Estimation of Acoustic Reflection Coefficients Through Pseudospectrum Matching

Estimating the geometric and reflective properties of the environment is important for a wide range of applications of space-time audio processing, from acoustic scene analysis to room equalization and spatial audio rendering. In this manuscript, we propose a methodology for frequency-subband in-situ estimation of the reflection coefficients of planar surfaces. This is a rather challenging task, as the reflection coefficients depend on the frequency and the angle of incidence and their estimate is highly sensitive to background noise and interfering sources. Our method is based on the assumption that we know the geometry of the reflectors; the position and the radiation pattern of the source; the position and the spatial response of the array. Applying beamforming algorithms on a single set of measured sensor data, we estimate the angular distribution of the acoustic energy (angular pseudospectrum) that impinges on a microphone array. We then apply a two-step iterative estimation technique based on an Expectation-Maximization (EM) algorithm. The first step estimates the scaling factors. The second one infers the reflection coefficients from the scaling factors. Under the assumption of additive white Gaussian noise, we finally determine the reflection coefficients with a Maximum Likelihood (ML) estimation method. The effectiveness and the accuracy of the proposed technique are assessed through experiments based on measured data.