Optimization of Planck/LFI on--board data handling

1.8 MB·English

by  M. Maris

PreprinttypesetinJINSTstyle-HYPERVERSION
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2 Optimization of Planck/LFI on–board data handling ∗

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.I M.Maris1 †,M.Tomasi2 ,S.Galeotta1 ,M.Miccolis3 ,S.Hildebrandt4 ,M.Frailis1 ,
h
p R.Rohlfs5 ,N.Morisset5 ,A.Zacchei1 ,M.Bersanelli2 ,P.Binko5 ,C.Burigana6 ,
- R.C.Butler6 ,F.Cuttaia6 ,H.Chulani4 ,O.D’Arcangelo7 ,S.Fogliani1 ,E.Franceschi6 ,
o
r F.Gasparo1 ,F.Gomez4 ,A.Gregorio8 ,J.M.Herreros4 ,R.Leonardi9 ,P.Leutenegger3
t
s ,G.Maggio1 ,D.Maino2 ,M.Malaspina6 ,N.Mandolesi6 ,P.Manzato1 ,M.Meharga5 ,
a
[ P.Meinhold9 ,A.Mennella2 ,F.Pasian1 ,F.Perrotta1 ,R.Rebolo4 ,M.Tu¨rler5 ,

1 A.Zonca10
v
7 1INAF-OATs,ViaG.B.Tiepolo11,I-34131,Trieste,ItalyE-mail:fi[email protected]
3
7 2UniversitádiMilano,DipartimentodiFisica,ViaG.Celoria16,I-20133Milano,ItalyE-mail:
4 fi[email protected]
1. 3ThalesAleniaSpaceItaliaS.p.A.,S.S.PadanaSuperiore290,20090Vimodrone(Mi),Italy
0 E-mail:fi[email protected]
0
4InstitutodeAstrofisicadeCanarias(IAC),C/oViaLactea,s/nE38205-LaLaguna,Tenerife,
1
: EspañaE-mail:fi[email protected]
v
5ISDCDataCentreforAstrophysics,UniversityofGeneva,ch.d’Ecogia16,1290Versoix,
i
X
SwitzerlandE-mail:fi[email protected]
r 6INAF-IASFBologna,ViaP.Gobetti,101,I-40129Bologna,ItalyE-mail:
a
fi[email protected]
7IFP-CNRviaCozzi53,20125MilanoE-mail:fi[email protected]
8UniversitádiTrieste,DipartimentodiFisica,ViaA.Valerio2,I-34127Trieste,ItalyE-mail:
fi[email protected]
9DepartmentofPhysics,UniversityofCalifornia,SantaBarbara,CA93106,USA.E-mail:
fi[email protected]
10INAF-IASFMilano,ViaE.Bassini15,I-20133Milano,ItalyE-mail:fi[email protected]
–1–
Abstract:Toassesstabilityagainst1/f noise,theLowFrequencyInstrument(LFI)on–boardthe
Planck mission will acquire data at a rate much higher than the data rate allowed by the science
telemetry bandwith of 35.5 kbps. The data are processed by an on–board pipeline, followed on–
groundbyadecodingandreconstructionstep, toreducethevolumeofdatatoalevelcompatible
withthebandwidthwhileminimizingthelossofinformation. Thispaperillustratestheon–board
processing of the scientific data used by Planck/LFI to fit the allowed data–rate, an intrinsecally
lossyprocesswhichdistortsthesignalinamannerwhichdependsonasetoffivefreeparameters
(N , r , r , q, ) for each of the 44 LFI detectors. The paper quantifies the level of distortion
aver 1 2
O
introducedbytheon–boardprocessingasafunctionoftheseparameters. Itdescribesthemethodof
tuningtheon–boardprocessingchaintocopewiththelimitedbandwidthwhilekeepingtoamini-
mumthesignaldistortion. Tuningissensitivetothestatisticsofthesignalandhastobeconstantly
adaptedduringflight. Thetuningprocedureisbasedonaoptimizationalgorithmappliedtounpro-
cessedanduncompressedraw dataprovidedeitherbysimulations, pre–launchtestsordatataken
from LFI operating in a special diagnostic acquisition mode. All the needed optimization steps
areperformedbyanautomatedtool,OCA2,whichsimulatestheon–boardprocessing,exploresthe
space of possible combinations of parameters, and produces a set of statistical indicators, among
them: the compression rate C and the processing noise (cid:15) . For Planck/LFI it is required that
r Q
C =2.4 while, as for other systematics, (cid:15) would have to by less than 10% of rms of the instru-
r Q
mental white noise. An analytical model is developed that is able to extract most of the relevant
informationontheprocessingerrorsandthecompressionrateasafunctionofthesignalstatistics
and the processing parameters to be tuned. This model will be of interest for the instrument data
analysis to asses the level of signal distortion introduced in the data by the on–board processing.
