COMMUNICATIONS RESEARCH LABORATORY

Serial No. 24 July 2004

NATIONAL INSTITUTE OF INFORMATION ANDCOMMUNICATIONS TECHNOLOGY

CONTENTS

Technical Reports

Rapid UT1-UTC estimation from Westford-Kashima e-VLBI experiment (2) . . . . . . 2Yasuhiro Koyama, Tetsuro Kondo, Hiroshi Takeuchi, Masaki Hirabaru, DavidLapsley, Kevin Dudevoir, and Alan Whitney

HAYABUSA VLBI observations for development of deep space tracking –Preliminary report–

. . . . . . 7

Ryuichi Ichikawa, Mamoru Sekido, Hiro Osaki, Yasuhiro Koyama, Tetsuro Kondo,Makoto Yoshikawa, and VLBI spacecraft tracking group

Development of software baseband converter . . . . . . 9

Hiroshi Takeuchi

Derivation of relativistic VLBI delay model for finite distance radio source(Part I)

. . . . . 11

Mamoru Sekido and Toshio Fukushima

The Australian experience with the PC-EVN recorder . . . . . 18Dodson, R., S. Tingay, C. West, A. Hotan, C. Phillips, J. Ritakari, F. Briggs, G.Torr, J. Quick, Y. Koyama, W. Brisken, B. Reid, and D. Lewis

- News - News - News - News -

CARAVAN-35, small radio telescope package released . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Announcement

3rd e-VLBI Workshop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1

ISSN 1882-3440

2 IVS NICT-TDC News No.24

Rapid UT1-UTC estimation

from Westford-Kashima e-VLBIexperiment (2)

Yasuhiro Koyama1 (koyama@nict.go.jp),Tetsuro Kondo1, Hiroshi Takeuchi1, MasakiHirabaru2, David Lapsley3, KevinDudevoir3, and Alan Whitney3

1 Kashima Space Research Center, NationalInstitute of Information and CommunicationsTechnology, 893-1 Hirai, Kashima, Ibaraki314-8501, Japan

2 Koganei Headquarters, National Institute ofInformation and Communications Technology

3 Haystack Observatory, Massachusetts Instituteof Technology

1. Introduction

After the previous report [Koyama, et al.,2003a], a test e-VLBI session was performed onJune 27 with the baseline between Kashima 34mstation and Westford 18m station to demonstratethe rapid UT1-UTC estimation from the actual ob-servations. The observations were performed forabout two hours at the total effective data rate of56Mbps, and the data were processed using bothMark-4 correlator at Haystack Observatory andK5 software correlator at Kashima. By using theK5 correlator outputs, UT1-UTC was estimated atabout 21 hours 20 minutes after the last observa-

tion completed [Koyama, et al., 2003b). Followingthis successful demonstration of e-VLBI techniqueto determine UT1-UTC value so rapidly, ObservingProgram Committee of the IVS started to discussthe possibility to introduce the e-VLBI techniqueto the routine international VLBI sessions coordi-nated by IVS. The capability of the rapid UT1-UTC estimation is considered to be best utilizedby the single baseline intensive sessions and it wasrecommended to try to establish routine e-VLBIsession series every Sunday. Currently, the inten-sive sessions are performed by using a baseline be-tween Kokee Park and Wettzell stations on week-days (from Monday through Friday), and by usinga baseline between Wettzell and Tsukuba stationson Saturdays. By filling the vacant Sundays by us-ing the e-VLBI intensive sessions, daily monitoringof UT1-UTC will be realized and it was consid-ered to be the best way to introduce the e-VLBIin the regular session. If these e-VLBI sessions areconsidered to be smooth and reliable, efforts willfollow to make the e-VLBI becomes possible forthe existing intensive sessions to improve the la-tency of the UT1-UTC estimation. In this scope,we have performed two e-VLBI sessions again bythe baseline between Westford and Kashima 34mstations to prepare the necessary softwares to es-tablish the routine e-VLBI intensive sessions. Inthis report, we will describe the recent develop-ments to improve the software correlations and thenetwork connectivities and will discuss about theresults obtained by the test sessions.

client host N

client host 2

request data set

inquire a-priori information

end

start

YEScompleted?

NO

processing (cor_all)

report the results

client host 1

client host 3

k5cor_init.sh

k5cor_start.sh

k5cor_end.sh

master.txt

server host

Figure 1. A schematic diagram of the server and client mechanism developed for the dis-tributed cross correlation processing.

