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 teamNational 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Kaguya(SELENE)

Selenological and Engineering Explorer●SELENE consists of ;1) Main Orbiter
2) Relay Satellite (Rstar)
3) VLBI Radio Satellite (Vstar)chemicalelements

X-ray Spectrometer
Gamma-ray Spectrometer

mineralogy

Spectral Profiler
Multi-band Imagersurfacestructure

Terrain Camera
Rader SounderLaser Altimetersurfaceenvironment

Magnetometer
Plasma Imager
Charged Particle Spectrometer
Plasma Analyzer
Radio Science Observation

imagingHigh Definition Television
Cameragravity field

Relay Satellite Transponder
Differential VLBI Radio Sources2

Two techniques for lunar gravity field

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

Differential VLBI technique(Sensitivity in direction perpendicular to LOS)SELENE VLBI observation
Differential phase delay
Orbit determination
3Gravity experiment by 2- and 4-way Doppler in SELENE

Sensitivity inline-of-sight(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 sideRstar

X-band dipole antenna
S-band dipole antenna

2051

2241
.579

.614

Main

Patchantenna

64mφ

8456z
M
H.466

地球

2081

UDSCmoon.125VstarRstar

20
286
1.466.41026

JAXA station（TACS）

anbSd

新GN(11mφ)

2way: m/s = 0.5 * C /( k1* fup) *Hz
4way: m/s=(f4way-fbias)*C/(k5*k6*fup)
fbias=fref-(k2+k5*k6)*fup; fref=8456.125M

first direct measurement of thegravity field on the far side（≒30kHz）

4

Doppler data, Time interval 0.1s

Hｚ
9000

Rstar−2Way

8900

53000

Rstar-Main-4Way

52000

8800
8700

-5600

Raw data

50000

-5800

49000

8500

20071101

8400

Vstar−2Way-5200
-5400

51000

8600

-5000

20071101

48000

-6000

20071020

-6200
0200

400

600

80010000Hｚ

1.0400

600

800

01000

residual

4

1.5

200

0.5

10.5

0.000.0-1

Time (s) -4
400

600

8000.293 Hz RMS

1000

1000

-1.0-3200

800-0.5-20600

1.02-1.0

400

1.5

3-0.5

200

Time (s)
0200

400

600

800

Time (s)

-1.5
1000

1.028 Hz RMS

0200

400

600

800

1000

0.355 Hz RMS

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
S/X Dipole antenna
for Doppler and VLBI

Rstar(Vstar)

Qinghui Liu
et. al ``New method ofmeasuring phasecharacteristics of antennausing Doppler frequency
measurement technique",IEEE Trans.,

Antenna and Propa.,
3312-3318, 2004.

Patch Antennalink Rstar and Main

Qinghui Liu

Octagonal prism bodyIEEE Trans., A&M,

et. al ``Effect of In-situ
Phase Characteristics ofAntennas Onboard Spin
Satellites on Doppler
Measurements for lunar
gravity field ",(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 axis
6

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

fs=4.39968/24=0.18332Hz
T=5.4549s

fs=4.39968/24=0.18332Hz fs=4.4988/24=0.18745Hz
T=5.3348s
T=5.4549s

Estimate spin frequency fs with an accuracy 0.0001 Hz
7

Remove spin influence using LPF

Hｚ

80000

input X(n)（simulation)

60000

Linear phase LPF using Kaiser
window function

40000

Doppler20000
0Kaiser function(⎧ I α 1 − (2k /( N − 1)) 2⎪Wk = ⎨I 0 (α )⎪⎩0，k > ( N − 1) / 2⎛ ( x / 2) n ⎞⎟⎟I 0 ( x) = 1 + ∑ ⎜⎜n! ⎠n =1 ⎝1∞Period3h-Amp50kHz＋
Period2h-Amp20kHz＋
0-0.05Hz-Amp0.3Hz/f 20個-20000)-40000k ≤ ( N − 1) / 2-60000
010000

20000

30000

40000

50000

60000

70000

Gravity information
Hｚ

20.00010

Output Y(n)-input X(n)0.00005

0.1
0.01
1E-3

0.00000

1E-4
1E-5-0.00005

1E-6

N=601，α=12.4226

Kaiser function

1E-7-0.00010

1E-8

0

1E-9
0100

200300400

500

Important to give a suitable value for α

10000

20000

30000

40000

50000

60000

70000

Accuracy for conserving gravity
information in 0-0.05Hz Æ0.00002Hz

8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 LPF
2. 4way-Doppler can also be determined at a high accuracy
after LPF, and the gravity signals on the far side weredetected firstly.
3. SELENE lunar gravity field model: SGM90e

Differential VLBI technique(Sensitivity in direction perpendicular to LOS)SELENE VLBI observation
Differential phase delay
Orbit determination
21

Why do VLBI observations in SELENE?

