LTP Drift Mode - NASAS2-iFR-TN-3006 S2-UTN-TN-3091 Apr. 17th 2012 . Data Analysis Challenge •...

Tuesday, April 17, 2012

LTP Drift Mode Alternate Analysis

Ira Thorpe (NASAlGSFC), Curt Cutler (NASAlJPL)

LTPDA Progress Meeting - Trento 17th April, 20 12

Motivation

LlSA/NGO:

•

•

• Tuesday, April 17, 2012

LTP: TM Sensitive directions are not co-linear

Both TMs can be operated drag-free (within measurement band)

•

•

•

LTPDA Progress Meeting -Trento

TM Sensitive directions are co-linear

Only one TM can be operated drag-free, the other must be forced

Potential noise source not present in LISA

Apr. 17th 2012

Drift Mode

•

concept:

• Concentrate TM2 forcing into small time windows,

k "k' k " a .. a. IC s

• Allow TM2 to fly free between kicks

• Compare measured TM noise with normal science mode to study force noise effects

"Clo~,ed- ! cop Kicks"

/'--' "

.... " ... r ~I

.~ ..... : .. .- , ..... ~-

.., •• It .. " ., " ,

~ , . ' . '.

• , , . . \ . ,.-

. . . . '.: , .. • • • • • •

" . •


Tuesday. Ap'" 17. 2012

z • , ~V ~~l5J/ .

_ .. ___ ~IJ ~~ ' ~2 I O2 , • Interferometer I:eam > ,

.i TM2 II: , /' " ,/

\// ~ Electrodes used to control X2 and b,

References:

• C&QG 26 094007 (2009)

•

• • •

Space Sci Rev I 5 I : 183-196 (20 I 0)

S2-iFR-TN-3008

S2-iFR-TN-3006

S2-UTN-TN-3091

Apr. 17th 2012

Data Analysis Challenge • Periods of low noise (free-flights)

separated by short periods of high noise (kicks)

• Must excise kicks

• Care about frequencies down to I mHz but flights only last -200s

• Need to combine information from multiple free flights to get low-frequency information

• have to remove deterministic part of the free-flight

• Desired Outputs

• Residual spectrum or parameters that describe it

• Parameters that describe Deterministic signal

. ,', , .

• LTPDA Progress Meeting -Trento


L ... . . ;i,', ,- 'I'"

",'\: ...... \,'\: .... ,. "

i , • , •••

~' ., " .~'

I

'"

Apr. 17th 2012

Pre-process i ng •

•

•

• •

Read data from dynamical simulations into LTPDA

Remove any known cross couplings

Convert from displacement to acceleration

Identify & excise kicks

Remaining data stream has deterministic part plus quasiperiodic gaps.

Tuesday. April 17. 2012

~

.§. x 10 -6 Time origin: 2010-01-01 00:00:00.000

j ~ ~ (\(\7\7\ f\N\fY/~=X=12:OS:Cc-=or:::;r!§;:ec=t=e::2~5;l_ o._2PL-'LJLJL_~V_~L __ L--l

~ 3 3.05 3.1 3.15 3.2 3.25 3.3 ~ Time [s] x 104

')I 1/1 ·8 Time origin: 2010-01-01 00:00:00.000

i'~r I : I I : I I : I I : II : §M 0.. 3 E

·9 -1 x 10

3.05 3.1 3.15 3.2 3.25 3.3 Time [s]

Time origin: 2010-01-01 00:00:00.000 -----,---.------,----.. -----.---;====~

Q)

" ::J .t: -1.05 L ___ .. ___ _ .. L ____ ._. _____ ...l..L _ ___ .:

0.. 3 E <C

3.05

LTPDA Progress Meeting -T rento

3.1 3.15 Time [s]

3.2 3.25 3.3

x 104

Apr. 17th 2012


Data Analysis Approaches

• Apply window function to data that goes to zero during the gaps

• Fill the gaps with randomly generated noise with the correct statistical properties

• Compute and correct for spectral leakage effects caused by gaps

LTPDA Progress Meeting -Trento Apr. 17th 2012

Gap-filling Approach Simultaneously do noise estimation and Bayesian parameter estimation of deterministic signals.