July 2004 3

2. Developments of the K5 Software Cor-relator

After the test e-VLBI sessions in 2003, the soft-ware correlation programs for the K5 software cor-relator have been improved for their processingspeed [Kondo, et al., 2003]. The previous ver-sion of the software correlation program processesthe FFT processing first and then calculate thecross correlation spectrum to obtain cross corre-lation function. The fast version of the softwarecorrelation program uses the XF algorithm, wherethe cross correlation function is calculated directlyfrom the observation raw data. The processingspeed was improved by a factor of about 6.2. Withthe lag length of 32, 8MHz sampling data can beprocessed at about the same speed of the recordingspeed by using an 1GHz Pentium 4 CPU. In addi-tion, efforts have been made to realize distributedprocessing by using multiple CPUs. One of theefforts is to utilize unused CPU powers of the con-ventional PC systems by developing a screen saverprogram to download the data files from a serverand perform the software correlation [Takeuchi, etal., 2004]. The mechanism, which we are callingas VLBI@home, is consisted by a screen saver pro-gram and a server system program. The serversystem program processes the requests from theclients systems running the screen saver program.Currently, the screen saver program has been de-veloped on the Microsoft Windows operating plat-forms. Any PCs connected to the Internet can beused as the clients. Once the screen saver programis installed, the program begins to communicatewith the server program over the Internet and be-gin to download the data files and then perform thecorrelation processing. Once the processing com-pletes, the results will be reported to the serverprogram and then the client system begins to pro-cess the next data set. If the user of the PC sys-tem starts to use the CPU for the other purposes,the screen saver program promptly terminates theprocessing but the processing can be resumed laterwhen the CPU is not used for a certain time spec-ified by the screen saver configuration.

In addition to the VLBI@home programs, a sim-ple server and client mechanism shown in Figure1 has also been developed by using simple shellscripts and a few Fortran programs. On the serversystem, a master control file ‘master.txt’ is main-tained and the file holds all the information nec-essary to control the distributed processing. Byreading the master control file, the server systemcan assign a set of data files with which the clientsystems can process. Each client system obtainsthe data files and necessary information from theserver system and starts to process the data. When

Figure 2. A WWW browser screen for monitoringdistributed processing status under developments.

the processing is completed at the client system,the client system places the results to a specificplace and then requests the server system for thenext data files. By using this simple mechanism,all the data files can be processed effectively us-ing available computing resources of the client PCsystems. Although the performance of each PCsystem may differ, each client PC systems can pro-cess the data files according to the available perfor-mance. Status monitoring capability is also underdevelopments as shown in Figure 2. Any WWWbrowsers will be able to show the current statushow the distributed processing is on going. In thisserver and client mechanism, data files are accessedby using the Network File Server (NFS) protocol.The disks where the data files are located are mu-tually mounted by multiple Linux and Free BSDunix servers by using amd (Auto Mount Daemon)or autofs programs. The processed results are writ-ten onto a single disk which is also mounted by theNFS from the clients. To avoid multiple access tothe master control file, the server system createsa empty file when it starts to process the mastercontrol file to prevent the other processes to accessthe file. After the modifications to the master con-trol file, the empty file is erased and the other pro-cesses is allowed to process the file. In this way, theclient systems can process the correlation process-ing independently without the tight control fromthe server system. This mechanism is very simplebut it works very well even when the performanceof the client systems are very different. The mas-

4 IVS NICT-TDC News No.24

ter control file contains information when the jobis started by which client system and can reset thestatus when the results are not reported within aspecified timeout time. By doing this, the clientprogram can start or stop at any time.

3. Improvements of the Network Connec-tivities

After the test e-VLBI sessions in 2003, theGALAXY network connection to the KashimaSpace Research Center was terminated. TheGALAXY network is a high speed dedicated re-search network for e-VLBI coordinated by thecollaborations among NICT, NTT Laboratories,National Astronomical Observatory, and JapanAerospace Exploration Agency [Uose, et al., 2003].Before the termination of the connection, Kashimaand Musashino R&D Center of the NTT Labora-tories used to be connected by the OC-48 ATMnetwork and GbE Ethernet was supported over theATM network. The TCP/IP connection was thenrouted to the Abilene network in the United Statesvia the GEMnet network coordinated by the NTTLaboratories. The connection was used for the twotest e-VLBI sessions in 2003.