Thismethodwasappliedduringgroundtestswhentheinstrumentwasoperatinginconditionsrep-
resentativeofflight. Optimizedparameterswereobtainedandinsertedintheon–boardprocessor
and the performance has been verified against the requirements, with the result that the required
datarateof35.5Kbpshasbeenachievedwhilekeepingtheprocessingerroratalevelof3.8%of
theinstrumentalwhitenoiseandwellbelowthetarget10%level.
RemarktotheArXiVversion
This is an author-created, un-copyedited version of an article accepted for publication in
JINST. IOP Publishing Ltd is not responsible for any errors or omissions in this version of
themanuscriptoranyversionderivedfromit. Thepresentversionisderivedfromthelatest
versionofthepaperbeforefinalacceptancefromJINST,thusitcouldhavesomeminordif-
ferencesinphrasing, spellingandstylewithrespecttothepublishedversion. Thedefinitive
publisherauthenticatedversionisavailableonlineat:
http://www.iop.org/EJ/article/-search=68871278.5/1748-0221/4/12/T12018/jinst9_12_t12018.pdf
Keywords: (Cosmology):CosmicMicrowaveBackground–Submillimeter–Methods:
numerical–Spacevehicles:instruments.
Contents
1. Introduction 2
2. Radiometermodelandacquisitionchain 3
2.1 Signalmodel 5
2.2 Datacompressionandon–boardprocessing 7
2.3 Downsampling 8
2.4 Losslesscompression,packetingandprocessingerror 9
2.5 Themixingalgorithm 12
2.6 Modellingthestatisticaldistributionofprocesseddata 16
2.6.1 Thelowaccuracyapproximation 16
2.6.2 Thehighorderaccuracyapproximation 18
2.7 Processingerrorofthemixing/demixingalgorithm 18
2.8 Saturation 19
3. OptimizingtheOn–boardProcessing 23
3.1 Targetfunction 24
3.2 AnalyticalOptimization 25
3.3 Dealingwithsaturation 28
3.4 OCA2K,nonidealitiesandnumericaloptimization 28
3.5 TheOCA2optimizationalgorithm 31
4. Results 32
5. Theimpactoftheon–boardprocessingnoiseonthePlanckscientificperformances 36
6. FinalRemarksandConclusions 38
A. Approximationofthebivariateentropy 39
B. ADCquantization 41
C. DAETuning 42
∗SubmittedtoJINST:23June2009,Accepted:10November2009,Received:23June2009,Accepted:10November
2009,Published29December2009.Reference:2009JINST4T12018DOI:10.1088/1748-0221/4/12/T12018
†CorrespondingAuthor,e–mail:[email protected]
–1–
1. Introduction
Oneofthemostchallengingaspectsinthedesignofanastronomymissioninspaceistheabilityto
sendthecollecteddatatothegroundfortherelevantanalysiswithintheallowabletelemetryband-
width. Infacttheincreasingcapabilitiesofon–boardinstrumentsgenerateseverlargerammounts
of data whereas the downlink capability is quite constant being mainly governed by the power
of the on–board transmitter and the length of the time window which can be allocated for data
down linking [Bertotti,Farinella,Vokrouhlický(2003)]. In the case of the ESA satellite Planck,
which will observe the CMB from the second Lagrangian point (L2) of the Earth – Sun system,
1.5 106KmfarfromEarth,thedown–linkrateislimitedtoabout1.5Mbps,andPlanckcanbein
×
contactwiththegroundstation(locatedatNewNorcia,WesternAustralia)fornomorethanacou-
pleofhourseachdaythusreducingtheeffectivebandwidthbyanorderofmagnitude. Inaddition,
Planckcarriestwoscientificinstruments: thePlanckLowFrequencyInstrument(Planck/LFI),to
whichthispaperisdevoted,andthePlanckHighFrequencyInstrument(Planck/HFI).Bothshare
thebandwidthtodownloaddatawithotherinternalspacecraftservicesandtheup–linkchannelThe
resultisthatLFIhasonlyabout53.5Kbpsaveragedownlinkratewhileproducingaunprocessed
data rate of about 5.7 Mbps. It is evident that some kind of on–board data compression must be
appliedtofitintotheavailabletelemetrybandwidth.