~ N/ a(t) == n(t) + L Ai¢i(t)

i=l

I. Make a guess for underlying noise spectrum and coupling parameters

2. Remove estimate of deterministic signal

3. Fill gaps using "constrained Gaussian noise"

4. Re-estimate spectrum

5. Re-estimate deterministic pieces (Fisher matrix)

6. Repeat 2-5 as necessary

Does not require periodic gaps

LTPDA Progress Meeting - Trento Apr. 17th 2012


Constrained Gaussian Noise

• Want data with correct spectrum in frequency domain

• In time-domain, this means correct 2-point correlation function

•

•

Fill gaps with random data but adjust the mean of each data point based on correlation function and data outside gap

Caveat: In practice, need to truncate Cij at finite length ... requires white or rising spectrum. Will need to pre-whiten.

10' -

,o·--~----<' _ .. --"~'''' ''''''''--~''''''''''''''' 10· 10" 10" 10' 10· 10'

Frequency [Hz)

[--_ .. _-_ .... -.... __ ._-_ .• -- - --" _ ~ .~:.eo.I!'!J~!'!I'!.!~!.\l.!t!J

-400

~ . .. 800 ~--.-.---.. -. i... __ . . _. __ .. _ 0 _____ _ -1. __ - _ ..... ___ ~

o 5 10 15 20 25 30 Time [s) • LTPDA Progress Meeting - Trento Apr. 17th 2012



Noise filling example

...... ,.... I

N :I: 10.2

N

E .....

Input Noise Sn(J) = So [1 + (f / fo)a]

--.------I

I ,

-----1

- .

.• HI· ! .' II !. • .............. ..-....1

10~ 10~ 10.1 10° 101

Frequency [Hz]

LTPDA Progress Meeting. Trento

- LPSD(yin) - fitSpeclLPSD(yi

Apr. 17th 2012



..... ... • N

Add gaps ( I s duration at 200s intervals)

I -. ::I: 10.2

N v -

I

... - - ,.. ..

E .....

.--- ~

I ,

10~LI ----~--~~~~~~----~--~~ 10-4 10-3 10.2 10.1 10° 101

Frequency [Hz]

LTPDA Progress Meeting. T rente

- LPSD(yin) - fitSpec[LPSD(yi - LPSD(lteratlon I -Best Fit 0

Apr. 17th 2012


Noise filling example First Iteration

i i

- LPSD(yin) - fitSpec[LPSD(yi - LPSD(lteration I -Best FitO - - LPSD(lteration .

. I - Best Fit 1

10~LI--~~\~'--~'i--~~~\--~~\~--~' 10-4 10-3 10-2 10-1 100 101

Frequency [Hz]

LTPDA Progress Meeting -T rento Apr. 17th 2012



..... r' ,

N

Second Iteration

- LPSD(yin) ----.--t----.;----

I - fitSpec{LPSD(yi i - LPSD(lteration t

::t: -2 10 --' ____ .j - Best Fit 0

I ! - LPSD(lteration . I - Best Fit 1

C'I

E ..... 10 -4 f-.. ---..:.....--A-P:IW~~1- - -. --.-.. -----.-- - ~ - LPSD(lteration :

: . ' . I - Best Fit 2

6 , ._.,. •. >--L-.....! 1 n~#. I i l...-______ _

- ' . _ I _4 .- 1" ' ... • . ' ! 10 " _ . - . - --- - . - - -----. I . I

1) ..... : . 'd' .w ~ 10-4 10.3 10.2 10"

- -~- - 1

I I ,

. ..' . • • •• ••• 1

Frequency [Hz]

LTPDA Progress Meeting. Trento Apr. 17th 2012


...... ..... I

N

Noise filling example Third Iteration

•

/ I - LPSD(yin) - fitSpec[LPSD(yi

I - LPSD(lteration ~

-Best Fit 0

:I: 10.2 , ('II

.- -1---- LPSD(lteration . - Best Fit 1 - LPSD(lteration :

--. - Best Fit 2 - LPSD(lteration :

Best Fit 3

E

- 10-4 I I I V •• ,:~' 1 0 ~ l~ Z-~....-,.,.-It'f'I'o;, I

I

10~~1 --~~--~~~~~~~~~--~~ 10-4 10~ 104 10.1 1~ 10'

Frequency [Hz]

LTPDA Progress Meeting. Trento Apr. 17th 2012


...... .,... , N

Noise filling example Fourth Iteration

i I

-----.-.---1.----.. I-/---~ ---~~S~~~i~~SD(yi 1- LPSD(lteration I - .------.-) r--- 1- Best Fit 0

I . - LPSD(lteration ' - Best Fit 1

! ' i I - LPSD(lteration :

:I: 10.2 ('oj

.,

I ~'

, i I - Best Fit 2 i

10-41-.... --~--....,'.....,....,rIT. ~=-~-:~.: -- ------1 1 - LPSD(lteration :

./ I: ! Best Fit 3 ~'-'l'''""~---'~n'~ " \ - LPSD(lteration • -6 . ~ ~'" .'-I~,I fC I

10 If' ~~. 'ii ' ,",' ~- 1 ! Best Fit 4

E - " ,;.

