1. ASTROMETRY OBSERVATION OF SPACECRAFT WITH VERY LONG BASELINE INTERFEROMETRY ---- A STEP OF VLBI APPLICATION FOR SPACECRAFT NAVIGATION ----
M.Sekido, R.Ichikawa,H.Osaki,
T.Kondo,Y.Koyama
(National Institute of Information and
Communications Technology :NICT,Japan)
M.Yoshikawa,T.Ohnishi(ISAS,Japan),
W.Cannon, A.Novikov (SGL,Canada),
M.Berube (NRCan,Canada), and
NOZOMI VLBI group(NICT,ISAS,NAOJ,GSI,Gifu Univ. Yamaguchi Univ., Hokkaido Univ., Japan)
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
Requirments for increased accuracy of orbit control for future space missions:
For landing, orbiting, & saving energy
SC Astrometry
R01
R02
VLBI +
R&RR
Requirements for navigation accuracy is increasing in space missions.

3. NOZOMI’s Earth Swing-by
NOZOMI was launched in July 1998.
Due to some troubles, new orbit plan with Earth swing-by was proposed.
R&RR observations were difficult in a period.
Apr.
May
Mar.
Jan.
Feb.
Jun.
May 22, 24, 27
June 4
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. For astrometry of S.C. Tasks to be done are
VLBI delay mode for Finite distance radio source
A New VLBI delay Model corresponding to the CONSENSUS model.
Narrow band width of the signal
Group delay or Phase delay
Delay Resolution: (nano/pico seconds)
Ambiguity problem
Data Processing and Analysis software
IP-sampler boards recording to HD
Software correlation & Analysis software
For astrometric analysis of SC coordinates, tasks to be done are
making a formulation of observation equation corresponding to the consensus model.
The signal from SC is not so wide as that of quasar. The delay resolution is up to oder of nano seconds in case of group delay. To increase the the resolution, we can use phase delay. But we need to solve ambiguity for that.
For this analysis we developed a software correlator and own analysis software.

6. VLBI delay model for finite distance radio source
Normal VLBI
VLBI for finite distance radio source B X Y S B X Y
RX0
RY0 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)

7. VLBI delay model for finite distance radio source
CONSENSUS MODEL (M.Eubanks 1991)
Finite Distance VLBI MODEL (Sekido & Fukushima 2003)
Obtained formula is quite similar with the Consensus model but different at some terms.

8. Finite-Infinite : Delay Difference

9. Analysis Procedure for SC Astometory
I. Compute a priori (delay, rate) (C) and partials
We modified “CALC9” for our use(finite VLBI).
(Thanks to GSFC/ NASA group for permission to use)
II. Extracting Observable (tg, tp)(O) with software correlator.
III. Computing O-C and least square parameter estimation
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.

10. Observable: Phase Delay & Group delay
2p n ambiguity
tg:Group Delay
Dtp ~ 1/RF
~1 pico second
Phase
Phase Delay
Dtg ~ 1/BW
~1 nano second
(Spacecraft)
Band width
Frequency

11. Group Delay(Post-fit Residual)
Rate residual
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.
Delay Residual

12. Group Delay (Domestic Baselines)
6/4(R&RR)
6/4(VLBI)
June 4
Orbit motion
May 27
This is preliminary result of radio source coordinates in celestial sphere estimated with Japanese domestic baselines. The reason of the Algonquin baseline is not included will be shown later. The origin of this plot is the coordinates of the SC orbit determined by R&RR measurements by ISAS. The SC is moving rather rapidly since it is near the earth and approaching.
Our results are almost consistent with OD of ISAS and JPL within the formal error.
But the error bar is in order of arc seconds because of low delay resolution and using Japanese domestic baselines.
Origin is Orbit on May 27, which was Determined by ISAS with R&RR
Origin is Orbit on June 4.

13. Phase delay Closure of Phase delay (Kashima-Usuda-Tsukuba)
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.

14. Phase Delay Analysis Predicted Orbit Determined Orbit 4 June 2003
Post Fit Delay Residual (sec)
Determined
Orbit
4 June 2003
Predicted　Orbit
By using these phase delay observables, we can estimate SC coordinates. The total amount of ambiguity is not known but it can was estimated with clock offset of each stations. The residual is distributing in order

15. Estimated Coordinates
Determined
Orbit
Estimated Coordinates
Predicted　
Orbit

16. Summary
NOZOMI VLBI observations were performed with domestic and intercontinental baselines.
Formula for Finite VLBI delay model was derived.
An analysis software is developed with that delay model based on CALC9.
Astrometric SC coordinates were obtained with Group/Phase delay observables.

17. Thank you for attention.
Summary
Least square solution with Predicted orbit did not give consistent solution with determined orbit.
=>Probably due to nonlinearity of observable.
=>Iterative solution will solve this problem.
Next step:
SC Astrometry => Orbit estimation
Thank you for attention.

18. Orbit of NOZOMI
Space
Apr.
May
Mar.
Jan.
Feb.
Jun.

19. Group Delay (Range signal)
Closure
Observation mode
= 2MHz, 2bit
Accuracy of delay observables is shown by closure delay in this panel. The range signal from space craft is moderated and spread in range of a few MHz. So group delay can be determined. But the precision of the delay is in the order of several tens of nano seconds. There is space for improvement of delay accuracy. Actually, JPL group are doing DDOR in order of nano seconds. In anyway, the delay resolution is much worse than usual geodetic VLBI using quasors. So long baseline is important if you use group delay for spacecraft navigation.

20. Spacecraft Navigation with VLBI : Motivation
Required for increased accuracy for future space missions:
For landing, orbiting, & saving energy
JPL/NASA has been employed
Japanese Space Agency (ISAS+NASDA=JAXA)
NOZOMI(Japanese Mars Explorer)
Needs to support orbit determination with VLBI.
Mission as our own Project
This sort of VLBI application is now new as you know. JPL/NASA is using it from 1980s.
But only NASA is doing that today. Japanese Space Agency want to use for their future space missions.
So we started collaboration with them.
There was a request of VLBI support for NOZOMI, especially. I will talk about it in next slide.
And we put it one of mission our own project.

21. Spacecraft Navigation
VLBI +
R&RR

22. Observation：IP-VLBI Sampler board
K5　VLBI　System
Sampling rate:40k-16MHz
Quantization bit: 1-8bit
4ch/board
10MHz,1PPS inputs
The data was taken by PC-based data acquisition system, a part of K5.