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Sep 14, 2016 - International Workshop on Acoustic Signal Enhancement. IWAENC 2016, Xi'an ... Chair for Multimedia Communications and Signal Processing.
Acoustic Signal Enhancement under Variable Speed of Sound Conditions Keynote presentation International Workshop on Acoustic Signal Enhancement IWAENC 2016, Xi’an, China (revised version) Rudolf Rabenstein and Paolo Annibale [email protected] [email protected] Chair for Multimedia Communications and Signal Processing Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany Sept. 14, 2016

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R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

0 -2 Sept. 14, 2016

Contents

I Introduction I Foundations from Physics I Source Localization I Estimation of the Propagation Speed I Applications I Conclusion I Literature

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

0 -3 Sept. 14, 2016

1 Introduction

Introduction

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

1 -1 Sept. 14, 2016

1 Introduction

Methods for acoustic signal enhancement require the localization of acoustic sources I

desired and competing sources

I

noise sources

I

mirror sources

I

position of reflectors

under a variety of operating conditions. Special focus here: temperature variations I

indoor and outdoor

I

day and night

I

seasonal variations

I

extreme working conditions R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

1 -2 Sept. 14, 2016

1 Introduction Delay-based localization of a sound source

p0 (t)

y

t

t0 p1 (t)

t

t1

1 p2 (t)

t

t2

x p3 (t) 3

0

2

t

t3 I

Estimate time differences

I

between source and receiver (time of arrival, TOA)

I

between receivers (time difference of arrival, TDOA)

I

turn estimated time delays into range differences

I

infer source position from range differences

The estimation of the arrival times is not as easy as it may look here!

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

1 -3 Sept. 14, 2016

2 Foundations from Physics

Foundations from Physics

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

2 -1 Sept. 14, 2016

2 Foundations from Physics Relation between travel time and travelled distance The relation between

r0

I

I I

travelled distance and the travel time

of sound waves is determined by the acoustic wave equation. I

From the acoustic wave equation follows under certain conditions the eikonal equation (see e.g. [1]).

I

It describes the shape of the propagation path.

I

Travel time ∆t between source and receiver: dρ c(ρ) = dt

∆t ∆r ρ

Z

r1

∆t = r0

1 dρ = c(ρ)

travel time c(ρ) 1 distance a(ρ) = c(ρ) coordinate along the propagation path

Z

r1

a(ρ) dρ

ρ

r0

propagation speed slowness

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

r1

2 -2 Sept. 14, 2016

2 Foundations from Physics Propagation speed The relation for the travel time

Z

r1

∆t = r0

1 dρ c(ρ)

is trivial if the propagation speed is constant c = const ∆t = Indeed, most papers assume

1 1 (r1 − r0 ) = ∆r c c c = 343 ms = const

or similar values.

However, the propagation speed I

depends on the air temperature and (to a lesser extent) on humidity,

I

may vary along the propagation path,

I

may vary with time at a fixed location. R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

2 -3 Sept. 14, 2016

2 Foundations from Physics Dependence of the speed of sound on the air temperature For a specific gas c(T ) =



γs Rs T ∼

√ T

T absolute temperature γs ratio of specific heat capacities, adiabatic index Rs specific gas constant I I

Celsius scale ϑ = T − T0 with the zero point T0 = 273.15 K Taylor expansion around the zero point gives a linear approximation c(ϑ) ≈

For dry air

γs = 1.40,





γs Rs T0 1 +

1 ϑ 2 T0 2

Rs = 287.1 ms2

at room temperature ϑ = 20◦C

1 , K



= c0 + c1 ϑ c0 = 331 ms ,

c (20◦C) = 343 ms

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

c1 = 0.6 ms ◦1C X 2 -4 Sept. 14, 2016

2 Foundations from Physics

speed of sound in m/s

370 room temperature

360

I

350

The linear approximation is a good fit to the square root.

zero point c(ϑ) = c0 + c1 ϑ

340 I

Considerable variation of the speed of sound.

