Addressing modelling errors in feedforward ANC systems: a new normalised semi-variable step size FxLMS algorithm

Despite the potential of active noise control (ANC) technology, its full utilisation remains a subject of ongoing research, particularly for environments as critical as intensive care units (ICUs), where noise reduction is an overwhelming and pressing concern. Conventional ANC systems, employing filtered-x least mean square (FxLMS) based algorithms, often face challenges balancing convergence speed and achievable noise attenuation, especially in high-noise settings like ICUs. To address this challenge and enhance the performance of ANC systems in noisy environments, the normalised semi-variable step size filtered-x LMS (NSVSS-FxLMS) algorithm is proposed in this paper. The step size of the proposed algorithm is changing corresponding to the power ratio of the primary input noise and desired signals modelling error, and the norm squared of the filter weight vector. Since the power ratio is not available directly, an indirect approach is used to track its variations using a hyperbolic function. This enables the algorithm to achieve a rapid initial convergence and then to smoothly transition for minor adjustments, thereby maintaining an adaptive steady state which could significantly improve the performance of the ANC system. Comparative analysis, conducted using narrowband and broadband noise signals recorded in ICUs and impulsive noise, illustrates the potential of the proposed adaptive algorithm against the existing fixed-step algorithms. The results demonstrate not only superior noise reduction but also improved convergence speed, indicating a potential for advancement in addressing noise challenges within ICUs.