mechanism for dynamically optimizing control performance-addressing a critical limitation of conventional adaptive algorithms, especially in uncertain environments. Additionally, we demonstrate that the proposed framework generalizes the widely used filtered-x least mean square algorithm as a special case. Numerical simulations and experimental results validate the effectiveness and robustness of the proposed approach.