I

Temperature sensitivity

330 320

-20

-10

0

linear approximation √ T 10 20 30 40

50

dc = c1 = 0.6 ms ◦1C dϑ

temperature in ◦C

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

2 -5 Sept. 14, 2016

2 Foundations from Physics Shape of the propagation path The curvature κ of the propagation path follows from the eikonal equation

R d 2

sin

α

` d 2

d/2 α = 2 R ` α= R

R

κ=

c0 (ρ) 1 =− R c(ρ) dc0 (ρ) d speed variation =− ≈ R c(ρ) mean speed

example: d ` = arcsin 2R 2R

 `=d 1+ ∆d 1 = d 24

1 24

 2 d R

arcsin x ≈ x +

 2  d R

1 3 x 6

` ∆d =1+ d d

ϑ 0◦ C 20◦ C

c(ϑ) 331 ms 343 ms

d 12 ≈− = −0.036, R 337

∆d ≈ 5 · 10−5 d

Propagation along a straight line is a very good approximation!

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

2 -6 Sept. 14, 2016

2 Foundations from Physics

What do we learn from physics? The travel time between source and receiver depends on I

the length of the propagation path

I

the speed of sound along the propagation path

For temperature variations as experienced by human users I

the propagation path is a straight line (almost)

I

variations in the propagation speed may require consideration

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

2 -7 Sept. 14, 2016

2 Foundations from Physics What is “the propagation speed”? Reconsider the relation for the travel time

Z

r1

∆t = r0

1 dr c(r)

for constant propagation speed c(r) = c = const ∆t =

1 1 (r1 − r0 ) = ∆r c c

otherwise introduce a mean propagation speed ∆t =

1 ∆r c¯

where

1 1 = c¯ ∆r

Z

r1

r0

1 dr c(r)

In the sequel, the notation “propagation speed c” is used in lieu of the mean propagation speed c¯. R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

2 -8 Sept. 14, 2016

2 Foundations from Physics

Different levels of assumptions: 1. The propagation speed is constant with respect to time and space and its value is known. This assumption is adopted in most of the literature. 2. The propagation speed is constant with respect to space and also with respect to time during a short measurement period. Its actual value is unknown. This case is considered in a few publications. 3. The propagation speed is constant with respect to time during a short measurement period but it may vary in an unknown way along the propagation path. This case can be reduced to assumption 2 by considering the mean propagation speed.

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

2 -9 Sept. 14, 2016

3 Source Localization

Source Localization

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -1 Sept. 14, 2016

3 Source Localization y

Source position ↑ range differences ↑ time differences

1

x 3

0

2

Estimate time differences I

between source and receiver (time of arrival, TOA) requires synchronization between source and receivers

I

between receivers (time difference of arrival, TDOA) no synchronization required

Focus here on TDOA methods, similar for TOA. R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -2 Sept. 14, 2016

3 Source Localization Time difference of arrival (TDOAs): y I

I

definition arrival time at sensor i arrival time at sensor j time difference of arrival

τ0,3 τ0,2

ti tj τij = ti − tj

1

simple properties τij = 0

for

j=i

τji = −τij

x 3

0

2

redundant TDOA matrix



τ0,1 τ0,2 τ0,3



  τ1,0 0 τ1,2 τ1,3   τ2,0 τ2,1 0 τ2,3 

    

0

τ3,0 τ3,1 τ3,2

0

I

The elements on the main diagonal are zero.

I

The elements in the upper triangle are equal to the lower triangle up to a sign change.

I

The elements in the lower triangle are sufficient. (Full TDOA set)

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -3 Sept. 14, 2016

3 Source Localization Graph representation of TDOAs weighted and directed graph

y

τ3,0 τ2,0

1

1

τ3,1

τ2,1

τ1,0 0

x 3

0

τ3,0 3

2

τ2,0 τ3,2

2

cyclic sum property: follow the blue path −τ2,0 + τ2,1 + τ1,0 = −(t2 − t0 ) + (t2 − t1 ) + (t1 − t0 ) = −t2 + t0 + t2 − t1 + t1 − t0 = 0 or

