Optimal estimation of acoustic intensity from pressure in the presence of mean flow

Abstract

Bayesian minimum mean-squared error (MMSE) estimators are constructed for obtaining pressure, velocity, and intensity in the near- or far-field of an extended acoustic source from near-field pressure measurements alone, in the presence of noise and mean flow. In the absence of mean flow, there is a unique relation between the local pressure gradient and the local velocity, but in the presence of mean flow this uniqueness is destroyed [D. Munro and K. Ingard, ‘‘On acoustic intensity measurements in the presence of mean flow,’’ J. Acoust. Soc. Am. 65, 1402–1406 (1979)]. This nonuniqueness makes an exact reconstruction of the velocity and intensity fields impossible, even in the absence of noise; however, accurate approximate reconstruction may be accomplished with a sufficient array of receivers. The MMSE estimation framework provides a prediction of the estimation accuracy which may be used to assess the sufficiency of a given pressure sensor array. Numerical examples of array performance assessment are presented for intensity estimation in the near field of an extended source in mean flows of Mach 0 to 0.8.