It is well known that the theoretical maximum compression rate achievable for a given data
stream decreases with its increasing variance. Thus it is very advantageous before appying any
compression algorithm to preprocess the data to reduce its inherent variance. In the ideal case
the preprocessing would not alter the original data, but in practice some information loss can not
be avoided when the variance is reduced. Thus the on–board preprocessing algorithm should be
tunable through some kind of free processing–parameters in order to asses at the same time the
required compression rate at the cost of a minimal degradation of the data. This paper addresses
theproblemoftheon–boardprocessingandthecorrespondinggroundprocessingofthescientific
data and the impact on its quality for the Planck/LFI mission. This has also been the topic of
twopreviouspapers,thefirstregardingtheexplorationofpossiblelosslesscompressionstrategies
[Marisetal. (2000)], and the second focused to the assessment of the distortions introduced by a
simplifiedmodeloftheon–boardpluson–groundprocessing[Marisetal. (2004)]. Herethework
presentedby[Marisetal. (2004)]iscompletedbyintroducinginSect.2abriefdescriptionofthe
instrumentfollowedbyaquantitativemodeloftheon–boardpluson–groundprocessingappliedin
Planck/LFI.Theprocessingcanbetunedwiththestatisticalpropertiesofthesignalandintroduce
as small as possible distortion. to asses the proper compression rate and as small as possible
processingdistortion. Thiscanbeperformedbyusingasetofcontrolparameters,asanticipatedin
[Marisetal. (2004)],whicharetunedontherealsignal. Thetuningalgorithm,whichhasnotbeen
discussed previously, is the most important contribution to the Planck/LFI programme presented
in this work and it is discussed in Sect. 3. The whole procedure has been validated both with
simulationsandduringthepre–flightgroundtesting. Themostsignifcativeresultsarereportedin
Sect. 4. Of course, processing has an impact on Planck/LFI science whose complete analysis is
outsidethescopeofthispaperbuthoweverisbrieflyanalyzedinSect.5. AtlastSect.6reportsthe
finalremarksandconclusions,whilesometechnicaldetailsarepresentedinappendicesA,Band
C.
–2–
Digitized
Sky Offset Gain Data Telemetry
T
sky
Detector 1
RCA 14 bits
ADC
REBA Spacecraft
DAE
T Detector 2
load
Reference
Load Telecommands
~
8192 Hz
Clock
Figure 1. A schematic view of the main flow of scientific data for a single RCA of Planck/LFI. Each

RCA has two detectors, but in this scheme only the first is represented and schematized. For graphical
purposestheschemerepresentsjustthefirstdetectorwhileconnectedtothereference–load,whileDetector
2wouldbeconnectedtosky.AtachangeoftheClockphasethetwodetectorswillswitchtheirconnections.
Theblockarrowsrepresentstheflowofdigitizeddataandtelemetrytowardthespacecraftandtheflowof
telecommandsfromthespacecraft.
2. Radiometermodelandacquisitionchain
Planck/LFI [Bersanellietal. (2009)] is based on an array of 22 radiometers assembled in 11 Ra-
diometric Chain Assemblies (RCA) in the Planck focal plane. Each RCA has 4 radio frequency
inputlinesand4radiofrequencyoutputlines,hencethenumberofradiofrequencyoutputstobe
measured by the on–board electronics is 44. Each feed–horn has one orthomode transducer with
two outputs: each extracting the two orthogonal components of linear polarization in the signal
receivedfromtheskyandfeedingoneoftheradiofrequencyinputlinesofaradiometer,theother
radio frequency input line is connected to a reference–load held at the constant temperature of
4.5K.