Since the GALAXY connection to Kashima wasterminated in 2003, the institutional LAN connec-tion inside NICT between Kashima and Koganeiheadquarters had been only available for the e-VLBI data transfer from the stations at Kashima.The connection between Kashima and Koganei hasthe maximum bandwidth of 100Mbps and the net-work is shared by many traffic form the variouspurposes among many projects of the NICT. Byusing this connection, we started to record all ofthe observation data for the IVS geodetic VLBIsessions at Kashima 34m station with the K5 sys-tem since October 2003, and to transfer K5 datafiles to the server at Haystack Observatory or inWashington D. C. and then used for correlationprocessing after converting the data file format tothe Mark-5 system [Koyama et al., 2003c]. Thetypical data transfer rate was about 30Mbps aftertuning various network parameters and using mul-tiple TCP/IP connections by using bbftp program.

On the other hand, an independent high speedresearch network in Japan based on ATM usedto be operated by Telecommunications Advance-ment Organization (TAO) to support advanced re-search and developments for the communicationstechnology. The network was called Japan GigabitNetwork (JGN) and it supported many researchprojects. In April 2004, the TAO and Communi-cations Research Laboratory were merged and thenew institute was established as NICT. At the sametime, the JGN network was upgrade and the new

research test-bed network Japan Gigabit NetworkII (JGNII) was established based on the TCP/IPnetwork. As shown in the Figure 3, Kashima andKoganei was connected by the OC-192 (2.4Gbps)connection and the GbE TCP/IP connection wasestablished between these sites. The TCP/IP net-work is then routed to the Abilene network in theUnited States via JGNII/TransPAC network. Asshown in Figure 4, the connection between JGNIIand the Abilene was recently upgrade to two linesof OC-48 connections.

KashimaKoganei

Tokyo NOC

JGN2 (10Gbps)

JGN2/TransPAC OC48 (2.4Gbps) x 2JGN2

(10Gbps)

Figure 3. Configuration of the high speed networkin Japan.

4. Experiments

As explained in the Introduction, two test e-VLBI session were performed in June 2004. Thefirst session was performed for about two hoursfrom 19:00 UT on June 22. The purpose of the firstsession is to use it as a rehearsal. By processing theobserved data in the first session, it was estimatedthat one hour of observations would be enoughto estimate UT1-UTC with the uncertainty of 20microsec. Therefore, the second session was per-formed for about one hour. After the observations,the data recorded at Westford station with theMark-5 system were extracted and transferred toKashima through Abilene/TransPAC/JGNII net-works. 13.5 GBytes of data were transferred inabout 1 hour and 15 minutes and the average datatransfer rate was 24 Mbps. The transferred datawere then converted to the K5 file format. Duringthe one hour session, 18 scans were recorded in to-tal. 13 scans were assigned to the NFS based dis-tributed software correlation using 12 CPUs run-ning on Linux and FreeBSD. The remaining 5 scanswere assigned to VLBI@home and 9 CPUs wereused. As soon as the data format conversion com-pleted, the software correlation was started. Atthis point, the network connection at Kashima be-came unstable and the data access became very

July 2004 5

Westford

Abilene Network

BOSSNET+GLOWNET(GigE)

10Gbps(OC-192)JGN2 / TransPAC OC-48(2.4Gbps)

Figure 4. Configuration of the high speed network in the United States.

slow. To solve this problem, the servers were re-booted a few times and these operations caused theunexpected delay of the processing. As the results,it took about 2 hours and 38 minutes. Immedi-ately after all the correlation processing completed,database files were generated and the data anal-ysis was performed by using CALC and SOLVEsoftwares developed by the Goddard Space FlightCenter of NASA. The data analysis was completedat 4 hours and 30 minutes after the last observa-tion in the session completed. Table 1 shows thetime sequence from the observations

Table 1. Time sequence from observations throughthe data analysis of the e-VLBI session on June29, 2004

Events Time in UT (Date)Observing session started 19:00 (June 29)Observing session finished 20:00File transfer started 20:13File transfer completed 21:28Correlation processing completed 00:16 (June 30)Data analysis completed 00:30

For both of the two test e-VLBI sessions, effec-tive data rate was 56Mbps. Frequency bandwidthfor each channel was 2MHz. For X-band, 8 chan-nels were used while the remaining 6 channels wereused for S-band. In the data analysis, atmosphericdelay and clock offset were estimated as well asthe UT1-UTC. The formal uncertainty of the UT1-UTC estimation was 22.0 microsec.

