ACTA ACUSTICA UNITED WITH ACUSTICA Vol. 98 (2012) 418 – 440 DOI 10.3813/AAA.918527 Acoustic Reflection Localization from Room Impulse Responses Sakari Tervo, Jukka Pätynen, Tapio Lokki Aalto University School of Science, Department of Media Technology, P.O. Box 15400, 00076 Aalto, Finland. Sakari.tervo@aalto.fi Summary The localization of acoustic reflections, i.e., the image-sources, is of interest when analyzing the acoustics of con- cert halls and auditoriums. The location is needed, for example, in room acoustic studies, auralization, inference of room geometry, or when estimating the acoustic properties of surfaces. This article studies the localization of acoustic reflections from spatial impulse responses. The contribution of this article is threefold. First, the article proposes a new method for localization that takes advantage of the time of arrival (TOA) estimation. Secondly, it is proposed that TOA and time difference of arrival (TDOA) information, present in the spatial room impulse responses, are combined in two novel ways. Thirdly, the performance of the proposed localization methods is compared to the existing state-of-the-art localization methods in the acoustic reflection localization task. Theo- retical performance is investigated and experiments using real and simulated data are conducted. The TOA-based methods are found to achieve reasonably good performance in the reflection localization task. When TOA and TDOA information is combined the performance clearly improves. PACS no. 43.60.Hg, 43.60.Jn 1. Introduction Location of acoustic reflections, i.e, the image-sources, is a useful piece of information in room acoustic studies, au- ralization, room geometry inference, and in-situ measure- ment of acoustical properties of surfaces from room im- pulse responses. The locations of the reflections can be used together with the sound source location to deduce the normals and the locations of the reflective surfaces [1, 2, 3], that is, to infer the room geometry. In addition, the location of the reflection is needed for accurate time win- dowing of the reflection from the room impulse response when estimating, for example, the absorption coefficient of the surface from in-situ measurements [4, 5]. Localization of acoustic reflections is often performed with methods developed for sound source localization. An overall framework of the methods, considered in this ar- ticle, is given in Figure 1 and in Table I. Many of the lo- calization methods are based on time difference of arrival (TDOA), which is the difference between the arrival times of a wave front at two sensor positions. In addition, meth- ods that are based on time of arrival (TOA), the time that the wave front takes to travel from the source to the re- ceiver location, have been presented for source localiza- tion. TOA is available when the signal of the sound source is known, for example, in a room impulse response. Re- cently, methods that combine the measurements (CM) of Received 26 August 2011, accepted 4 February 2012. TOA and TDOA have been introduced. In addition, some methods that use directly the received signals exist. The objective of this article is to evaluate which of the localization methods are best applicable for the localiza- tion of acoustic reflections from spatial room impulse re- sponses recorded with compact microphone arrays. The evaluation of the methods is done by theoretical compari- son with Cramér-Rao lower bound (CRLB), Monte-Carlo simulations, and real data experiments in two enclosures. The contribution of the article is the following. First, a new method for localization that takes advantage of TOA estimation is proposed. Second, it is proposed that TOA and TDOA information, present in the spatial room im- pulse responses, are combined in two novel ways. In the first combination approach, the TOA and TDOA estima- tion functions are combined by addition in the spatial do- main. In the second one, the estimation functions are first considered as pseudo-likelihoods and then combined by multiplication in the spatial domain. Third, the perfor- mance of the methods is compared to the existing state-of- the-art localization methods and studied in the reflection localization task. The rest of the paper is organized as follows. Research related to the localization methods applied in this article are presented in Section 2. The signal model for acoustic reflection localization is presented in Section 3. Methods for reflection localization are presented in Sections 4-6. Theoretical limits are yielded in Section 7. Simulation and real data experiments are conducted and discussed in Sec- tion 8. Finally, section 9 concludes the paper. 418 © S. Hirzel Verlag · EAA