τ2,1 = τ2,0 − τ1,0

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -4 Sept. 14, 2016

3 Source Localization 1 Full TDOA set and spherical TDOA set Similar for the other outer edges:

τ3,1

τ2,1

τ1,0

τ2,1 = τ2,0 − τ1,0 0

τ3,1 = τ3,0 − τ1,0 τ3,0

τ3,2 = τ3,0 − τ2,0 3 redundant TDOA matrix



τ0,1 τ0,2 τ0,3



  τ1,0 0 τ1,2 τ1,3   τ2,0 τ2,1 0 τ2,3 

    

0

τ3,0 τ3,1 τ3,2

0

τ2,0 τ3,2

2

I

Under ideal conditions (no noise, constant speed of sound) also the full TDOA set is redundant.

I

The elements in the first column of the lower triangle are sufficient. (Spherical TDOA set)

I

Microphone 0 is chosen as the reference microphone.

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -5 Sept. 14, 2016

3 Source Localization

TDOA-based source localization General procedure (subject to many variations) I

estimate TDOAs between different microphone locations,

I

calculate range differences from time differences,

I

establish geometrical relations between sensor locations and estimated range differences,

I

turn these gemetrical relations into a system of equations,

I

simplify this system of equations, if necessary and possible,

I

make assumptions on different kinds of noise,

I

estimate the source positions from the simplified system of equations.

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -6 Sept. 14, 2016

3 Source Localization y

x

||x || x



The square of this relation gives

d2,0

ai T x + di,0 ||x|| =

a2

||



x

I

a0

I



a1 T  .. Φ= . aN T

d1,0 ..  .  dN,0

a2

Relate time differences and range differences by a constant speed c c τi,0 = di,0 ,



or in matrix notation

a1

||

a3

||ai ||2 − d2i,0

1 2

 y(x) =

x ||x||





||a1 ||2 − d21,0 1  .. b=   . 2 2 2 ||aN || − dN,0

 Φy(x) = b

i = 1, . . . , N I

The presence of both x and ||x|| makes the system of equations nonlinear.

I

With noise: nonlinear estimation

The unknown source position x must satisfy di,0 = ||x − ai || − ||x||

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -7 Sept. 14, 2016

3 Source Localization Popular approaches for solving the estimation problem A linear problem results by replacing

 Φ

Unconstrained least squares method (ULS) Solve (1) with the pseudo-inverse Φ†



x =b ||x||

  yˆ =

by

  Φ

x =b r

(1)

ˆ as position estimate, accept x and disregard rˆ. Constrained least squares method (CLS)

with the contraint r = ||x||

ˆ x = (ΦT Φ)−1 ΦT b = Φ† b, rˆ

(2)

Exploit the constraint (2), e.g. by minimizing the residual error



(x) = Φ y(x) − y ˆ . R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

3 -8 Sept. 14, 2016

4 Estimation of the Propagation Speed

Estimation of the Propagation Speed

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -1 Sept. 14, 2016

4 Estimation of the Propagation Speed What for? I

Robust source localization

I

TDOA disambiguation

I

Array calibration

I

Estimate the numerical value of the speed of sound

I

Estimate the mean air temperature

How? I

Extension of the ULS method

I

Plane wave approximation

I

Exploit the constraint of the ULS method

I

Exploit the residual term of the CLS method

I

Exploit the full TDOA set

I

Exploit multiple sources

I

Extend to uncertain sensor positions R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -2 Sept. 14, 2016

4 Estimation of the Propagation Speed

General procedure Build the linear problem in different ways as Φ y(x, c) = b(c)

where Φ contains

b(c) may contain

I

known sensor positions ai ,

I

known sensor positions ai ,

I

measured TDOAs τij .

I

measured TDOAs τij ,

I

unknown propagation speed c.

y(x, c) contains I

unknown source position x,

I

unknown propagation speed c.

Various approaches are presented in detail on the following slides.