Position error of Rstar

Anticipated coefficient sigma
degree variances of sphericalharmonic of lunar gravity field

2-way Doppler

2-way Doppler+Differential VLBI

Matsumoto et. al

Simulation results
22

VLBI observations in SELENE(Sensitivity in direction perpendicular to LOS)
Rstar Vstar
Differential phaseφR(t )- φV(t )Rstar

Differential phase delay
Accuracy: ps(First time in the world)

2400
km

800k

Separate angle
between Rstar
and Vstar is lessthan 0.9deg

mVstarMoon

Main
IonosphereQuasarAtmospherecorrelator

km010

Main satelliteGroup delay
Accuracy: ns(Conventional method)23

RadiosourceSELENE MAIN and other spacecrafts
Bandwidth 10MHzgeτVLBI
principle
ytim

Delaα

Group delay τg=Δphase/Δfreq.
B

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

τg=Phase/frequency
2π ambiguity

Rstar&Vstar Differential phase delay
X18000Phase

Time delay τg=Bsinα/c

2280

6000

2260

4000

S32240
2220

2000
2200
2200

Error of phase in SELENE
have to be less than
<4.3 deg in S-bandsevere condition

S-band

2300

2220

2240

2260

2280

2300

00

2000

4000

6000

8000

Freq (MHz)When error of phase is 10 deg
Error of phase delay 3.6/360/8456M=1ps

24

satellite

Origin of phase fluctuation

It is difficult to obtain thecorrelation phase with anaccuracy of 4.3 deg

ionosphere

atmosphere

PLO〜

PLO〜

H-Maser

PLO

H-Maser・frequency variation ofradio wave
（temporal、spatial）・ionosphere・atmosphere・thermal noise・phase variation inreceiver〜

PLO〜

Correlation processing
25

Atmosphericphase fluctuation

Qinghui Liu, et. al, IEEE Trans., Antenna and Propa., Apr. 2005.
Nishio Masanori, Qinghui Liu, et.al, IEEE Trans.,
Antenna and Propa., July 2007.

alternately
φR(t )
φV(t )

Switching VLBI

Using switching VLBI
observation
Condition for determiningφR(t )- φV(t ) with an errorof 4.3 deg cannot besatisfied when ionosphereand atmosphere fluctuationis strong.
26referenc

Same-beamdifferential VLBI

2395kmφR(t )Vstar

φV(t )

e792kmRstar

φR(t )- φV(t )k76
43Ionosphere

Antenna beam

MoonAtmospherecorrelator

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

Influences ofthe receiver,atmosphere andionosphere arenearly canceled

mkm
012Rstar period 4 hours
Vstar period 2.5 hours
inclination 90deg

LIU et. al IEICE, 2006
LIU et. al Adv. SpaceRes, 2007

Kikuchi, Liu et. al,2008
27

Stations for SELENE VLBI observations

Wettzell 26mφVERAUrumqi 25mφ
8265 kmShanghai 25mφ
Ishigaki
247Ogasawara 20mφ
8337 km12IrikiMizusawa 20mφkm

Hobart 26mφ

外国局： 2ヶ月； VERA：１年以上

31

Observation system

X-bandS-band
2.2-2.32 G

8.18-8.6 G
P-cal
Per １M

coupler

coupler

5M

Front end

LNA

LNA
100520M

8.08 G

LO1
10 M

Per tens 10k
PulsesIF P-cal2.02 G

LO1
10 M

coupler

coupler
100520 M
IF

LO2100512MHz

10M

IF100520 M

10 M

Video
Converter

Back end
K4、Mark4,50-2MHz
ch1 LPF <100kHz ch21pps
10M

ch3ch40-100 kHz
SRTP 200 kHz、6 bit
32

Correlation Processing (soft correlater)

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

Only use the signal in a
bandwidth of several Hz
120000100000

Bandwidth B 100Hz—>10Hz
S/N 10dB UP! PN=kTB

80000
60000
40000
20000
00

20

40

60

80

100

34

Procedure and conditions for obtaining phase delay
Differential phase

ionosphere

2π ambiguity

phase errorφR(t )- φV(t )s1: 2212, s2: 2218, s3: 2287, x: 8456 MHz

procedurecondition
Eq.1

1.
6MHz

<83 ns
Eq.2

2.
75MHz

<10.2 deg

2212MHz<4.3 deg

8456MHz<45.6 deg <59 ps

3.
4.

