Interpolation between plant responses in a head-tracked local active noise control headrest system

Abstract

Active Noise Control (ANC) headrest systems reduce noise at the listener’s ears, but their performance can degrade with user movement. Integrating head-tracking into Local ANC systems improves performance over a wider frequency range by updating the controller for different head positions and orientations. However, practical implementations often rely on a limited set of pre-calibrated system response models, resulting in mismatches between actual and modelled head positions. Increasing the resolution of the measurement grid can mitigate this, but increases the complexity of pre-calibration. This study investigates interpolation strategies – such as inverse distance weighting, high-degree and cubic spline interpolation – to estimate plant responses between pre-calibrated positions and improve control performance. The effects of interpolation are analysed by evaluating the condition number and noise reduction achieved, with separate interpolation applied for head translations and rotations. The findings show that accurate methods, such as cubic spline and high-degree interpolation, produce more accurate plant models, which improve controller robustness, particularly at higher frequencies. In addition, frequency-dependent regularisation maximises control performance, with accurate interpolation requiring less regularisation to achieve greater noise reduction. These findings highlight the importance of selecting appropriate interpolation methods and strategic pre-calibration grid designs to ensure effective ANC system performance.