5. Conclusions and Future Plans

In conclusion, the capability of estimating UT1-UTC from one baseline e-VLBI session was success-

fully demonstrated from the actual test e-VLBI ses-sion. After the demonstration, the distributed soft-ware correlations were performed for a few timeswith the same condition, but the network prob-lem which caused the delay did not occur again.If the problem did not occur, the software correla-tion processing would have been completed within30 minutes. Therefore, it will be possible to esti-mate UT1-UTC from the similar test session within3 hours from the last observation, since it tookabout 1.5 hours to solve the problem. During thetest e-VLBI sessions in June 2004, many proce-dures were still performed manually while manyprocedures have been automated. But the situa-tion will improve as the software developments ad-vance. The network connection from the Westfordstation of the Haystack Observatory to the Abilenenetwork will be upgraded in near future. Tsukubastation has already been connected to the highspeed network and the Geographical Survey Insti-tute has participated in the regular IVS sessionswith the K5 system since May 2004. To connectthe network, 2.4Gbps ATM link between Tsukubaand NTT Musashino R&D Center operated as theGALAXY network is used and TCP/IP interfaceis used to allow GbE TCP/IP data transfer. Atpresent, TCP/IP connection is only possible whenthe other purposes do not use the ATM connec-tion, but there is a plan to improve the situationby using an ATM switch at Tsukuba station. On-sala and Wettzell stations also have capability toperform e-VLBI operation by using the Mark-5 sys-tems and the good network connectivity situations.Therefore, it will be possible to start e-VLBI in-tensive sessions by using Tsukuba station and onestation from Wettzell, Westford, and Onsala sta-tions. Also at present, discussions about the stan-

6 IVS NICT-TDC News No.24

dard mechanism of the e-VLBI data transfer is un-der discussion. By standardizing the data transfermechanism, the file conversion processing will be-come unnecessary and we can expect to improvethe latency.

Acknowledgment: The authors would like to appre-ciate many members of the Haystack Observatoryand NICT for supporting the e-VLBI developmentsand observations. Research partners at the NTTCommunications Corporation, KDDI R&D Labo-ratories, NTT Laboratories, JGNII, Internet2 havemade the e-VLBI session possible together. e-VLBIresearch and developments in Japan have been pro-moted by a close collaboration among NICT, Geo-graphical Survey Institute, NTT Laboratories, Na-tional Astronomical Observatory, Japan AerospaceExploration Agency, Gifu University and Yam-aguchi University.

References

Kondo, T., Y. Koyama, and H. Osaki (2003), CurrentStatus of the K5 Software Correlator for GeodeticVLBI, IVS CRL-TDC News, No. 23, pp. 18–20.

Koyama, Y., T. Kondo, H. Osaki (2003a), Rapid UT1-UTC estimation from Westford-Kashima e-VLBI ex-periment, IVS CRL-TDC News, No. 22, pp. 6–9.

Koyama, Y., T. Kondo, H. Osaki, A. Whitney, and K.Dudevoir (2003b), Rapid turn around EOP measure-ments by VLBI over the Internet, in Proceedings ofthe IAG G02 Symposium in the 23rd. IUGG GeneralAssembly, Sapporo Japan, July 2003 (in printing).

Takeuchi, H., T. Kondo, Y. Koyama, and J. Nakajima(2004), VLBI@home - VLBI Correlator by GRIDComputing System, in International VLBI Servicefor Geodesy and Astrometry 2004 General Meet-ing Proceedings, eds. N. R. Vandenberg and K. D.Baver, NASA/CP-2004-212255 (in printing).

Uose, H. (2003), Application of Ultrahigh-speed Net-work to Advanced Science, NTT Technical Review,Vol. 1, No.5, pp.39–47

3rd e-VLBI WorkshopOctober 6-7, 2004Makuhari, Japan

Logo designed by S. Arimura

and Y. Koyama

hosted byNational Institute of Information and

Communications Technology

Objectives: The 1st e-VLBI workshop washeld at MIT Haystack Observatory in April2002. The purpose of the workshop was topromote global real-time and near-real-timeVLBI observations using the high speed net-work infrastructure, and it made a greatsuccess. Following the success, the 2nd e-VLBI workshop was held at Joint Institutefor VLBI in Europe (JIVE) in May 2003and enormous progress was seen both in thenetwork infrastructure and the e-VLBI ob-servations and processing systems. The 3rde-VLBI workshop is expected to present anideal opportunity to further enhance and ac-celerate the e-VLBI research and develop-ments, again.

