位相遅延量を使った飛翔体のVLBI位置計測 VLBI Astrometric Observation of Spacecraft with phase delay 関戸　衛、市川隆一、大崎裕生、近藤哲朗、小山泰弘（NICT）、 吉川真（ISAS/JAXA）、大西隆史（富士通）、 「のぞみ」相対ＶＬＢＩ研究グループ （ISAS/JAXA、NICT、国立天文台、国土地理院、岐阜大、 山口大、北海道大、SGL,NRCan Canada） 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.

VLBIによる飛翔体ナビゲーション :目的 精密軌道決定の要求：惑星への精密着陸・軌道投入、軌道修正のエネルギー節約 SC Astrometry R01 R02 VLBI + R&RR Requirements for navigation accuracy is increasing in space missions.

「のぞみ」 の地球スイングバイ 日本の最初の火星探査機「のぞみ」 を2つの地球スイングバイの間の期間で観測した。 VLBI Observations NOZOMI was Japanese first Mars mission lunched 1998. 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.

日本国内及びカナダのVLIB観測局がVLBI観測に参加した。 宇宙研、NiCT、天文台、国土地理院、岐阜大、山口大、北海道大学と、カナダのアルゴンキン局 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)

有限距離の電波源に対するVLBI 遅延モデル 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 1993. Based on this form, we made a coordinates transformation in terms of general relativity. (Fukuhisma 1993 A&A)

有限距離電波現に対する 相対論的VLBI遅延モデル コンセンサス モデル (M.Eubanks 1991) 有限距離 VLBIモデル (Sekido & Fukushima 2004) Obtained formula is quite similar with the Consensus model but different at some terms.

解析手順 C: 予測遅延量と偏微分係数の計算 標準予測値計算パッケージCALC9 を修正して使用. (Thanks to NASA/GSFC group) O:ソフトウェア相関器により観測遅延量 (tp)の抽出. O-C:最小二乗法によるパラメータ推定 真の軌道 予測軌道 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.

群遅延の場合(Post-fit 解析残差) ~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.) 飛翔体の信号

位相遅延量 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.

併合位相 苫小牧（北大) 1280km ９００ｋｍ 山口大 岐阜大 ５００ｋｍ 位相接続の結果、非常に高精度な遅延量計測が長時間（24時間以上）のスパンで実現した。 (June 4th experiments)

基線を増やしたときの位相遅延解析解（飛翔体位置）の 軌跡 (6月4日の観測) Tobs Nstn Nbase 6/4 26 h 7 21 Algonquin基線を含む 原点はR&RR による確定軌道

まとめ 国内・国際基線を使って「のぞみ」のVLBI 観測を実施した 相対論的有限距離電波源遅延モデルを導出し、CALC9に組み込んだ. 20ピコ秒精度の位相遅延量が長期のスパンで計測できた. 位相遅延量を使って飛翔体の天球座標を推定し、R&RRで計測した確定軌道とほぼ同じ位置が推定された（確定軌道 を予測軌道として与えた場合）. 次の問題は、 予報軌道（Predicted orbit）を使って解を収束させること。 相対VLBI観測により大気などの伝播遅延誤差を相殺する技術の採用。

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

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.

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.

Spacecraft Navigation VLBI + R&RR

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.

Predicted Orbit Final 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

For astrometry of S.C. Tasks to be done are VLBI for Finite distance radio source A New VLBI delay Model corresponding to the CONSENSUS model. Narrow band width 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.

SC coordinate solutiion with Group Delay (Domestic Baselines) 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 determined orbit with R&RR

Phase delay solution Obs. duration Nstn Nbase May22 3.5 + 4 hours 6 15 10 May27 3 hours 4