A schematic representation of the flow of information in a single radiometer belonging to a
RCAisgiveninFig.1. Eachradiometeractsasapseudo–correlationreceiver[Villaetal. (2009)]
measuringthedifferenceinantennatemperatures,∆T,betweentheskysignal,T ,andthereference–
sky
load T ,[Valenzianoatal.(2009)]. However,giventheskyandthereference–loadhavedifferent
load
meantemperaturesthereferencesampleshavetobescaledbyaGainModulationFactor,r,which
balancesthedifferencebetweenT andT toamean[∆T]=0sothat
sky load
∆T =T rT . (2.1)
sky load
−
A proper choice of r will allow near cancellation out most of the first order systematic errors
–3–
[Mennellaetal. (2003), Mehinoldatal.(2009)], assuring in this way optimal rejection of system-
atics, inparticulardriftsandthe1/f noise[Mennellaetal. (2009)]. Asafirstapproximationitis
possibletoput
mean T +T
sky noise
r , (2.2)
≈ mean[hTloadi]+Tnoise
whereT isthenoisetemperature. Eq.(2.2)makesevidenthowdifferentvaluesofrareneeded
noise
inthevariousphasesofthemission. Inparticularthreecasesareimportant: groundtests,in–flight
cooling phase and finally in–flight operations with the instrument in nominal conditions. As an
exempleconsiderthecaseofthe30GHzchannel,whichistheleastnoisychannelofPlanck/LFI
havinganexpectedT 10K.Duringon–groundtestingmean T mean[T ]andsor 1
noise sky load
≈ ≈ ≈
([Bersanellietal. (2009), Mennellaetal. (2009)]). In flight meanh Tskyi 2.725 K but during the
≈
cooling mean[T ] varies from 20 K down to the nominal mean[T ] 4.5 K. Thus r varies
load ≈ h loiad ≈
from 0.4 when the instrument starts to cool–down to 0.88 at the end of the process when it
≈ ≈
reachesitsnominaltemperature. WithhighervaluesofT theotherchannelswillshowsmaller
noise
departuresintheirrfrom1aswellasalowersensitivitytotheenvironmentalconditions.
To acquire sky and reference–load signals each radiometer has two separate radio frequency
inputs,andcorrespondinglytworadiofrequencyoutputs,eachoneconnectedtoaradiofrequency
detectorandtoanacquisitionchainendingina14bitanalog–to–digitalconverter(ADC)housed
intheDigitalAcquisitionElectronicsbox(DAE)[Bersanellietal. (2009),Villaetal. (2009)]. The
outputoftheDAEissenttotheRadiometerElectronicsBoxAssemblybox(REBA)1 whichpro-
cessesthedatafromtheDAE,ofinterpretingandexecutingtelecommands,andofinterfacingthe
instrument with the spacecraft Central Data Management Unit. This unit produces the scientific
packetstobesenttotheground[Herrerosetal. (2009)].
The DAE applies a individually programmable analogue offset to each input signal prior to
applyingindividualprogrammabltgainsandperformingdigitization. Thecontributiontotheread–
out noise budget from the ADC quantization is in general considered marginal. Appendix B dis-
cussesthecaseinwhichthishypothesisisnolongervalid. Theoffsetandthegainareadjustable
parametersoftheDAEanditisassumedthattheircalibrationisindependentfromtheREBAcali-
bration[Cuttaiaatal.(2009)]withanexceptionwhichisdiscussedinAppendixC. TheADCsare
fetched in turn and the data are sent to the Science Processing Unit (SPU), a Digital Signal Pro-
cessor (DSP) based computer which is part of the REBA [Herrerosetal. (2009)] not represented
in Fig. 1. The SPU stores the data in circular buffers for subsequent digital processing and and
thenappliestheonboardsoftwarepipelinetothedata,Intheprocessthe14bitsinglesamplesare
convertto16bitssignedintegers. ThecontentofeachADCbufferisprocessedseparatelybythe
on–boardprocessingpipelineandsenttoground.
As usual in these kinds of receivers, the required stability of the radiometers is assured by
switching each radiometer between the sky and reference–load. Thus each output alternatively
holdstheskyandthereference–loadsignal(orthereference–loadandthesky)withopposedphases
1LFIhastworedundantREBAunits,butsincetheyareperfectlyequivalentinwhatregardtheon–boarddatapro-
cessing,inthispaperwewillconsiderLFIashavingoneREBAonly.