Topics to be discussed will include:

• Reports on e-VLBI tests and demon-strations

• Plans for ongoing e-VLBI development

• Status of interaction with networkproviders and developers

• International networking facilities -now and future

• Standards and protocols for e-VLBIdata transfer.

• Hardware and software interfaces totelescope back-ends and correlators

• Related projects

More information is available on Web Site“http://www.nict.go.jp/ka/radioastro/evlbi2004/index.html”.

July 2004 7

HAYABUSA VLBI Observa-

tions for Development of DeepSpace Tracking –PreliminaryReport–

Ryuichi Ichikawa1 (richi@nict.go.jp), MamoruSekido1, Hiro Osaki, Yasuhiro Koyama1,Tetsuro Kondo1, Makoto Yoshikawa2, andVLBI spacecraft tracking group3

1Kashima Space Research CenterNational Institute of Information andCommunications Technology893-1 Hirai, Kashima, Ibaraki 314-8501, Japan

2Institute of Space and Astronautical Science,Japan Aerospace Exploration Agency

3JAXA, GSI, NAO, Hokkaido Univ., Gifu Univ.,Yamaguchi Univ.

The precise and realtime navigation of the inter-planetary spacecrafts using VLBI technique is cur-rently under development at NICT (National Insti-tute of Information and Communications [formerCRL]). We performed more than 30 VLBI experi-ments for the Japan’s NOZOMI Mars probe fromSeptember 2002 until June 2003 [Ichikawa et al.,2003; Sekido et al., 2003]. The fringe products ofgroup delays were successfully detected from theseVLBI experiments in spite of weak and narrow-bandwidth NOZOMI signal. The group delayswere used to validate the operational orbit determi-nation based on the range and range rate (R&RR)data sets by ISAS (Institute of Space and Astro-nautical Science).

Though the rms scatter of the group delays ofVLBI data from the R&RR results are relativelylarge up to several tens nanoseconds, the both re-sults are consistent with each other. We also de-tected phase delay fringes using updated correla-tion software [Sekido et al., 2003]. The estimatedposition based on the phase delays are good con-sistent with the R&RR results. In particular, thedeclinations determined by phase delay signals areidentical with those obtained by R&RR values.Unfortunately, ISAS scientists gave up to inject theNOZOMI into orbit around Mars due to unrecov-erable malfunction on December 9, 2003.

We perform another VLBI experiments for track-ing of HAYABUSA spacecraft. HAYABUSA,which means “Falcon” in Japanese, was launchedon May 9 2003, and has been flying steadily to-wards an asteroid named “Itokawa”, after the lateDr. Hideo Itokawa, the father of Japan’s spacedevelopment program. HAYABUSA is travelingthrough space using an ion engine. It will orbitthe asteroid, land on it, and bring back a samplefrom its surface [JAXA, 2003].

The first HAYABUSA VLBI experiment wasperformed at X-band(8.4 GHz) using six VLBI sta-tions in Japan on November 26, 2003. We usedthe “K5 VLBI system [Kondo et al., 2003]” toacquire the VLBI data at the stations. Figure1 shows two examples of group delay fringes ofHAYABUSA range and telemetry signals for theKashima-Usuda baseline. According to the com-parison between group delays and R&RR results,large residuals more than 100 nanoseconds are rep-resented as shown in Figure 2.

Figure 1. Detected HAYABUSA group delay fringes for the Kashima 34m – Usuda 64mbaseline on November 26, 2003. (left: range signal, right: telemetry signal)

8 IVS NICT-TDC News No.24

The large scattering of the group delays areshown at the first four epochs and after about07:30UT in Figure 2. On the other hand, the rel-atively small scattering less than 10 nanosecondsare shown during the period between 05:00UT andabout 07:30UT. It is considered that the differencebetween them is caused by the characteristic of theradio signals transmitted from HAYABUSA. Thegroup delays with large residuals are obtained bythe telemetry signal which has narrow band-widthless than 1 MHz. The other group delays are ob-tained by the range signal which has band-widthmore than 1.5 MHz. To improve the signal to noiseratio of the telemetry-based group delays, we arenow planning to apply the DBBC (Digital Base-band Converter) filtering technique to the originalK5 data set [Tateuchi, 2004]. The advantage of us-ing the DBBC technique is to be possible applyingour state-of-art Gigabit VLBI system for the wideband-width data acquisition to the narrow band-width signal such a spacecraft signals. We will re-port this issue in another paper.

