1. Astrometry Observation of Spacecraft with Phase delay
M.Sekido, R.Ichikawa, H.Osaki,
T.Kondo, Y.Koyama(NICT)
M.Yoshikawa, T.Ohnishi(ISAS),
W.Cannon, A.Novikov (SGL),
M.Berube(NRCan), NOZOMI VLBI group (NICT,ISAS,NAOJ,GSI,Gifu Univ., Yamaguchi Univ., Hokkaido Univ.)
Today, I wish to report current statue of our approach to SC navigation with VLBI. We are collaborating with ISAS of Japan,
SGL, and NRCan.

2. Spacecraft Navigation with VLBI: Motivation
Precise orbit determination is requested for precise landing, orbiting, & saving energy in maneuver :
SC Astrometry
R01
R02
VLBI +
R&RR
Requirements for navigation accuracy is increasing in space missions.

3. NOZOMI’s Earth Swing-by
Japanese first Mars mission NOZOMI was observed during the period between two earth swing-bys.
VLBI Observations
NOZOMI was Japanese first Mars mission lunched Its orbit plan was changed due to some problems.
And eventually, it went to Mars with two Earth swing-by. During these two swing-bys, a request for supporting with VLBI was arose.
Because they are afraid loosing R&RR data during that period, since the high gain antenna of the SC faced to the the instead of the Earth.
I will talk here about the experiments at the end of May and beginning of June. The NOZOMI was approaching to the earth for the second swing-by at these time.

4. Japanese and Canadian VLBI
Stations participated in NOZOMI VLBI observations.
ISAS,CRL,NAOJ, GSI,Gifu Univ, Yamaguchi Univ. Hokkaido Univ.
SGL, NRCan supported.
Algonquin
SGL & NRCan
Tomakomai
(Hokkaido Univ.)
Mizusawa
(NAO)
Usuda
(ISAS)
Gifu
(Gifu Univ.)
Tsukuba
(GSI)
Yamaguchi
(Yamaguchi Univ.)
VLBI observations were made by wide support from Japanese VLBI community and Canadian groups.
We appreciate for their support and could get important experience of SC VLBI observations.
Koganei
(CRL)
Kagoshima(ISAS)
(uplink)
Kashima
(CRL)

5. VLBI delay model for finite distance radio source
Normal VLBI
VLBI for finite distance radio source B X Y S B X Y
RX0 K
I will introduce the formulation of delay model of Finite distance radio source, briefly here.
Delay of Normal VLBI is expressed by solar products of source vector and baseline vector.
Corresponding one for finite distance radio source can be expressed in the same form, if we used a pseudo source vector defined by this way. This was proposed by Fukushima in Based on this form, we made a coordinates transformation in terms of general relativity.
(Fukuhisma 1993 A&A)

6. Relativistic VLBI delay model for finite distance radio source
CONSENSUS MODEL (M.Eubanks 1991)
Finite Distance VLBI MODEL (Sekido & Fukushima 2004)
Obtained formula is quite similar with the Consensus model but different at some terms.

7. Analysis Procedure C: Compute a priori (delay) and partials
We modified CALC9 for our use(finite VLBI).
(Thanks to NASA/GSFC group)
O:Extracting Observable (tp) with software correlator.
O-C: least square parameter estimation
True Orbit
Apiori Orbit
We made implementation this new delay model in a software by modification of CALC9. Thanks to GSFC/NASA group for permission to use that.
Observables are derived by software correlator.
Then residual of O-C was analyised by least square fitting of parameters.

8. Group Delay(Post-fit Residual)
~100 nano sec.
quasor
This is an example of post fit residual of least square analysis with group delay and delay rate.
The delay residual are distributed in the same order of the closure of dela, as you see.
~1MHz
(frq.)
Signal type from Spacecraft

9. Phase delay
Phase delay is also another approach to get high angular resolution even with short baselines.
A correlation software to extract phase delay with main carrier signal was developed. The signal to noise ratio was much improved since only frequency around the main carrier is used. Fringe phase was extracted with high SNR.
Since the SC was observed for a long time without switching, we could connect phase delay without ambiguity in this case.
Closure of the phase delay was taken to see the accuracy of observable. This is a plot of time span of about 3 and half hours.
The drifting parts of phase are due to known problem of recording or processing. Please ignore that.
The closure delay is distributing quite uniformly in flat line. This indicates phase delay observable is extracted correctly and its precision is about a few tens of pico seconds.

10. Closure phase delay Tomakomai 1280km ９００ｋｍ Yamaguchi Gifu ５００ｋｍ
As result of phase connection, Very precise delay observable was obtained over 24 hours.
(June 4th experiments)

11. Phase delay solution’s track by adding baselines (June 4th)
Tobs
Nstn
Nbase
6/4
26 h 7 21
Including Algonquin
Baseline
Origin is determined orbit with R&RR

12. Summary
VLBI observations of spacecraft were performed with domestic and intercontinental baselines.
Relativistic Finite VLBI delay model and analysis software were developed and implemented based on CALC9.
Phase delay was derived in precision of 20 pico sec for long time span.
SC coordinates estimated by VLBI agreed with that of R&RR when Determined (R&RR) orbit was used as a priori.
Next problem is SC coordinates started from Predicted orbit.