SELENEのVLBIとDoppler技術を

用いた月重力場の計測

　劉慶会　菊池冬彦　花田英夫　Sander Goossens松本晃治　河野宣之　浅利一善　鶴田誠逸　石川利昭

　原田雄司　石原吉明　岩田隆浩2　並木則行3　野田寛大　

　　佐々木晶　柴田克典　岩館健三朗　田村良明　

寺家孝明　酒井俐　VERA team

National Astronomical Observatory of Japan (RISE+VERA);2JAXA, Japan; 3Kyushu University, Japan

第6回VERAユーザーズミーティング@三鷹

Selenological and Engineering ExplorerKaguya(SELENE)

Terrain CameraRader SounderLaser Altimeter

surface structure

Spectral ProfilerMulti-band Imager

mineralogy

X-ray SpectrometerGamma-ray Spectrometer

chemical elements

High Definition Television Camera

imaging

Relay Satellite TransponderDifferential VLBI Radio Sources

gravity field

MagnetometerPlasma Imager

Charged Particle SpectrometerPlasma Analyzer

Radio Science Observation

surface environment

●SELENE consists of ;

1) Main Orbiter

2) Relay Satellite (Rstar)

3) VLBI Radio Satellite (Vstar)

2

Two techniques for lunar gravity field

Doppler technique (Sensitivity in line-of-sight)Spin influence on Doppler measurementRemove spin influence using LPFOrbit determination Global lunar gravity field Phase characteristic of onboard antenna

Differential VLBI technique(Sensitivity in direction perpendicular to LOS)SELENE VLBI observationDifferential phase delayOrbit determination

3

(1) 4-way Doppler of main-satellite for far side　(2) 2-way Doppler and range of Rstar and Vstar(3) Doppler and range of satellites for near side

Gravity experiment by 2- and 4-way Doppler in SELENE

JAXA station（TACS）

地球

first direct measurement of the gravity field on the far side

4

2way: m/s = 0.5 * C /( k1* fup) *Hz4way: m/s=(f4way-fbias)*C/(k5*k6*fup)

fbias=fref-(k2+k5*k6)*fup; fref=8456.125M　　（≒30kHz）

Sensitivity in line-of-sight

Patchantenna

Main

64mφ 2260.416UDSC

Vstar moon

Rstar

2081

.466 M

HzRstar

S-band dipole antennaX-band dipole antenna

2081.4668456

.125

2241.579

2051.614

新GN(11mφ)S-band

0 200 400 600 800 1000-6200

-6000

-5800

-5600

-5400

-5200

-5000

0 200 400 600 800 1000

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 200 400 600 800 1000

8400

8500

8600

8700

8800

8900

9000

0 200 400 600 800 1000

-1.0

-0.5

0.0

0.5

1.0

1.5

0 200 400 600 800 1000-4

-3

-2

-1

0

1

2

3

4

0 200 400 600 800 1000

48000

49000

50000

51000

52000

53000Rstar－2Way Rstar-Main-4Way

Time (s)Time (s)

HｚDoppler data,　Time interval 0.1s

Hｚ

Vstar－2Way

Time (s)

Raw data

0.355 Hz RMS

20071020

0.293 Hz RMS

20071101

1.028 Hz RMS

20071101

residual

RMS is larger than the desired accuracy 0.0033Hz（0.2mm/s）even if by using 10 s integration 5

Irregularities in the phase characteristics of antennas onboard spin satellites

Patch Antennalink Rstar and Main

Rstar(Vstar)

S/X Dipole antennafor Doppler and VLBI

Octagonal prism body

Qinghui Liu et. al 　 ``New method of measuring phase characteristics of antenna using Doppler frequency measurement technique",IEEE Trans.,Antenna and Propa., 3312-3318, 2004.

