Wireless Communications and Mobile Computing

Volume 2017 (2017), Article ID 9524943, 17 pages

https://doi.org/10.1155/2017/9524943

## Acoustic Source Localization under Variable Speed of Sound Conditions

^{1}Chair for Multimedia Communications and Signal Processing, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany^{2}International Audio Laboratories, Fraunhofer-IIS, Erlangen, Germany

Correspondence should be addressed to Rudolf Rabenstein

Received 19 May 2017; Revised 14 July 2017; Accepted 1 August 2017; Published 17 October 2017

Academic Editor: Fabio Antonacci

Copyright © 2017 Rudolf Rabenstein and Paolo Annibale. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The rich literature on acoustic source localization mostly relies on the assumption of a constant value for the speed of sound. This hypothesis allows establishing simple relations between range differences and time differences and leads to effective estimation algorithms. However, it must be challenged for certain applications of wireless acoustic sensor networks in multizone buildings and outdoor environments. This article revisits the source localization problem for the more general case of an unknown value for the speed of sound. It reviews the physical foundations for the dependence of the speed of sound on the air temperature and presents the essential approaches to acoustic source localization. On this basis, several methods for source localization under uncertain or variable speed of sound conditions from the literature are discussed. Applications from different fields are shown. They comprise the localization of sources, sensors, and reflecting surfaces, time-difference-of-arrival disambiguation, and the direct determination of the speed of sound or the air temperature from acoustic measurements.

#### 1. Introduction

Acoustic sensor networks attempt to record one or more desired sound sources in the presence of other unwanted sources. These unwanted sources may be competing sources, noise sources, or reflections thereof. A popular way to distinguish between desired and unwanted sources is by their direction or location. For mirrored reflections also the reflector position may be of interest. The localization of sound sources provides information to enhance the desired source and to attenuate unwanted sources by beamforming techniques [1]. Source localization is also a topic in its own right for the analysis of acoustic scenes or for tracking of sound sources.

Several methods for source localization from multimicrophone recordings are available [2]. Among these, the classical time-of-arrival (TOA) and time-difference-of-arrival (TDOA) methods are still competitive due to their computational simplicity and reasonable performance. This property carries over to wireless acoustic sensor networks where the computing power is restricted by hardware and energy constraints.

Both TOA- and TDOA-methods estimate time differences between source and receiver or between receivers and convert them to range differences. The conversion factor is the propagation speed of the sound waves or briefly the speed of sound. In many applications it is considered to be constant. This choice is derived from the historical roots of TDOA-methods (and similar for TOA) in phased array antennas. There, the corresponding conversion factor is the propagation speed of electromagnetic waves in the earth’s atmosphere which is not subject to appreciable environmental influence.

The corresponding assumption of a constant speed of sound is also justified for indoor applications under controlled environmental conditions, in particular for constant room temperature. Typical applications are laboratory environments or office spaces for video and speech communications. However, wireless acoustic sensor networks have potential outdoor applications where the air temperature may be subject to considerable daily or seasonal variations. Also large temperature variations along the propagation path are conceivable for communication in spaces with extreme working conditions like steel mills or cold storage houses.

The fact that environmental conditions may affect wave propagation strongly is well known from underwater acoustics. Here the variation of the salinity degree in ocean water leads to nonstraight propagation paths and multiple reflections at the water surface [3–6]. Are similar effects possible also for outdoor sound propagation and how would TDOA measurements be affected?

This article reviews the effect of temperature variations on sound propagation in air and further on the accuracy of source localization with acoustic sensors. These results are of interest also to wireless acoustic sensor networks where synchronization between all sensors is not guaranteed.

Wireless networks have received considerable attention in the recent literature. A hierarchical approach has been presented in [7] where a distributed network consists of multiple compact arrays, the so-called network nodes. The microphones in each node are synchronized and allow TDOA estimates but there is no synchronization between the nodes. Ranging and self-positioning in wireless acoustic sensor networks are considered in [8]. Here active nodes with one microphone and one loudspeaker each permit TOA estimation by emitting test signals. The nodes are not synchronized among each other. A similar problem is addressed in [9] where TDOA estimates with unknown time offset are used. The special problems of low-cost wireless acoustic sensor networks are discussed in [10]. Here a statistical framework is invoked to provide an efficient localization algorithm. Unsynchronized communication between wireless acoustic sensors is studied in [11] where bearing-only information is exchanged between the network nodes. In all these cases, the conversion from time delay estimates to range estimates (where required) is based on the assumption of a common and known speed of sound.

This limiting assumption is dropped here and the consequences for source localization are investigated. This article is an extended version of a slide presentation at [12]. It is structured as follows: Section 2 gives a brief overview on delay-based source localization. Then Section 3 investigates the influence of the propagation speed on the shape of the propagation path and on the travelled distance of sound waves. Section 4 discusses the mathematical formulation of the TDOA-based source localization problem in some detail. This formulation is extended in Section 5 to include the propagation speed as an additional unknown in the estimation process. Some applications from the literature are reviewed in Section 6 before Section 7 concludes the article.

#### 2. Delay-Based Localization of a Sound Source

This section reviews briefly the foundations of delay-based localization. It is meant to be a first introduction to the basic idea. A more profound discussion follows in Section 4. The topic is also well covered in the literature; see, for example, [1, 2, 13–17].

Figure 1 shows on the left a point-like sound source. Its sound waves are recorded by four microphones in an arbitrary geometric arrangement. All four microphones record the same waveform , but with a slightly different time delay according to their individual distance from the source. An example for the resulting microphone signals is shown on the right hand side.