Direction of Arrival Algorithm for Acoustic Sensors Operating Near Resonance

Recently, it has been possible to detect sound direction using phase-sensitive sensors placed much closer to each other than the sound wavelength. A typical setup combines two phase-sensitive sensors placed perpendicular to each other with a third omnidirectional sensor, the latter to determine the bearing quadrant. So far, algorithms that extract the sound direction from the sensor voltages have only been applicable to sensors with identical frequency responses. However, we have developed microelectromechanical systems (MEMS) sensors with simple harmonic oscillator-like resonance behavior for which these algorithms no longer apply. The operation near resonance greatly increases their performance, but the frequency dependencies of any two sensors are different from each other and from the omnidirectional sensor. In this letter, we show how to accommodate these differences, first, by forcing the two sensor peaks to conform to each other in both magnitude and phase, and second, by adjusting the phase of the omnidirectional sensor to approximately match the phases of the resonant sensors near their resonant frequencies. We then present two algorithms to extract the sound direction. We lay out the theoretical basis for our algorithms and present measurements of acoustic noise to show the algorithms’ effectiveness.