Figure 2. Residual delays between determined posi-tion using R&RR data by ISAS/JAXA and VLBIgroup delay observables.

References

Ichikawa, R., M. Sekido, H. Osaki, Y. Koyama, T.Kondo, T. Ohnishi, M. Yoshikawa, and NOZOMIDVLBI group, An evaluation of VLBI observationsfor the positioning of the NOZOMI Spacecraft andthe future direction in research and development ofthe deep space tracking using VLBI, IVS CRL-TDCNews No.23, pp.31–33, 2003.

JAXA web site, http://www.muses-c.isas.jaxa.jp/English/index.html, 2003.

Kondo, T., Y. Koyama, R. Ichikawa, M. Sekido, andH. Osaki, Quasi real-time positioning of spacecrafts

using the Internet VLBI system, IUGG proceedings,2003.

Sekido, M., R. Ichikawa, H. Osaki, T. Kondo, Y.Koyama, M. Yoshikawa, and NOZOMI VLBI ob-servation group, VLBI application for spacecraftnavigation (NOZOMI) –follow-up on model andanalysis–, IVS CRL-TDC News No.23, pp.34–35,2003.

Takeuchi, H., Development of software baseband con-verter, IVS NICT-TDC News No.24, pp.9–10, 2004.

July 2004 9

Development of Software Base-

band Converter

Hiroshi Takeuchi (ht@nict.go.jp)

Kashima Space Research Center, NationalInstitute of Information and CommunicationsTechnology, 893-1 Hirai, Kashima, Ibaraki314-8501, Japan

1. Introduction

NICT has been developing software-based base-band converters which down-convert signals frombroadband IF (intermediate frequency) to base-band using PC-based gigabit data acquisition sys-tem. While the DBBCs (Digital Base Band Con-verters) used in the conventional system consist ofelectric devices like FPGAs and ASICs, recent de-velopment of PCs enables us using PC software forthe converter. By using PCs, simple and highlyflexible system is expected to be realized at lowcost.

2. System Configuration

The software-based BBC system consists of gi-gabit sampler ADS-1000 and a PC equipped witha PC-VSI data capture card and RAID hard diskdrives [Kimura, et al., 2003]. IF-signals are sam-pled at the rate of 1Gpbs/2bit or 512Mbps/2bitsby ADS-1000 and the sampled data are transferredto the memory in the PC via PC-VSI card (SeeFigure 1). When the baseband conversion is notnecessary, obtained data are written to the hard

disk drives directly. When the BBC mode is on,data in the memory are filtered by band-pass filter-ing software and resulting data are written in real-time. The bandwidth of a resulting baseband datais selectable from 512kHz to 32MHz (data ratesare twice than those). Quantization bits can be setfrom 1, 2, 4, and 8, and one or two baseband chan-nels can be extracted in real-time with the PC.The band-pass filtering software is written in as-sembler language for the purpose of effective useof SSE/SSE2 function, which handles vector op-erations on x86 machines. It runs 10-times fasterthan that written in high-level languages like C andC++ language. An example of the frequency re-sponse of the system is shown in Figure 2.

Figure 2. Frequency response of 4095-tap FIRband-pass filter, which generates 2-MHz bandwidthof baseband signals from 512-MHz bandwidth of IF-signals.

Figure 1. Schematic diagram of the software baseband converter system. Sampled VSI dataare written not to HDDs (Hard Disk Drives) directly but to PC memory so that various kindof real-time data operations are possible before recording to the HDDs.

10 IVS NICT-TDC News No.24

Figure 3. Detected fringe signals of J006-06 between Parks and Kashima.

3. Observational result

In order to evaluate the performance of the sys-tem, a VLBI experiment was performed betweenKashima (Japan) and Parkes (Australia) VLBI sta-tions on 18 April, 2004. At Kashima station, 256-MHz IF-signals were directly sampled and con-verted to 16-MHz signals by the software BBC sys-tem. At Parkes station, PC-EVN system was usedfor a data acquisition. A detected fringe signal isshown in Figure 3. The calculated correlation am-plitude was confirmed to be reasonable comparedto a value with the conventional system.

