Map estimation of driving signals of loudspeakers for sound field reproduction from pressure measurements

Sound field reproduction methods calculate driving signals of loudspeakers to reproduce the desired sound field. In common recording and reproduction systems, sound pressures at multiple positions obtained in a recording room are only known as the desired sound field; therefore, signal transformation algorithms from sound pressures into driving signals (SP-DS conversion) are necessary. Although several SP-DS conversion methods have been proposed, they do not take into account a priori information about the recorded sound field. However, approximate positions of sound sources can be obtained by using the received signals of microphones or other sensor data. We propose an SP-DS conversion method based on the maximum a posteriori (MAP) estimation when array configurations of the microphones and loudspeakers are planar or linear. The optimal basis functions and their coefficients for representing driving signals of the loudspeakers are optimized based on the prior information of the source positions. Numerical simulation results indicate that the proposed method can achieve higher reproduction accuracy compared to the current SP-DS conversion methods, especially in higher frequencies above the spatial Nyquist frequency.