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -3 Sept. 14, 2016

4 Estimation of the Propagation Speed Extension of the ULS method [2, 3, 4] Write the square of x y(x, c) = c||x|| c2

"

di,0 = ||x − ai || − ||x|| in the form ai T x+di,0 ||x||+ 21 d2i,0 = 12 ||ai ||2 and replace range differences by time differences di,0 = cτi,0 2 ai T x+cτi,0 ||x||+ 21 c2 τi,0 = 12 ||ai ||2 .

Matrix notation



a1 T  .. Φ= . aN T

τ1,0 .. . τN,0

1 2 τ 2 1,0



..  .  1 2 τ 2 N,0

#





||a1 ||2 1 .  b =  ..  2 ||aN ||2

Obtain from the unconstrained solution ˆ x yˆ = yˆ3 = Φ† b yˆ4

" #

estimates for the position

ˆ x

and the speed

cˆ =

p

yˆ4 .

Caveat: Φ might be ill-conditioned.

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -4 Sept. 14, 2016

4 Estimation of the Propagation Speed Plane wave approximation [5] Matrix notation

y



a1 u

d2,0 x

a3

a0

a2

no source position, only a unit vector u





a1 T  ..  Φ =  . , aN T

y(u, c) = 1c u,

Φy(u, c) = b ˆ= u

1 yˆ ˆ ||y||



τ1,0  .  b = −  ..  τN,0 yˆ = Φ† b 1 cˆ = ˆ ||y||

Works well for plane waves, erroneous estimates for nearby sources.

ai T u = −di,0 = −cτi,0 ai T

1 u c

= −τi,0 R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -5 Sept. 14, 2016

4 Estimation of the Propagation Speed Exploit the constraint of the ULS method [6, 7, 8]





ˆ x(c) = Φ† (c) b(c) = rˆ(c)

ˆ y(c) =





Γ b(c) 1 Θ c

exploit the constraint

with the pseudo-inverses of the projection matrices

1 Θb → 0 c

ˆ δ(c) = ||x(c)|| − rˆ(c) = ||Γb|| − ˆ 2 = rˆ2 squaring both sides: ||x||

Γ = (Pτ⊥0 A)† Θ = (PA⊥ τ0 )†

∆(c2 ) = c2 (Γb)T (Γb) − (Θb)T (Θb) = 0

and the first-order polynomial in c2

 b(c) =

1 2

2

||a1 || ..  2 . −c ||aN ||2

 





1 2

2 τ1,0



 ..   .  2 τN,0

I

∆(c2 ) is a cubic polynomial in c2

I

can be solved in closed form for values of c which satisfy the ˆ constraint ||x(c)|| = rˆ(c)

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -6 Sept. 14, 2016

4 Estimation of the Propagation Speed Exploit the constraint of the ULS method by a linear approximation [9] To minimize the constraint ˆ δ(c) = ||x(c)|| − rˆ(c) = ||Γb|| −

1 Θb, c

δ(c) and δlin (c) for an actual temperature of 33 ◦ C

δ(c) ≈ δlin (c) = δ¯ + δ¯0 (c − c¯) around a suitable value c¯, e.g. c¯ = 343 ms at room temperature.

δ(c) in m

expand δ(c) into a Taylor series

Then estimate the speed of sound as cˆ =

δ¯0 c¯ − δ¯ δ¯0

temperature in ◦C

δ¯ and δ¯0 follow from Γ and Θ. R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -7 Sept. 14, 2016

4 Estimation of the Propagation Speed Exploit the full TDOA set [9] Exploit the redundancy in the full TDOA set for a better estimate of the speed of sound cˆ by using different reference microphones j = 0, . . . , N spherical TDOA set

full TDOA set

j=0

j = 0, . . . , N

δ0 (c) = ||xˆ0 (c)|| − rˆ0 (c)

N X j=0

δ¯0 c¯ − δ¯0 cˆ = 0 0 δ¯0

δj2 (c) =

N X

||xˆj (c)|| − rˆj (c)

2

j=0

¯ cˆ = (δ¯0 )† (δ¯0 c¯ − δ)





δ¯0 (c)  ..  ¯ δ =  . , δ¯N (c) R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany





δ¯00 (c)  .  δ¯0 =  ..  0 δ¯N (c) 4 -8 Sept. 14, 2016

4 Estimation of the Propagation Speed

Exploit multiple sources [9] I

The full TDOA set is not always available, e.g. when the TDOAs are estimated from measured acoustic room impulse responses.

