An online modeling virtual sensing technique based on kriging interpolation for active noise control

Combined with virtual sensing techniques, active noise control can generate quiet zones in places without error microphones. Many existing virtual sensing techniques require pretraining of the system with physical microphones placed temporarily at the control location as well as retraining if the primary sound field or the secondary paths change. This process responds slowly and is infeasible in many application scenarios. In this paper, we propose a virtual sensing technique based on kriging interpolation, which gives an unbiased sound pressure estimator with minimum variance, assuming the spatial correlation model. The proposed method only depends on the distances between physical and virtual microphones and does not depend on the prior information of the primary noise field, implying that the method naturally tracks the variations of the noise sources. Further, when the secondary paths change due to variations in the secondary sources or the position of the virtual microphones, we combine the virtual sensing technique with a secondary path online modeling method, which enables the system to track the time-varying secondary paths and thus ensure the convergence of the active noise control system.