the first ltp mock data challenge€¦ · 7th international lisa symposium – barcelona, spain /...
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7th International LISA Symposium – Barcelona, Spain / June 16-20, 2008 Albert Einstein Institute Hannover, Germany
LISA Group AEI Hannover, Germany LTP Data Analysis, 17/06/2008
Albert Einstein Institute
www.lisa.aei-hannover.de Max Planck Institute for Gravitational Physics
Hannover
The First LTP Mock Data Challenge
Anneke Monsky for the LTP Team
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Outline
• Organisation
• Model of LTP Dynamics
• Prediction of simulated IFO Data
• Prediction of TM acceleration
• Calibration of IFO Data to TM acceleration
• Summary and Outlook
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Two teams for the LTP mock data challenge:
3
Data GenerationTeam
Organisation
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Two teams for the LTP mock data challenge:
3
Data GenerationTeam
Organisation
Model LTP Dynamics
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Two teams for the LTP mock data challenge:
3
IFOMock Data
Data GenerationTeam
Organisation
Model LTP Dynamics
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Two teams for the LTP mock data challenge:
3
Data AnalysisTeam
IFOMock Data
Data GenerationTeam
Organisation
Model LTP Dynamics
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Two teams for the LTP mock data challenge:
3
Data AnalysisTeam
IFOMock Data
Data GenerationTeam
Organisation
Model LTP Dynamics
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Two teams for the LTP mock data challenge:
3
Data AnalysisTeam
IFOMock Data
Data GenerationTeam
Analysis Result(TM acceleration)
Organisation
Model LTP Dynamics
UTN (Trento) - simulated
IFO output data using
Mathematica
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
IFO/DMU
x
A
A 1
A2
x2
k1x1
k3x2
AN AT
Csus
CdfTM 1
TM 2
r =
0.3
m
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
r =
0.3
m
x
x1
x2
IFO/DMU
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
• TM1:
r =
0.3
m
x
x1
x2
IFO/DMU
TM 1
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
• TM1:– drag free
– S/C follows TM1
r =
0.3
m
x
x1
x2
IFO/DMU
TM 1
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
• TM1:– drag free
– S/C follows TM1
– drag free control loop
r =
0.3
m
x
x1
x2
IFO/DMU
CdfTM 1
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
• TM1:– drag free
– S/C follows TM1
– drag free control loop
• TM2: r =
0.3
m
x
x1
x2
IFO/DMU
CdfTM 1
TM 2
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
• TM1:– drag free
– S/C follows TM1
– drag free control loop
• TM2:– position electrostatically
relative to TM1
r =
0.3
m
x
x1
x2
IFO/DMU
CdfTM 1
TM 2
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (operation mode)
• TM1:– drag free
– S/C follows TM1
– drag free control loop
• TM2:– position electrostatically
relative to TM1– electrostatic control loop
r =
0.3
m
x
x1
x2
IFO/DMU
Csus
CdfTM 1
TM 2
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (Input force noises)
TM 1
r =
0.3
m
IFO/DMU
TM 2
Cdf
Csus
x
A
x1
x2
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (Input force noises)
• AT - thruster forceTM 1
r =
0.3
m
IFO/DMU
TM 2
Cdf
Csus
x
A
x1
x2
AT
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (Input force noises)
• AT - thruster force
• AN - additional force noisesTM 1
r =
0.3
m
IFO/DMU
TM 2
Cdf
Csus
x
A
x1
x2
AN AT
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (Input force noises)
• AT - thruster force
• AN - additional force noises
• - k1 x1 and -k3 x2 coupling between TM and S/C
TM 1
r =
0.3
m
IFO/DMU
TM 2
Cdf
Csus
x
A
x1
x2
AN AT
k1x1
k3x2
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Dynamical Model (Input force noises)
• AT - thruster force
• AN - additional force noises
• - k1 x1 and -k3 x2 coupling between TM and S/C
• A1, A2 - force noises on TM1 and TM2
TM 1
r =
0.3
m
IFO/DMU
TM 2
Cdf
Csus
x
A
x1
x2
AN AT
A1
A2
k1x1
k3x2
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Definitions
• Dynamics– stiffness
• TM coordinates
• Force noises
• IFO output data
D =[
s2 + ω21 0
ω2∆ s2 + ω2
3
]=
[Sω1 0ω2
∆ Sω3
]
!q =[
x1
x∆
]
!o =[
o1
o∆
]
!gn =[
AN −A1
A2 −A1
]
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Equations of motion
• Result of Euqations of motion in Laplace domain:
• Relating IFO data to TM coordinates:
• Combining equations:
!o = S!q + !on
[DS−1 + C]!o = D!on S−1 + !gn
a_calibrated→ a_predicted→
D!q = C!o + !gn
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Prediction of simulated Interferometer output data
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Prediction of simulated X1 and X12 Interferometer Data
!o =
[1
Sω1+C10
−β(Sω1+C1)(Sω3+C2)
1Sω3+C2
] [Sω1on1 + A1 −AN
βon1 + Sω3on∆ + A2 −A1
]
β = ω2∆ − δSω3
!o = [DS−1 + C]−1 [DS−1!on + !gn]• Prediction of IFO
output data:
where
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Prediction of simulated X1 Interferometer Data
AN
A1 + S−1ω1
+
on1
Sdf o1
• output data contains:
– force noise on TM1
– force noise on S/C
– X1 IFO sensing noiseo1 = Sdf on1 +
Sdf
Sω1
(A1 + AN )
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Prediction of simulated X12 Interferometer Data
β S−1ω1
on1++
Sdf
Re{Sdf}
A2 ++
Sdf S−1ω1
on∆
β
−2
A1
AN
Ssus
++
2 Re
{Sdf
Sω1
}
S−1ω3
o∆
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Prediction of IFO Data
10-4
10-3
10-2
10-1
100
10-12
10-11
10-10
10-9
10-8
Frequency [Hz]
Am
plitu
de
[ms−
2/√
Hz]
o1 predicted
o! predicted
o1 generated
o! generated
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Reference:Prediction of test mass
acceleration
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Predicting TM acceleration
a1 = Sω1on1 + A1 + AN
ANA1
on1 a1++ ++Sω1
From Equations of motion: !apredicted = D!on S−1 + !gn
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Predicting differential acceleration
a∆ = βon1 + Sω3on∆ + A2 + A1
Sω3on1
on∆
A2
A1
−δ ++
−ω2∆
Sω3
++ ++
++
a∆
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Prediction of acceleration
10-4
10-3
10-2
10-1
100
Frequency [Hz]
Am
plitu
de
[ms−
2/√
Hz]
10
10
10
10
10
10
10
10
10
10
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
a1 predicted
a! predictedThruster noise
TM noise
IFO noise TM2
IFO noise TM1
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Result:Calibration of simulated IFO data to test mass
acceleration
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Calibrating simulated IFO Data to TM acceleration
a1Sω1o1 S−1df
• From Lagrangian: !acalibrated = [DS−1 + C]!o
a1 = [Sω1 S−1df ] o1
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Calibrating simulated IFO data to differential TM acceleration
Sω3 −δ ++
ω2∆
Sω3
++ a∆
o∆ S−1sus
o1
a∆ = [ω2∆ + Sω3 · (−δ)] o1 + [Sω3 S−1
sus] o∆
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Results: calibration to acceleration
10-4
10-3
10-2
10-1
100
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
Frequency [Hz]
Am
plitu
de
[ms−
2/√
Hz]
a1 calibrated
a1 predicted)
a! calibrated
a! predicted
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Results of 11 Data Sets for a1
10-4
10-3
10-2
10-1
100
10-10
10-9
10-8
10-7
10-6
Frequency [Hz]
Am
plitu
de
[ms−
2/√
Hz]
Data set 1
" 2
" 3
" 4
" 5
" 6
" 7
" 8
" 9
" 10
" 11
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Results for all 11 Data Sets for a∆
10-4
10-3
10-2
10-1
100
10-14
10-13
10-12
10-11
10-10
10-9
10 -8
Frequency [Hz]
Am
plitu
de
[ms−
2/√
Hz]
Data set 1
" 2
" 3
" 4
" 5
" 6
" 7
" 8
" 9
" 10
" 11
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Average a1
10-4
10-3
10-2
10-1
100
10-10
10-9
10-8
10-7
10-6
Frequency [Hz]
Am
plitu
de
[ms−
2/√
Hz]
a1 averaged
error
a1 predicted
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Average a∆
10-4
10-3
10-2
10-1
100
10-14
10-13
10-12
10-11
10-10
10-9
10-8
Frequency [Hz]
Am
plitu
de
[ms−
2/√
Hz]
a! averaged
error
a! predicted
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Calibration vs. Prediction
10-4
10-3
10-2
10-1
100
0
0.5
1
1.5
2
2.5
3
3.5
Frequency [Hz]
Rati
o
a_1 calibrated / a_1 predicted
a_! calibrated / a_! predicted
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Summary / Outlook
• Verified theoretical model for LTP dynamics– predicted generated data
• Calculated theoretical reference– predicted TM acceleration
• Analysed generated data– calibrated given IFO output to TM acceleration– analysed 11 data sets and averaged
• Next MDCs– Parameter estimation (stiffness)– XY Crosstalk
The First LTP Mock Data Challenge
Albert Einstein Institute Hannover, Germanyhttp://www.lisa.aei-hannover.de/
LISA Group AEI Hannover, Germany Anneke Monsky, 17/06/2008
Thank you!