Causality and Robustness in the Remote Sensing of Acoustic Pressure, with Application to Local Active Sound Control

It is often difficult to position microphones at the ear position of listeners to directly monitor the perceived sound, in local active sound control systems for example. The pressure at these positions can be estimated using virtual sensing with an array of remote monitoring microphones, however, if some assumptions are made about the sound field. In active control, the sound field due to the secondary sources can be reasonably easily accounted for but the primary sound field, which is to be controlled, will in general be due to a number of potentially correlated primary sources, whose positions are unknown and may vary in time. The virtual sensing in this application thus needs to be robust to the properties of the primary sound field, both in the choice of the remote monitoring microphone positions and in the design of the filters used to process these to estimate the pressure at the desired position. If the controller is feedforward, the causality of these filters may also be relaxed if the adaptive algorithm is designed to minimise a delayed virtual error signal. This paper describes examples of such robust design, particularly applied to the local active control of road noise in vehicles.