4. Future plan

We believe that this system will be a useful toolfor differential VLBI observations for spacecraftnavigations [Ichikawa et al., 2004]. In the observa-tions, target source is switched between spacecraftand phase-reference QSOs in order to cancel outphase variations. To prepare a sufficient numberof phase-reference QSOs near the spacecraft, wide-bandwidth IF sampling is effective. On the otherhand, DBBC is useful for the observations of space-crafts because the bandwidth of the spacecraft sig-nals is very narrow. Using the software BBC sys-tem, total data size can be reduced and the signal-to-noise ratio of the data can be improved for thenarrowband spacecraft signals. Because the phase

relationship is preserved through the baseband con-version processes, we can use wideband quasar sig-nals as phase reference for narrowband spacecraftsignals.

Because the present system is based on the band-pass sampling method, selectable baseband fre-quencies are restricted. In more general cases, weshould emulate the image rejection filter by usingHilbert filter, digital synthesizer and digital mixer.FPGA-based hardware system is suitable for thecases at present, but software-based system willalso be usable in near future. The conventionalmulti-channel VLBI backend system will be ableto be replaced with the system.

References

Ichikawa, R., M. Sekido, H. Osaki, Y. Koyama, T.Kondo, M. Yoshikawa, and VLBI spacecraft trackinggroup, HAYABUSA VLBI Observations for Develop-ment of Deep Space Tracking –Preliminary Report–,IVS NICT TDC News, No.24, pp. 9–10, 2004.

Kimura, M., J. Nakajima, H. Takeuchi, and T. Kondo,2-Gbps PC Architecture and Gbps data processingin K5/PC-VSI, IVS CRL-TDC News, No.23, pp.12–13, 2003.

11

Derivation of relativistic VLBI

delay model for finite distanceradio source (Part I)

Mamoru Sekido1 (sekido@nict.go.jp) andToshio Fukushima2

1Kashima Space Research CenterNational Institute of Information andCommunications Technology, 893-1 Hirai,Kashima, Ibaraki 314-8501, Japan

2National Astronomical Observatory of Japan,2-21-1 Osawa Mitaka Tokyo 181-8588, Japan

Abstract: For the purpose to be used in correla-tion processing and data analysis of VLBI appli-cation in spacecraft navigation, relativistic VLBIdelay model for finite distance radio source was de-veloped. This delay model has precision of a picosecond or better for any spacecraft including evenlow earth orbit satellite with 100km altitude. Theformula of delay expression is in quite similar formwith the consensus model, which is standard VLBIdelay model. Thus it is relatively easy to be im-plemented in the current VLBI analysis packages.Detailed derivation procedure of the delay modelis described in this paper (Part I). Delay rate andpartial derivative with respect to radio source co-ordinates and station coordinates will be describedin the paper part II in the next issue.

1. Introduction

Relativistic VLBI delay models had been ac-tively discussed in the end of 1980s and beginningof 1990s. Eubanks [1991] has summarized thosemodels as ’Consensus Model’, and it is currentlyused in world wide VLBI community as a standardVLBI model. The consensus model uses plane waveapproximation by assuming the radio source at in-finite distance from observer. This assumption isvalid for ordinary natural radio sources, which arefarther distance than hundreds of light year away,in geodetic and astronomical VLBI observations.When VLBI technique is applied to radio sourcesat distance closer than 30 light years (e.g. planets,asteroids, and spacecraft in the solar system), how-ever, the consensus model is not accurate enoughand alternative relativistic VLBI delay model is re-quired, since the curvature of wavefront need tobe taken into account [Sovers and Jacobs, 1996].Fukushima [1994] and Sovers and Jacobs [1996] dis-cussed on VLBI delay mode for finite distance radiosource, although a relativistic VLBI delay modelcorresponding to the consensus model was not pro-posed in those papers. Moyer [2000] derived VLBI

delay model based on light time (LT) solution forspacecraft navigation (hereafter LT-like approach).The LT requires iterative computation to solve itand it is different approach from that of conven-tional VLBI delay model. We preferred to use al-ternative formula corresponding to the consensusmodel (VLBI-like approach), so that it can eas-ily be implemented in current VLBI analysis soft-ware. Additionally our VLBI-like approach mayhave advantage for distant radio source, becauselarger part of delays of two legs from spacecraftto observation stations are canceled out in LT-likeapproach as the radio source distance get farther.

We derive a relativistic VLBI delay model forfinite distance radio source (hereafter finite-VLBI)by following the approaches of Hellings [1986],Shahid-Saless and Hellings [1991], and Fukushima[1994]. Relativistic delay model for finite-VLBI hasalready derived by Sekido and Fukushima [2004]with first order approximation. Although that ap-proximation was valid when radio source is fartherthan 109 meters away. We describe a corrected andmore detailed derivation procedure in this paper.The new formular derived here has precision bet-ter than 1 pico second for any spacecraft includinglow earth orbit satellites.

