Geometric Calibration of Acoustic Camera Star48 arrayInstitute for Geodesy and Geoinformation...
Transcript of Geometric Calibration of Acoustic Camera Star48 arrayInstitute for Geodesy and Geoinformation...
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
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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.
3 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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
4 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
Sound pressure image
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5 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
Sound pressure image before calibration
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6 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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.
7 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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:
8 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
Create a sound pressure image
28/06/2008Slide: 8
z
microphone - array with M sensors i = 1 ... M
y
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:
9 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
Create a sound pressure image
28/06/2008Slide: 9
z
microphone - array with M sensors i = 1 ... M
y
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:
10 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
Create a sound pressure image
28/06/2008Slide: 10
z
microphone - array with M sensors i = 1 ... M
y
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:
11 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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
12 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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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13 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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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14 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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
15 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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
16 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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
17 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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
18 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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= + + + −
19 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
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.
20 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
28/06/2008
before calibrating the software
after calibrating the software
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
Technische Universität Berlin
… thank you. Are there any questions?
Christian [email protected]
22 C. Manthe C. Manthe –– Geometric Calibration of Acoustic CameraGeometric Calibration of Acoustic Camera Star48 array
Department of Engineering Surveying and Adjustment TechniquesDepartment of Engineering Surveying and Adjustment Techniques
28/06/2008
Since the mechanical construction is a subject to inexactness the as-built microphone positions must be calibrated.