I

Apply the same principle as above, but replace I I

TDOA sets for different reference microphones by TDOA sets for different sources.

multiple reference mics j = 0, . . . , N N X j=0

δj2 (c) =

N X

2

ˆ j (c)|| − rˆj (c) ||x

j=0

ˆ j (c), rˆj (c): distance between x single source and reference mic j

multiple sources q = 0, . . . , Q Q X q=0

δq2 (c) =

Q X

2

ˆ q (c)|| − rˆq (c) ||x

q=0

ˆ q (c), rˆq (c): distance between x source q and single reference

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 -9 Sept. 14, 2016

4 Estimation of the Propagation Speed Extend to uncertain sensor positions [10] Start with the unconstrained LS method (ULS)



a1 T  .. Φ= . aN T ∆

τ1,0 .. . τN,0

1 2 τ 2 1,0



..  . , 1 2 τ 2 N,0

Φy = b + ∆ + n

x y(x, c) = c||x|| , c2

sensor position error

"

n

#





||a1 ||2 1 .  b =  ..  , 2 ||aN ||2

sensor noise

Establish the cost function J(x, c) = (Φy − b)T Σ−1 (Φy − b)

Σ

error and noise covar. matrix

Minimize the cost function by a bi-iterative procedure min J(x, c) x

min J(x, c) c

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

4 - 10 Sept. 14, 2016

5 Applications

Applications

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

5 -1 Sept. 14, 2016

5 Applications

I

Improvement of localization results I

source or sensor localization

I

reflector localization

I

TDOA disambiguation

I

determination of the mean air temperature along the propagation path

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

5 -2 Sept. 14, 2016

5 Applications Improvement of sensor localization [8] title 3.5

3 2

4

3

1 3

2.5 4

2

2 y

1 1.5

1

loudspeaker pos. microphone pos. estimated pos.(c at 20° C) estimated pos.(c estimated)

0.5

0 −1

I

six loudspeakers with known positions

I

four microphones to be localized

I



temperature unknown (actually 27 C)

−0.5

0

0.5

1 x

1.5

2

2.5

3

position estimates for values of c I

assumed at 20◦ C



I

estimated



R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

5 -3 Sept. 14, 2016

5 Applications Improvement of reflector localization [9] Find the reflecting walls of a rectangular room

4 estimated wall (estimated speed) microphone loudspeaker estimated wall (assumed speed) actual wall

3.5

3

2.5

I

microphone positions known

I

loudspeaker positions known

I

reflector positions unkown

I

temperature unkown (actually 23◦ C)

y

2

1.5

wall positions 1

I

0.5

0

−0.5 −0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

I

actual assumed c = 375 ms

I

estimated c = 345 ms

Larger rooms are more sensitive to temperature variations.

x

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

5 -4 Sept. 14, 2016

5 Applications TDOA disambiguation [9] Determine TDOAs from generalized cross correlations (GCC)

TDOA ambiguity problem: In multi-source and reverberant environments GCCs show many extrema many TDOA candidates! (ambiguity)

TDOA disambiguation excludes correlations I

due to self similarity

I

from reflections

keeps only direct path TDOAs R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

5 -5 Sept. 14, 2016

5 Applications Existing approaches to TDOA disambiguation are based on I

I

correlation among the outputs of BSS algorithms [11] statistical models of the acoustical propagation delay [12, 13]

I

consistent graph synthesis (zero-cyclic sum condition) [14, 15]

I

speed of sound estimation [5]

Different kinds of drawbacks: I

high computational cost

I

reflections are not detected

I

speed of sound only for plane waves

Suitable combination I

consistent graph synthesis removes all correlations which do not satisfy the zero-cyclic sum conditions, i.e. keeps only direct and reflected path TDOAs

I

speed of sound estimation removes reflected path TDOAs i.e. only direct path TDOAs are left!