Eq.3
<0.42TECU

Eq.4<0.23 TECU
35

Sorry!
About 20 pages were deleted for VLBI

35

Close phase delay

20080120

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

Hobart, Shanghai, Urumqi, Ishigaki
baseline(ns)

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。
水沢
VLB I
mizw GPS入来VLB Iirik GPS
石垣VLB Iisgk GPS父島VLB I
ogsa GPS上海VLB Ish ao GPS
ウルムチ VLB I
gu ao GPS
HobartVLBI
h ob2 GPS
We ttze ll VLB I
wtzr GPSX (m)

Y (m)

Z (m)

距離 (m) 高度 （ m）

-3857241.85-3857164.39-3521719.59-3521735.46-3263994.73-3263984.04-4491068.81-4491042.33-2831686.91-2831733.57
228310.72
228380.79-3950236.74-3950074.52
4075539.899
4075578.273

3108784.791
3108693.067
4132174.674
4132137.51
4808056.288
4808036.484
3481544.791
3481573.606
4675733.666
4675666.07
4631922.795
4631962.42
2522347.561
2522418.574
931735.27
931852.7652

4003900.608
4004047.332
3336994.224
3337007.646
2619949.219
2619983.118
2887399.567
2887390.838
3275327.69
3275369.496
4367063.988
4367041.08-4311562.54-4311640.86
4801629.352
4801567.306

189.58231 116.523
117.7
42.582571 573.522
565.287
40.688873 65.026
58.65
40.097662 273.048
266.157
92.159441 29.43
22.20983.694217 2033.205
2048.67
193.62816 65.105
46.055138.30185 669.124
663.796

各局のVLBIとGPS受信機の位置。近く設置。

42

Correct ionospheric delay using GPS

電離層モデルz ' = arcsin

0.60

IonosphericPierce Point(φ PP , λ PP )z = π / 2 − El
RE sin z
RE + Hφ PP = arcsin(cos α sin φ+ sin α cos φ cos Az )sin α sin Az
λ PP = λ + arcsin
φ PPz’El

IonosphereREα0.40

MZ Rstar

0.35
11.5

12.00.0001

球面調和関数展開∑∑ P (sin φ )(C cos mλ + S sin mλ )n =0 m =0s(φ , λ )nmλSun-Fixed座標

m13.0

13.5

IR R-V

MZ R-Vs0°-0.0001

MZ-IR-0.0002
11.5

λ s = LT − π ≈ UT + λ − π12.50.0000

TEC (UT , φ , λ ) =nm

IR Rstar

0.45

TEC(15*15)
モデル
CODEGLOBAL
GIM Model

nm

Ino. delay

0.50

0.0002

nmax nm0.55z(φ , λ ) H

α = z − z'

20080115-12 MZ-IR

12.0

12.5

13.0

13.5

UTLTTime (h)45Differential phase delay bias in SELENE: several psPhase (rad)4(c) Phase characteristics oftelescope

0B1
C2
D3
E4F5G6321R V
Y =-0.3696-1.6845 X-60

linearPhase-freq.
Characteristics
of receiving system-120

flat0-180-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00Offset (deg)20406080

100Offset (deg)After correction, 1.7degRMS
0.20

Rstar

0.15

Vstar

0.10
0.05
0.00
-0.05
-0.10-0.15(b) After correction-0.2-0.1

0.00.10.2

B1C2D3E4F5G6H7I8J9K10L1112M

Qinghui Liu, et. al, ``Effect ofPhase Characteristics of Telescopes on
Same-Beam Differential VLBI",IEEETrans., A&P. May 2007.

46

Summary
Differential VLBI technique in SELENE
1. Same-beam VLBI observations were performed
2. Differential phase delay can be obtained byhigh 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