Effects of simultaneous sound arrivals on direction-of-arrival estimates of the polar energy time curve

Acoustic reflections in rooms are best understood and controlled when their causal surfaces have been accurately localized. Several in situ measurement techniques have been proposed over the years to pinpoint reflections via estimated directions of arrival at chosen field positions. The polar energy time curve (Polar ETC) is one approach requiring six cardioid impulse response measurements along the Cartesian axes about a point in a room. This paper presents a theoretical, numerical, and experimental investigation of its estimation errors due to simultaneous sound arrivals. Theoretical developments provide insights into their causes. Numerical examples based on the method of images explore conditions leading to the errors and likely error magnitudes. Experimental work using discrete planar reflectors in an anechoic chamber produced controlled reflections to further investigate the effects. An altazimuth-mounted laser and mirrors enabled reflection tracing and a means of measuring and comparing arrival directions to those estimated by the Polar ETC. The efforts demonstrate that the Polar ETC provides credible angular estimations for individual arrivals, but spurious results for most simultaneous arrivals. Single arrivals produce absolute errors of only a few degrees, while simultaneous arrivals of similar amplitudes produce errors ranging sporadically from a few degrees to many degrees.