–4–
betweenthetwochannels. Hence, eachbuffercontainsstringsofinterlacedsky––reference–load
(orreference–load––sky)samplesinincreasingorderofacquisitiontime,ti.e.
TADC ,TADC ,TADC ,TADC ,..., (2.3)
sky,t=0 load,t=1 sky,t=2 load,t=3
or
TADC ,TADC ,TADC ,TADC ,.... (2.4)
load,t=0 sky,t=1 load,t=2 sky,t=3
TheswitchingfrequencyisfixedbytheLFIinternalclockat8192Hz. Theswitchclockgivesalso
thebeatfortheADCs,whicharethensynchronizedwiththeswitchingoutput,anditissensedby
the on-board processor, which uses it to reconstruct the ordering of the signals acquired from the
ADCsandtosynchronizeitwiththeon–boardtime. ThisfrequencyalsosynchronisestheADCs
withtheinputandisusedbytheSPUtoreconstructtheorderingofthesignalsacquiredfromthe
ADCsandtosynchronisethemwiththeonboardtime.
The data flow of raw data is equivalent to 5.7 Mbps; a large amount of data that cannot be
fullydownloadedtotheground. Theallocatedbandwidthfortheinstrumentisequivalenttoonly
53.5 kbps including all the ancillary data, less than 1% of the overall data generated by LFI. The
strategy, adopted to fit into the bandwidth, relies on three on–board processing steps, downsam-
pling, preprocessing the data to ensure lossless compression, and lossless compression itself. To
demonstrate these steps, a model of the input signal shall be used. It has to be noted that while
thecompressionislossless,thepreprocessingisnot,duetotheneedtorescalethedataandconvert
theminintegers,(aprocessnameddatarequantizzation). However,thewholestrategyisdesigned
toassesastrictcontrolofthewayinwhichlossyoperationsaredone,oftheamountofinformation
lossinordertoassesoptimalcompressionratewithminimalinformationloss.
2.1 Signalmodel
Wedescribequantitativelythekindofsignalthepipelinehastoprocessbymodelingtheoutputof
theDAEasafunctionoftime,t,as
T (t) = T +∆T (t)+n , (2.5)
sky sky sky sky
T (t) = T +∆T (t)+n . (2.6)
load load load load
whereT ,T aretheconstantpartofthesignal. ∆T ,and∆T apossibledeterministictime
sky load sky load
dependent parts, representing drifts, dipoles, oscillations and so on, n and n represents the
sky load
randomnoisewhosemomentsareσ2 ,σ2 ,andwhosecovarianceisσ .
n,sky n,load n,sky,load
The pipeline described in the following sections needs to be tuned to obtain a proper level
of data compression which is largely determined by the covariance matrix of the signal whose
componentsare
σ2 = var ∆T +σ2 (2.7)
sky sky n,sky
σ2 = varh[∆T i]+σ2 (2.8)
load load n,load
σ = cov ∆T ,∆T +σ (2.9)
sky,load sky load n,sky,load
h i
–5–
g
N n
aver Mixing Compression ssi
e
c
o
pr
ADC Coadding Requantization ding oard
a b
Interlaced Interlaced o n
nl O
8 KHz 8 KHz r, r ow
Analog Data Digitized Data 1 2 O, q D
Demixing Decompression
r
g
ADU to Volts Dequantization ssin
e
c
Differentiation T s k y Tload pro
d
n
u
o
Gr
T – r T TOI
sky load
Figure2. SchematicrepresentationofthescientificonboardandgroundprocessingforthePlanck/LFI.
