Geometric Calibration of Acoustic Camera Star48 array

Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques

Technische Universität Berlin

Geometric Calibration of Acoustic Camera Star48 array

Christian Manthe

Institute for Geodesy and Geoinformation ScienceTechnische Universität Berlin, Germany

2 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array


Early analog “Acoustic Cameras”

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Hexagonal Array by Jean Baptiste Perrin (determine direction of aircrafts in WW I )Source: (C) AIP Niels Bohr Lib.

"Topophon" (1880) by Prof. A.M. Mayer

Devices to improve the human sense of hearing.

Used to locate sound emitting objects.



The Acoustic Camera:

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Acoustic Camera were developed by theSociety for the Promotion of Applied Computer Science .

- Portable system - fixed on a tripod- size about 3 m - 3 microphone arms- on each arm 12 (star36) or 16 (star48)

microphones- a digital camera in the center- data recorder to collected the data

Microphone arm

Hinge Digital Camera



Sound pressure image

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Sound pressure image before calibration

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Time Delay in the Brain

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Localization Model by L.A. Jeffress (1948)

source position

left ear right ear

delay lineCochlear Nucleus

Nucleus laminaris

Barn Owl

Barn Owls use this techniques to hunt animals in the dark.



Create a sound pressure image

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z

microphone - array with M sensors i = 1 ... M

y

x

actual image section (Pixel) for the location x

measurement object

different distances |ri| between sensor No. i and location x lead to various absolute run times τi = |ri| / c

virtualmeasurementplane

Delay & Sum – Beamforming:




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z


y

x

measurement object







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z


y

x

measurement object







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z


y

x

measurement object






Principle of the acoustic camera

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sound event ( )∑=

∆−=M

iiii tfw

Mtf

1

1),(ˆ x

+

∆1

∆2

∆3

∆4

),(ˆ tf x1/M

w2

w3

w4

w1

),(ˆ tf x

∑−

==≈

1

0

2 ),(ˆ1),(ˆ)(ˆn

kkeffeff tf

nnpp xxx

Effective value of p at x:

),( tf x

ci

i

r=τ

( )iii ττ min−=∆

)(tfip(t)

t

p(t):time function

of sound pressure

τ1

τ2

τ3

τ4

microphones



Tasks?

• The resolution of the sound pressure image is influenced by the precession of the relative positions of the microphones.

• Inaccurate coordinates of the microphones implicate inexact time delay sets. Which results in smudgy sound pressure images.

task:• Localize the microphones with height precision

• Calculate residuals to calibrate acoustic software

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Firstly:Geometric coordination of the microphones in the (left hand) measurement system.

Secondly:Transform the calculated coordinates into the (right hand) camera system to calculate the residuals

General workflow

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Measurement Design

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Observations:- zenith angles (±0.3mgon)- horizontal directions (±0.3mgon)- slope distance AB (±1mm)- a priori known distances (±0.1mm)

- adjusted observations- Precision of the observations- local coordinates of the microphones- Precision of the coordinates- statistic values

Parametric adjustment

A

Z

Y

Microphone array

B

X

Basically we used an intersection of zenith and horizontal directions.

Measurement devise Leica TCA 2003



2 2

2 4 2

( ) ( )arctan A B A BA

B n BA B A

y y x xv

z z hϑ + +

− + − + = − −

Measurement Design

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X mic

Aα

βδ

YB

sinsin( )A Mic A Bs sβ

α β− −=+

( )cos(100 ( ))gMic A MicX sα δ −= − +

( )sin(100 ( ))gmic A MicY sα δ −= − +

tan( )A Mic

Mic MicA

sZz−=

Determine the approximate valuesObservations equations

arctanmic mic AA i A

mic A

y yr vx x

ω −+ = − −

arctanmic mic BB i n B

mic B

y yr vx x

ω+

−+ = − −

1 2 arctanB B AA n A

B A

y yr vx x

ω+

−+ = − − 2 2 arctanA A B

B n BA B

y yr vx x

ω+

−+ = − −

( )2 2

2 2

( )arctan mic A mic Amic

A i nmic A

y y x xv

z zϑ + +

− + − + = −

( )2 2

3 2

( )arctan mic B mic Bmic

B i nmic B

y y x xv

z zϑ + +

− + − + = −

2 2

1 4 2

( ) ( )arctan B A B AB

A n BB A A

y y x xv

z z hϑ + +

− + − + = − +

2 2 21 4 4 ( ) ( ) ( )B

A n B A B A B As v x x y y z z+ ++ = − + − + −

2 2 22 4 4 ( ) ( ) ( )A

B n A B A B A Bs v x x y y z z+ ++ = − + − + −

2 2 24 6 ( ) ( ) ( )i

i i i

micmic i n mic mic mic mic mic mics v x x y y z z+ ++ = − + − + −

point of origin



Results of the localization

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number of the star array 1 2 3 4 5

distance to the star array [m] 4.36 4.37 4.73 5.48 6.14

baseline length [m] 4.21 4.21 4.59 4.59 4.59mean of absolute corrections

of the horizontal angles [mgon]

0.4 0.3 0.5 0.5 0.7

mean of absolute corrections of the zenith angles [mgon] 0.6 0.3 0.6 0.5 0.6

mean of the mean point errors of the local coordinates

[mm]0.22 0.13 0.3 0.45 0.51

maximum mean error of the local coordinates [mm] 0.26 0.15 0.41 0.51 0.59

max NV 1.1 0.7 2.1 2.8 2.1

after the adjustment 0.4 0.2 0.6 0.7 0.8



Transformation into the target system

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rotation parameter- quaternion rotation instead of the Euler rotation- prevents us from calculating approximate values for

the rotation parameters

Workflow:1.centroid reduction for the microphone coordinates in both systems2.Compute the translation parameter by the difference between the both centroids3.Estimate the rotation parameters4.Transform the local coordinates into the target system5.Calculate the residuals of the vendor given coordinates

2 2 2 20 1 2 3 1 2 0 3 1 3 0 2

2 2 2 21 2 0 3 0 1 2 3 2 3 0 1

2 2 2 21 3 0 2 2 3 0 1 0 1 2 3

2 2 2 22 2 2 22 2 2 2

q q q q q q q q q q q qR q q q q q q q q q q q q

q q q q q q q q q q q q

+ − − − − = + − + − − − + − − +

_ _cam centroid loc centroidT x R x= − ⋅r r



Estimation of rotation parameters

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Results:- rotation parameters- standard deviations of the parameters

given:- construct coordinates by the vendor (GfAI)- localized coordinates

Parametric adjustmentwith one additional condition betweenthe unknowns

1

0

T T

T

x A PA B A P lk B w

− =

2 2 2 20 1 2 3 1b q q q q= + + + −



Residuals to calibrate the acoustic software

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Star max ∆X [mm]

max ∆Y [mm]

max ∆Z [mm]

1 4.8 -6.3 1.9

2 6.4 -13.0 11.4

3 -9.3 7.8 -2.6

4 9.0 7.7 -6.2

5 -8.1 4.4 -5.9

1. The residuals are significant (σ=±0.5mm).

2. Residuals show the diversity of the stars. Each star array slightly different.

3. Thus, a calibration is need for every new Acoustic Camera because the precision by constructing the device is to low.



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before calibrating the software

after calibrating the software


Technische Universität Berlin

… thank you. Are there any questions?

Christian [email protected]



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Since the mechanical construction is a subject to inexactness the as-built microphone positions must be calibrated.

Documents

Geometric Calibration of Acoustic Camera Star48 array