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

5 -6 Sept. 14, 2016

5 Applications

y

temperature in ◦C

Determination of the mean air temperature [9]

44 42 40 38 36 34 32 30 28 26 24 22 20 18

I

10 microphones (white circles)

I

one of 48 loudspeakers in a circular array

I

electric heater

I

speed of sound based temperature estimation with 10 microphones and one loudspeaker

proposed method ULS extended (plane wave)

I

I

I

0

45

90

135

180

225

x angle in degrees

270

315

constraint of ULS with linearization and full TDOA set plane wave approach

experiment conducted twice at 22◦C and 27◦C (point sensor)

360

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6 Conclusion

Conclusion

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

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6 Conclusion Variations of the speed of sound may affect source localization from microphone recordings I

Neglegible in controlled environments (air conditioning)

I

Otherwise, two possible effects I I

curvature of the propagation path (negegible) unknown relation between time differences and range differences

I

speed of sound: additional unknown variable in algorithms for position estimation

I

variety of methods for positions estimation under variable speed of sound conditions

I

increasing importance with new applications of acoustic signal enhancement: I I I I

mobile devices for mixed indoor/outdoor use outdoor devices robust against day/night or seasonal variations speech controlled aerial vehicles speech driven robots to assist steel workers or fire fighters R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

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6 Conclusion

New research possibilities

I

comparisons of the different estimation methods

I

experimental validation for different applications

I

comparison with related work in underwater acoustics

I

effect of speed of sound variations on source localization in spherical coordinates

I

etc.

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

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Thank You!

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

7 -1 Sept. 14, 2016

8 Literature

Literature

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

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8 Literature

I

[1]

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[2]

C. W. Reed, R. Hudson, and K. Yao, “Direct joint source localization and propagation speed estimation,” in Proc. of Int. Conf. on Acoustics, Speech and Signal Processing, (ICASSP), vol. 3. IEEE, 1999, pp. 1169–1172.

[3]

A. Mahajan and M. Walworth, “3-D position sensing using the differences in the time-of-flight from a wave source to various receivers,” IEEE Trans. on Speech and Audio Processing, vol. 17, no. 1, pp. 91–94, 2001.

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J. Zheng, K. W. K. Lui, and H. C. So, “Accurate three-step algorithm for joint source position and propagation speed estimation,” Signal Processing, vol. 87, pp. 3096–3100, December 2007. [Online]. Available: http://dx.doi.org/10.1016/j.sigpro.2007.06.014

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J.-S. Hu and C.-H. Yang, “Estimation of sound source number and directions under a multisource reverberant environment,” EURASIP Journal on Advances in Signal Processing, vol. 2010, no. 1, p. 870756, 2010, article ID 870756.

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J. Chen, K. Yao, T. Tung, C. Reed, and D. Chen, “Source localization and tracking of a wideband source using a randomly distributed beamforming sensor array,” Int. Journal of High Performance Computing Applications, vol. 16, no. 3, pp. 259–272, 2002.

R. Rabenstein and P. Annibale: Variable Speed of Sound Conditions Friedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg (FAU), Germany

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II

[7]

A. Oyzerman and A. Amar, “An extended spherical-intersection method for acoustic sensor network localization with unknown propagation speed,” in Proc. of IEEE 27th Convention of Electrical Electronics Engineers in Israel (IEEEI), Nov. 2012, pp. 1 –4.

[8]

P. Annibale and R. Rabenstein, “Closed-Form Estimation of the Speed of Propagating Waves from Time Measurements,” Multidimensional Systems and Signal Processing, vol. 25, no. 2, p. 361–378, April 2014.

[9]

P. Annibale, J. Filos, P. A. Naylor, and R. Rabenstein, “TDOA-based speed of sound estimation for air temperature and room geometry inference,” IEEE Trans. on Audio, Speech, Language and Signal Processing, vol. 21, no. 2, pp. 234 – 246, February 2013.