CyanboxesrepresentREBAoperations,yellowboxesgroundoperations.Greenpadsspecifytheparameters
neededbyeachoperation.TOIcouldbeproducedbothinundifferentiatedform(T ,T storedseparately)
sky load
orindifferentiatedform.
whereithasbeenassumedthattherandomanddeterministicpartsareuncorrelated. Itisusefulto
identifytwoextremecases: thedatastreamissignaldominated,whenvar ∆T +var[∆T ]
sky load
(cid:29)
σ2n,sky+σ2n,load, or the data stream is noise dominated, when var ∆Tsky +hvar[∆iTload](cid:28)σ2n,sky+
σ2n,load. Inthenoisedominatedcase,thestatisticsofdatawillbelarhgelydieterminedbythestatistics
of noise, which in general could be considered normally distributed and uncorrelated over short
time scales, given the 1/f–noise will introduce correlations over long time scales. In the signal
dominated case the statics of data will be instead determined by the kind of time dependence in
the signal. As an example, if T T is large compared to the noise while ∆T and ∆T
sky load sky load
| − |
are negligible, the histogram of the signals will resemble the sum of two Dirac’s delta functions
δ(x T )+δ(x T )convolvedwiththedistributionofnoise.
sky load
− −
Ifalineartimedependenceofthekind∆T(t)=A˙t+C ispresent, thenthedistributionofthe
sampleswillbeuniformandboundedbetweenT A˙τ/2,whereτisthetimeintervalrelevantfor
±
thesignalsampling. ThevariancewillbeA2/12whereA =A˙τisthedriftamplitudeoverthetime
τ τ
scaleτ. Thesignalcouldbeconsiderednoisedominatedifτ< √12σ/A˙. Fromthepointofview
| |
ofdatacompression,indeterminingwhetherasignalisnoisedominatedornot,thecriticalfactor
is the time scale τ. For our coupled signals, denoting with A˙ and A˙ the drift rate in the sky
sky load
andreference–loadsignals,andwithA ,A therelativeamplitudes,therelevantcomponents
sky,τ load,τ
–6–
ofthecovariancematrixwillbe
A2
sky,τ
var ∆T = (2.10)
sky
τ 12
h i A2
load,τ
var[∆T ] = (2.11)
load τ
12
A A
sky,τ load,τ
cov ∆T ,∆T = (2.12)
sky load
τ 12
h i
Inthisregard,themostimportantτtobeconsideredinthisworkisthetimespanforthechunkof
datacontainedinapacket,whichistheminimumunitofformatteddatasentbytheREBAtothe
ground. EachscientificpacketproducedbytheREBAhasamaximumsizecorrespondingto1024
octects, part of which has to be allocated for headers carring ancillary informations such as the
kindofdatainthepacketorthetimestamp. So,eventakingintoaccountdatacompression,onlya
smallamountofdatacanbestoredinapacketcorrespondingtoabout6 22secs,whichdepends
−
on details such as the attained compression rate and the frequency channel involved, as will be
shown in Sect 2.3. More complicated distributions may occur for a polynomial time dependence
ofthekind∆T tn,orforasinusoidaltimedependenceofperiodP: ∆T sin(2πt/P),butinmost
∝ ∝
casesasimplelineardrift∆T tcouldbetakenasareferencemodelgiventhatnonperiodicdrifts
∝
areboundedinamplitudebycorrectiveactionscommandedfromthegroundstation,whileperiodic
variationshaveperiodsmuchlongerthanthetimespanofapacket. Alsoingeneralitisassumed
that the mean mean ∆T =0 and the mean[∆T ]=0 but it is interesting to discuss even the
sky load
caseinwhichthisisnotstrictlytrue.
h i
2.2 Datacompressionandon–boardprocessing
Thestrategyadoptedtoremaininsidethedownlinkbandwidthisbasedonthreeprocessingsteps:
i) signal downsampling, ii) signal conditioning and entropy reduction, iii) loss-less compression
[Bersanellietal. (2009), Miccolis(2003)]. A schematic representation of the sequence in which
these steps are applied on–board and whenever possible reversed on–ground is given in Fig. 2.
Thefigurereferstoasingleradiometerchainandisideallysplittedintotwoparts: theupperpart
depictstheon–boardprocessingwithcyanboxesdenotingthemainsteps. Thecorrespondingon–
groundprocessingisdepictedinthelowerpartwiththemainstepscolouredinyellow. Greenpads
represents the processing parameters. The first four of them are refered to as REBA parameters,
andtheyareappliedbothon–boardandon–ground. Theparametersare: thenumberofADCraw
samplestobecoaddedtoformaninstrumentalsample,N ,thetwomixingparametersr ,r ,the
aver 1 2
offset tobeaddedtodataaftermixingandpriortorequantization,andtherequantizationstepq.