Qinghui Liu et. al 　 ``Effect of In-situPhase Characteristics of Antennas Onboard Spin Satellites on Doppler Measurements for lunar gravity field ",IEEE Trans., A&M, (submitted)

Influence on Doppler measurement：　2WAY：　 phase characteristics of S-band antenna＋ octagonal prism body 4WAY：　 phase characteristics of S- ,X-band and patch antennas＋

octagonal prism body ＋ offset of patch antennas from the rotation axis6

Doppler-Residual Spectrum (harmonic components of n*fs)

fs=4.4988/24=0.18745HzT=5.3348s

fs=4.39968/24=0.18332HzT=5.4549s

fs=4.39968/24=0.18332HzT=5.4549s

Estimate spin frequency fs with an accuracy 0.0001 Hz7

Linear phase LPF using Kaiser window function

( )2/)1(

2/)1(0)(

))1/(2(1

0

2

−≤⎪⎩

⎪⎨

⎧

−>

−−= Nk

NkI

NkIWk

　　　　　，

αα

2

10 !

)2/(1)( ∑∞

=⎟⎟⎠

⎞⎜⎜⎝

⎛+=

n

n

nxxI

0 10000 20000 30000 40000 50000 60000 70000-0.00010

-0.00005

0.00000

0.00005

0.00010

Output Y(n)-input X(n)

N=601，α=12.4226

0 10000 20000 30000 40000 50000 60000 70000-60000

-40000

-20000

0

20000

40000

60000

80000 input X(n)（simulation)

Period3h-Amp50kHz＋Period2h-Amp20kHz＋0-0.05Hz-Amp0.3Hz/f　20個

0 100 200 300 400 5001E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Kaiser function

Remove spin influence using LPF

Kaiser function

Accuracy for conserving gravity information in 0-0.05Hz0.00002Hz

Doppler

Gravity information

Hｚ

Hｚ

Important to give a suitable value for α8

Sorry! 10 pages (10-20) were deleted for Doppler

21

Summary on Doppler technique(Sensitivity in line-of-sight)

1. 2way-Doppler: 0.1mm/s RMS @ 0.1s after LPF2. 4way-Doppler can also be determined at a high accuracy

after LPF, and the gravity signals on the far side were detected firstly.

3. SELENE lunar gravity field model: SGM90e

Differential VLBI technique(Sensitivity in direction perpendicular to LOS)SELENE VLBI observationDifferential phase delayOrbit determination

21

Why do VLBI observations in SELENE?

Matsumoto et. al

Anticipated coefficient sigma degree variances of spherical harmonic of lunar gravity fieldPosition error of Rstar

2-way Doppler

2-way Doppler+Differential VLBI

Simulation results22

VLBI observations in SELENE(Sensitivity in direction perpendicular to LOS)

100km

800km

Moon

2400km

Atmosphere

Ionosphere

Rstar

Vstar

correlator

Rstar VstarDifferential phaseφR(t )-φV(t )

Differential phase delayAccuracy: ps(First time in the world)

Separate angle between Rstar and Vstar is less

than 0.9deg

Main

Quasar

Main satelliteGroup delayAccuracy: ns(Conventional method)

23

Time delayτg=Bsinα/c

α

Correlater

X Y

Delay t

ime τ

g

Radio sourceVLBI

principle

B

τg=Phase/frequency

Freq (MHz)

Phas

e

When error of phase is 3.6 deg,Error of group delay 3.6/360/10M=1ns

When error of phase is 10 degError of phase delay 3.6/360/8456M=1ps

24

Error of phase in SELENEhave to be less than　<4.3 deg in S-band

severe condition

2π ambiguity2200 2220 2240 2260 2280 2300

2200

2220

2240

2260

2280

2300

0 2000 4000 6000 80000

2000

4000

6000

8000

SELENE MAIN and other spacecrafts　Bandwidth 10MHz

Group delay　τg=Δphase/Δfreq.

