Chair of
Multimedia Communications and Signal Processing
Prof. Dr.-Ing. André Kaup

Speed of sound and air temperature estimation

Field of activity: Multidimensional Signals and Systems Theory
Research topic: Multidimensional Signals and Systems
Staff:

In the context of the SCENIC project we have investigated the joint solution of two problems with strong relevance in multidimensional signal theory and array signal processing, i.e.,

 

Although these two problems are inherently connected, in most cases they are addressed separately by a two-step approach:

  1. the propagation speed is guessed from some a priori knowledge, e.g., the value for the speed of sound in standard air, or it is derived by measurmenets of the conditions of the propagation medium,
  2. the position of the target is obtained geometrically by means of range estimates derived from the observed time delays and the previously obtained value for the propagation speed.     

 

This two-step approach is not always favorable as in some applications the characteristics of the propagation medium might be unknown and additional invasive measurements undesired.
Thus, techniques have been proposed in order to solve both problems jointly by relying merely on the time delays observed at the sensor array, i.e., Time Of Arrival (TOA) or, in absence of source-receiver synchronization, Time Difference Of Arrivals (TDOA) .

In the following we give a brief description of the major results and achievements yielded by our research:

 

 

 


Source localization under temperature variations

The dependence of the speed of sound on the air temperature is well known in acoustics.

TDOA-based acoustic source localization requires accurate knowledge about speed of sound in order to convert time differences into range differences related by geometric constraints.

In uncontrolled scenarios, e.g., due to seasonal temperature variations or temperature variations in a room caused by waste heat from equipment or presence of people, the standard value for the speed of sound at 20 °C degrees might lead to unsatisfactory localization results.

In this case the deployment of extra temperature sensors is not always favorable and therefore the direct estimation of the actual speed of sound from TDOAs becomes a crucial part of the localization algorithm.

 

LMS has studied the effects of temperature variations on the localization accuracy.

It turned out that undesired temperature variations yield an error in the source distance estimation. The magnitude of the error depends on the array geometry as well as on the localization algorithm; the pictures below show a square microphone array and the corresponding 2D error distribution in cm.

 

array

 

error_map

In order to compensate for this error we proposed an efficient TDOA-based speed estimation algorithm that enables high localization accuracy even if temperature variations occur.

 


Estimation of air temperature from speed of sound estimates

The effectiveness of the proposed speed estimation algorithm has been shown by inferring the average air temperature of a room from the so-obtained speed of sound estimates. A demonstration of this technique was given during the Industry Day organized in Milan in the context of the SCENIC project.

 

thermo

 


Inference of room geometry with the aid of speed of sound estimation

Speed of sound estimates were also used in combination with a reflector localization technique developed by the Speech and Audio Processing Group of the Imperial College (London). The goal was to perform accurate room geometry inference regardless of the actual air temperature. The following pictures show the block diagram of the proposed approach and the obtained results for real measurements carried out in our laboratory.

 

schemageometry

 


Synthesis of consistent TDOA-graphs with the aid of speed of sound estimation

Everton-West Ham
This thesis focuses on the joint solution of two problems with strong relevance in several application fields, i.e.,
\begin{enumerate}
 \item the estimation of the speed of propagating waves, allowing a partial characterization of the propagation medium, and
 \item the estimation of the position of an emitting target from the time delays observed by a passive sensor array.  
\end{enumerate}

Although these two problems are inherently connected,
in most cases they are addressed separately by a two-step approach:
\begin{itemize}
 \item the propagation speed is guessed from some \emph{a priori} knowledge, e.g., the value for the speed of sound in standard air,
 or it is derived by measurmenets of the conditions of the propagation medium,
 \item the position of the target is obtained geometrically
 by means of range estimates derived from the observed time delays and the previously obtained value for the propagation speed.     
\end{itemize}

This two-step approach is not always favorable as in some applications the characteristics of the propagation medium might be unknown
and additional invasive measurements undesired.
Thus, techniques have been proposed in order to solve both problems jointly by relying merely on the time delays measured by the sensor array.
These approaches constitute the leading topic of this thesis.

Temperature dependency of source localization

Temperature dependency of source localization

Publications

2014-32
CRIS
Ladan Zamaninezhad, P. Annibale, R. Rabenstein
   [link]   [bib]

Localization of Environmental Reflectors from a Single Measured Transfer Function
IEEE Int. Symp. Communications, Control, and Signal Processing (ISCCSP), Pages: 157-160, Athens, Greece, May 2014
2014-12
CRIS
P. Annibale, R. Rabenstein
   [link]   [doi]   [bib]

Closed-Form Estimation of the Speed of Propagating Waves from Time Measurements
Springer Journal on Multidimensional Systems and Signal Processing (MDSSP) Vol. 25, Num. 2, Pages: 361-378, 2014
2013-36
CRIS
P. Annibale, R. Rabenstein, Martin Kreissig, Bin Yang
   [link]   [bib]

Joint consistent graph synthesis and speed of sound estimation for acoustic localization in multi-source reverberant environments
8th International Workshop on Multidimensional Systems (nDS 2013), Pages: 1-6, Erlangen, Germany, Sep. 2013
2013-11
CRIS
P. Annibale, J. Filos, P. A. Naylor, R. Rabenstein
   [link]   [doi]   [bib]

TDOA-based Speed of Sound Estimation for Air Temperature and Room Geometry Inference
IEEE Transactions on Audio, Speech and Language Processing (IEEE TASLP) Vol. 21, Num. 2, Pages: 234 - 246, Feb. 2013