I r

I : ! 10-8 " ,

10-4 10-3 10.2 10.1 10° 101

Frequency [Hz]

LTPDA Progress Meeting. T rento Apr. 17th 2012


Convergence Sn (f) == So [1 + (f / fo )a]

Spectrum So fo a

Input 9.S0E-07 2.94E-02 3.990

Iteration 0 3.31 E-02 1.88E-0 I 2.638

Iteration I 1.09E-04 9.72E-02 4.002

Iteration 2 3.07E-06 4.00E-02 4.006

Iteration 3 1.08E-06 3.06E-02 3.998

Iteration 4 9.S0E-07 2.94E-02 3.990


X2

1.07

232

7.51

2.80

1.23

1.13

Apr. 17th 2012


40

30

20

...... E 10 ..... QI

-g 0 :t: -a. E -10 c(

-20

-30

-40

Time domain r • i

I -+-original .

, ,_ ·t·,- I - gap ,

-.'.- j - --- '!'-~-- - ---, -

1 It I I I

-@- final , I .,

I I

. , , 1

! J

I i ~ I ! I I ~

, I

! . I

1 j - i r

~ , I I , ,

N-~ + ! --_. .- -- -'._. _. -- _. -_. __ I .- J

~. I V I , I

[ ! - o'

r

~ , 1 ,

I i ,

I I ,

'.A "._-- - --:- -- - --- _L r ----- +- --- -_.' • , I I i I

t I I • , 0

! J . ~

I I I i , i I • I

4216.5 4217 4217.5 4218 4218.5 4219 4219.5 4220 Time [s]

LTPDA Progress Meeting - Trento Apr. 17th 2012

Bayesian Parameter Estimation

a(t) = L )..k¢k(t) + n(t) k

)..k = L (r-1 )kl (a l¢l) l


7 f

A II

r - deterministic ! , - re&ldual

, , T··~' 1

I

6

o I -, ----_.- --~

o 500 '000 1500 2000 2500 3000

-.. ~ I '., he 10''"t

I ... 1

10 . ; i I

Time [sl

--------=-1 - slgn81 -Input noise

.. _ ~u)P,~t noise I

10..JO~, '_._~_ " __ ._ . _ ._.-,-~_ . _., .• __ .••• .-1. • •• •• .••• • _ . _ _ • .•• • _ _ _ " .... _ ----'

10" 10" 10" 10" 10" 10' 10' Frequency 1Hz)

LTPDA Progress Meeting -T rento Apr. 17th 2012

Combine the two steps - first try


.-. ... , N :t:

- ,

I i

- PSO(Nin) - fitSpec[PSO(Nin)] - PSO(n(1» -PSO(n(2»

PSO(n(3» - fitSpec[PSO(n(1))] - fitSpec[PSO(n(2))] - fitSpec[PSO(n(3))]

..,. 1 0 -20 .- II)

. --_J --.J.--~ ·lHt .~~ ...

('oj

E -

10-30 '---"-_ -'-_...L..-_--'--, _--'-~----'-_----"

1~ 10~ 1~ 1~ 104 1~ 10

1

Frequency [Hz]

LTPDA Progress Meeting - T rento Apr. 17th 2012

•

Next Steps

• Work on combined problem

• Investigate other noise shapes, esp. red noise (pre-whitening?)

• Apply to more realistic data (STOC?, SSM?)

LTPDA Progress Meeting - T rento

Tuesday, April 17,2012

Apr. 17th 2012

LTP Drift Mode - NASAS2-iFR-TN-3006 S2-UTN-TN-3091 Apr. 17th 2012 . Data Analysis Challenge •...

Documents

Transcript of LTP Drift Mode - NASAS2-iFR-TN-3006 S2-UTN-TN-3091 Apr. 17th 2012 . Data Analysis Challenge •...