O
Theexactmeaningofeachoftheseparameterswillbeexplainedlaterinthetext,wheneachstep
willbeexplainedinfulldetail. Itisimportanttorecallthattheon–boardparametersareimposed
bytelecommandssentfromtheground. Theyarecopiedineachpacketcarringscientificdataand
on–groundtheyarerecoveredfromthepacketstobeappliedbytheon–groundprocessing. Ther
factorisaparameterofthegroundprocessingandiscomputedfromthetotalpowerdatareceived
ontheground. ThefinalproductsintheformofTimeOrderedData(TOI)eitherintotalpoweror
differentiatedarestoredinanarchiverepresentedbythelight–bluecylinder.
–7–
Beforeenteringintothedetailsofthevariousstepsithastobenotedthatinprincipleafactor
of two compression would be immediately gained by directly computing the difference between
sky and reference–load on–board, i.e. sending differentiated data at Earth. Although on–board
differentiation seems straightforward 2, it implies at least a couple of major disadvantages. First,
once the difference is made, separate information about the sky and the reference–load is lost,
preventing an efficient detection and removal of other many second order systematics. Second a
setof44rfactorscouldbeinprincipleeasilyuploadedon–boardandappliedtothedata,butther
foreachdetectorhastobefine–tunedontherealdata. Thiswouldmeanthattheoptimalrshould
be continuously monitored and adjusted to avoid uncontrolled drifts for each radiometer, but this
is inpractical, having just 3 hours of connection per day. In addition, an error in calibrating the r
willcauseanirremediablelossofdata. Therefore,thebestsolutionistodownlinktheskyandthe
reference–loadsamplesseparatelyallowingtheapplicationonthegroundoftheoptimalr.
2.3 Downsampling
Eachskysamplecontainstheskysignalintegratedoveraskyareaaswideasthebeam,butsince
eachradiometerissampledatafrequencyof8192Hztheskyissampledatanapparentresolution
of about 1/2 arcsec. On the other hand the beam size for each radiometer goes from 14 arcmin
forthe70GHzto33arcminforthe30GHz. Consequentlyitispossibletoco–add N ,consec-
aver
utivesamplesproducingaveragedsampleswhosesamplingtimecorrespondtoamorereasonable
resolutionwithoutanylossofinformation.
1. ThedownsamplingalgorithmtakesN couplesofsky––reference–load(reference–load–
aver
–sky) samples from a given ADC; 2. separates the two subsets of signals; 3. computes the sum
ofskyandloadsubsets(representedby32–bitssignedintegers);4. interlacesthem;and5. stores
them as sky––reference–load (reference–load––sky) couples in an circular buffer for subsequent
processing. InnormalprocessingtheREBAconvertsthesesumsintoaveragesbyconvertingthem
into floating–point format and then dividing them by N prior to perfom the subsequent steps
aver
of mixing, requantization and compression. In the case of diagnostic data processing the REBA
transfersdirectlyasoutputthesesumsastheyarei.e. withoutanyotherprocessingorcompression.
Inthiscasetheground–segmentpipelinehasthetaskofconvertingthemintoaverages. Thisisa
trade–offbetweentheneedforpacketstocarryjustdatarepresentedby16or32bitsintegers,and
the need to avoind uncontrolled round–off errors in the conversion of floating–point averages in
integervalues. Notethatthediagnostictelemetryisverylimitedinflightbytelemetrybandwith.
ThevalueofN dependsonthebeam–width,b ,forthegivendetector
aver rad
ω n sinβ
spin over
N = (2.13)
aver
b f
rad sampling
ω [rad/sec]istherateatwhichthesatellitespinsaboutitsspinaxis[ThePlanckBlueeBook(2005),
spin
Dupac,Tauber(2005),Marisetal. (2005)],βistheboresightanglebetweenthetelescopeline–of–
sight and the spin axis, and n =3 is the the number of samples per beam. Nominal values for
over
the N are 126, 88, 53 respectively for the 30 GHz, 44 GHz and 70 GHz frequency channels.
aver
The corresponding sampling frequencies in the sky are then 65 Hz, 93.1 Hz and 154.6 Hz, while
2Thiswasthebaselineoftheon–boardprocessingfor[Marisetal.(2000),Marisetal.(2004)].
–8–