Comparative study of microphone arrays comprising omnidirectional and first-order directional microphones applied to remote virtual sensing

Virtual sensing techniques have been variously investigated within the context of active noise control, and it has been demonstrated that accurate estimation is critical to active control performance. The current work aims to compare the performance and robustness of monitoring microphone arrays used for virtual sensing, comprising omnidirectional pressure sensors and microphones with first-order directivity characteristics. Configurations with the standard first-order directivity patterns, dipole, cardioid, hyper-cardioid and super-cardioid, and their combinations are investigated and compared to conventional arrays with omnidirectional microphones. The estimation is performed through the formulation of observation filters that project the measured responses to the estimate of the sound field at the position of virtual microphones, using the Remote Microphone Technique. The study explores the performance and robustness of the monitoring configurations when used to estimate the pressure in a diffuse sound field. A closed-form formulation of the problem is presented, and simulations are performed to validate the theoretical results.