Rstar&Vstar　Differential phase delay

S 3

X1S-band

Correlation processing

atmosphere

H-M

aser

PLO～PLO～

H-M

aser

PLO～PLO～

ionosphere

Origin of phase fluctuation satellite

・frequency variation of radio wave　（temporal、spatial）・ionosphere・atmosphere・thermal noise・phase variation in 　　receiver

It is difficult to obtain the correlation phase with an

accuracy of 4.3 deg25

Qinghui Liu, et. al, IEEE Trans., Antenna and Propa., Apr. 2005.

Nishio Masanori, Qinghui Liu, et.al, IEEE Trans., Antenna and Propa., July 2007.

Atmosphericphase fluctuation

φR(t )

φV(t ) Switching VLBI

alternately

Using switching VLBI observation

Condition for determining φR(t )-φV(t ) with an error of 4.3 deg cannot be satisfied when ionosphere and atmosphere fluctuation is strong.

26

Same-beamdifferential VLBI

Influences of the receiver, atmosphere and ionosphere are nearly canceled

27

120km

792km

Moon

3476km

2395km

Atmosphere

Ionosphere

Rstar

Vstar

correlator

Antenna beam

In same beam VLBI・Rstar and Vstar can be observed simultaneously ・System is nearly same・Elongation is small

Rstar period　4 hoursVstar period　2.5 hoursinclination　90deg

φR(t )

φV(t )

φR(t )-φV(t )

LIU et. al IEICE, 2006LIU et. al Adv. Space Res, 2007Kikuchi, Liu et. al, 2008

reference

Stations for SELENE VLBI observations

Hobart 26mφ

IshigakiOgasawara 20mφShanghai 25mφ

Wettzell 26mφUrumqi 25mφ

IrikiMizusawa 20mφ

12247 km

8265 km

8337

km

VERA

外国局：　2ヶ月；　VERA：１年以上31

P-calPer １M

LPF <100kHz

VideoConverter

SRTP　200 kHz、6 bit

LO2

ch1 ch2 ch3 ch4

I F I F

Back endK4、Mark4,5

X-band

coupler

Front end

LO1

8.18-8.6 G

8.08 G100-520M

S-band

coupler

LO1

2.2-2.32 G

2.02 G

0-2MHz

100-512MHz

0-100 kHz

5M

10 M10 M

10M

10 M

couplercoupler

IF P-cal100-520 M

100-520 M

Per tens 10kPulses

LNA LNA

Observation system

1pps10M

32

Correlation Processing (soft correlater)

F. Kikuchi et al, Earth Planets Space, vol.56, pp.1041-1047, 2004.

0 20 40 60 80 100

0

20000

40000

60000

80000

100000

120000

S/N 10dB UP! PN=kTB

Only use the signal in a bandwidth of several Hz

Bandwidth B 100Hz—>10Hz

34

35

Procedure and conditions for obtaining phase delayDifferential phaseφR(t )-φV(t )

2π ambiguity ionospherephase error

s1: 2212, s2: 2218, s3: 2287, x: 8456 MHz

1.

2.

3.

4.

procedure　　　　　　　　　　　　condition

<83 ns

<4.3 deg

<0.23 TECU<59 ps<45.6 deg

6MHz

75MHz

2212MHz

8456MHz

Eq.1

Eq.2

Eq.3

Eq.4<0.42TECU

<10.2 deg

Sorry! About 20 pages were deleted for VLBI

35

Close phase delay 20080120

VERA: Ishigaki, Iriki, Mizusawa, Ogasawara(ns)baseline

Hobart, Shanghai, Urumqi, Ishigaki(ns)baseline

41

Correct atmospheric delay--GPS + Niell Mapping function

SELENE8局のGPSデータをIGS或いは天文台のvgrからDownload し、GpsTools 解析ソフトを用いて各局の天頂方向の大気遅延ZTDを推定する。推定精度：10mm；　時間間隔：１分或いは５分。