[10] G.-H. Zhu, D.-Z. Feng, and Y. Zhou, “Efficient bi-iterative method for source position and propagation speed estimation using tdoa measurements,” International Journal of Distributed Sensor Networks, vol. 10, no. 12, 2014. [Online]. Available: http://dsn.sagepub.com/content/10/12/689871.abstract [11] A. Lombard, H. Buchner, and W. Kellermann, “Improved wideband blind adaptive system identification using decorrelation filters for the localization of multiple speakers,” in Proc. IEEE Symposium on Circuits and Systems (ISCAS), New Orleans, USA, 2007, pp. 2974 – 2977.

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8 Literature

III

[12] P. Teng, A. Lombard, and W. Kellermann, “Disambiguation in multidimensional tracking of multiple acoustic sources using a gaussian likelihood criterion,” in Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Dallas, TX, USA, March 2010, pp. 145–148. [13] F. Nesta and M. Omologo, “Enhanced multidimensional spatial functions for unambiguous localization of multiple sparse acoustic sources,” in Proc. of IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Kyoto, Japan, 2012, pp. 213–216. [14] J. Scheuing and B. Yang, “Disambiguation of TDOA Estimation for Multiple Sources in Reverberant Environments,” IEEE Trans. on Audio, Speech, and Language Processing, vol. 16, no. 8, pp. 1479–1489, Nov. 2008. [15] Martin Kreißig and Bin Yang, “Fast and reliable TDOA assignment in multi-source reverberant environments,” in IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 2013, pp. 355 – 359. [16] P. Annibale and R. Rabenstein, “Accuracy of time-difference-of-arrival based source localization algorithms under temperature variations,” in Proc. of 4th Int. Symposium on Communications, Control and Signal Processing, (ISCCSP). Limassol, Cyprus: IEEE, 2010, pp. 1 – 4. [17] ——, “Acoustic source localization and speed estimation based on time-differences-of-arrival under temperature variations,” in Proc. of European Signal Processing Conference (EUSIPCO), Aalborg, Denmark, August 2010, pp. 721 – 725.

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8 Literature

IV

[18] ——, “Speed of sound and air temperature estimation using the TDOA-based localization framework,” in Proc. of Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP). Kyoto, Japan: IEEE, 2012, pp. 229 – 232. [19] ——, “Sound speed estimation from time of arrivals: Derivation and comparison with TDOA-based estimation,” in Proc. of European Signal Processing Conference (EUSIPCO), Bucharest, Romania, August 2012, pp. 1014 – 1018. [20] P. Annibale, J. Filos, P. A. Naylor, and R. Rabenstein, “Geometric inference of the room geometry under temperature variations,” in Proc. of Int. Symposium on Communications, Control and Signal Processing, (ISCCSP). Rome, Italy: IEEE, 2012, pp. 1 – 4. [21] P. Stoica and J. Li, “Lecture notes - source localization from range-difference measurements,” Signal Processing Magazine, IEEE, vol. 23, no. 6, pp. 63–66, November 2006. [22] I. Jovanovic, L. Sbaiz, and M. Vetterli, “Acoustic tomography method for measuring temperature and wind velocity,” in Proc. of Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), vol. 4. IEEE, May 2006, p. IV. [23] E. K. Skarsoulis and G. S. Piperakis, “Use of acoustic navigation signals for simultaneous localization and sound-speed estimation,” The Journal of the Acoustical Society of America, vol. 125, no. 3, pp. 1384–1393, 2009. [Online]. Available: http://link.aip.org/link/?JAS/125/1384/1

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V

[24] R. Diamant and L. Lampe, “Underwater localization with time-synchronization and propagation speed uncertainties,” Mobile Computing, IEEE Transactions on, vol. 12, no. 7, pp. 1257–1269, 2013. [25] G. S. K. Wong, “Speed of sound in standard air,” The Journal of the Acoustical Society of America, vol. 79, no. 5, pp. 1359–1366, 1986. [Online]. Available: http://link.aip.org/link/?JAS/79/1359/1 [26] G. W. Elko, E. Diethorn, and T. Gaensler, “Room impulse response variation due to temperature fluctuations and its impact on acoustic echo cancellation,” 2002. [Online]. Available: https://www.researchgate.net/publication/2478722

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