X (m) Y (m) Z (m) 距離 (m) 高度 （m）水沢 VLBI -3857241 .85 3108784 .791 4003900 .608 189 .58231 116 .523

mizw GPS -3857164 .39 3108693 .067 4004047 .332 117 .7

入来 VLBI -3521719 .59 4132174 .674 3336994 .224 42 .582571 573 .522

irik GPS -3521735 .46 4132137 .51 3337007 .646 565 .287

石垣 VLBI -3263994 .73 4808056 .288 2619949 .219 40 .688873 65 .026

isgk GPS -3263984 .04 4808036 .484 2619983 .118 58 .65

父島 VLBI -4491068 .81 3481544 .791 2887399 .567 40 .097662 273 .048

ogsa GPS -4491042 .33 3481573 .606 2887390 .838 266 .157

上海 VLBI -2831686 .91 4675733 .666 3275327 .69 92 .159441 29 .43

shao GPS -2831733 .57 4675666 .07 3275369 .496 22 .209

ウルムチ VLBI 228310 .72 4631922 .795 4367063 .988 83 .694217 2033 .205

guao GPS 228380 .79 4631962 .42 4367041 .08 2048 .67

Hobart VLBI -3950236 .74 2522347 .561 -4311562 .54 193 .62816 65 .105

hob2 GPS -3950074 .52 2522418 .574 -4311640 .86 46 .055

Wettze ll VLBI 4075539 .899 931735 .27 4801629 .352 138 .30185 669 .124

wtzr GPS 4075578 .273 931852 .7652 4801567 .306 663 .796

各局のVLBIとGPS受信機の位置。近く設置。 42

11.5 12.0 12.5 13.0 13.50.35

0.40

0.45

0.50

0.55

0.60

Correct ionospheric delay using GPS 20080115-12 MZ-IR

MZ Rstar

IR Rstar

MZ R-V

IR R-V

11.5 12.0 12.5 13.0 13.5

-0.0002

-0.0001

0.0000

0.0001

0.0002

MZ-IR

m

m

電離層モデル電離層モデル

Ionosphere

Ionospheric Pierce Point

z’

zH

RE

PPPP

PP

E

E

AzAz

zzHRzRz

Elz

φαλλ

φαφαφ

α

π

sinsinarcsin

)coscossinsinarcsin(cos

'

sinarcsin'

2/

+=

+=

−=+

=

−=

α

),( PPPP λφ

),( λφ El

GLOBAL TECGLOBAL TECモデルモデル

∑∑= =

+nmax

nsnmsnm

n

mnm mSmCP

0 0

)sincos()(sin λλφ

πλπλ −+≈−= UTLTs UT

λ °0

LT

=),,( λφUTTEC球面調和関数展開

Sun-Fixed座標

),( λφ

CODE GIM Model (15*15)

Ino. delay

Time (h)45

0 20 40 60 80 100-180

-120

-60

0

Y =-0.3696-1.6845 X

Phase-freq. Characteristicsof receiving system

-1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0

0

1

2

3

4

B C D E F G

(c) Phase characteristics oftelescope

Phas

e (r

ad) 1

23456

Differential phase delay bias in SELENE: several ps

flat

Offset (deg) Offset (deg)

linear

-0.2 -0.1 0.0 0.1 0.2-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20 B C D E F G H I J K L M(b) After correction

123456789101112

After correction, 1.7degRMS

Qinghui Liu, et. al, ``Effect of Phase Characteristics of Telescopes on

Same-Beam Differential VLBI", IEEETrans., A&P. May 2007.

R V

Rstar Vstar

46

SummaryDifferential VLBI technique in SELENE

1. Same-beam VLBI observations were performed

2. Differential phase delay can be obtained by

high accuracy several ps + little bias <several ps

3. Orbit-determination accuracy several meters

Doppler + differential VLBI Data

Global gravity field (include far side and limb) will be accurately determined soon.

50