Derivation of relativistic VLBI delay model isdescribed in this paper (part I), and time derivativeand partial derivative of VLBI delay with respectto the radio source coordinates and station coor-dinates will be described in a article (Part II) inthe next issue of IVS NICT-TDC news. Authorstried to describe rather detail of derivation proce-dure of formulae and modification of each equa-tions, so that the derivation procedure is under-standable and readers could follow the derivation.

Notation of variables used through out these ar-ticles are as follows. Variables of large Roman char-acter indicate quantity in flat (Minkowskian) coor-dinate system of solar system barycenter (TCB-frame or TDB-frame, which are introduced later).Those of small Roman character indicates quantityin geocentric frame of reference and small Greekcharacter means quantity on the geoid.

Most of variables used in this paper are listedas follows and subscript i =0, 1, 2, and E means re-spectively, 0:Radio source, 1: station-1, 2: station-2, and E: geocenter.

�Xi : Position vector of i in Solar System Barycen-ter (SSB) frame of reference (TCB-frame orTDB-frame).

�xi : Position vector of i in geocentric coordinateframe of reference (hereafter TCG-frame),whose time like argument is Geocentric Co-ordinate Time (TCG).

12 IVS NICT-TDC News No.24

�ξi : Position vector of i in local reference frame onthe geoid, whose time like argument is Ter-restrial Time (TT).

�Rij : Relative vector in the SSB frame of reference(TCB-frame or TDB-frame). �Rij = �Xi − �Xj

�rij : Relative vector in the TCG-frame. �rij =�xi − �xj

�ρij : Relative vector in the TT-frame. �ρij = �ξi−�ξj

�Vi : Coordinate velocity vector of i in SSB frameof reference.

�wi : Coordinate velocity vector of i in the TCG-frame.

Ti : Coordinate time (TCB or TDB) in SSB frameof reference, when radio signal arrived at ordeparted from station i.

ti : Coordinate time (TCG) in the TCG-frame,when radio signal arrived at station i.

τi : Proper time on the geoid (Terrestrial Time:TT), when radio signal arrived at station i.

c : Definition of speed of light: 299792458 m/s.

UE : Gravitational potential at geocenterUE =

∑J �=E

GMJ

rJ

γ : One of the Post-Newtonian parameters andγ = 1 for general relativity.

γs : Lorentz Factor 1/√

1 − V 2/c2

Rij : Amplitude of vector �Rij. Rij = |�Rij|

�Rij : Unit vector of �Rij. �Rij =�RijRij

βij : βij = �Rij · �Vj

c

βi : βi = Vi/c

Barycentric Coordinate Time (TCB) is the timelike argument of Barycentric Coordinate Frameof reference (TCB-frame). Barycentric DynamicalTime (TDB) is the time like argument of Barycen-tric Dynamical Frame of reference (TDB-frame).Planetary coordinates in JPL Ephemeris are givenin TDB-frame with time argument of TDB. Thusspacecraft coordinates are usually given in TDB,and here we also derive the delay model based onit. However, discussion based on TCB-frame is pos-sible by setting scaling factor LB = 0, which isintroduced in the next section.

2. Coordinate Transformation

It is well accepted that linearized post Newto-nian (post Galilean) metric

g00 = 1 − 2 Uc2 + O(c−4)

g0k = O(c−3)gmn = −δmn(1 + 2γ U

c2 ) + O(c−4)(1)

is appropriate to describe relativistic effects inmoderate speed and gravitational field [Moyer,2000; Hellings, 1986; Shahid-Sales and Hellings,1991]. Infinitesimal line element of events scaledby a factor

l = 1 + L (2)

is given as

ds2 = l2��

1 − 2U

c2

�c2dT 2 −

�1 + 2γ

U

c2

� 3�i=1

dXi2

�,

(3)

where U =∑

jGMj

Rjis gravitational potential at

the position of interest, and G is gravitational con-stant. The summation is taken for all sources ofgravitation. An interval of proper time dτ is re-lated with the interval ds along its world line by

dτ =ds

c(4)

Substituting equations. (2) and (4) into (3), ex-panding and retaining terms to order of 1/c2 givesequation

dτ

dT= 1 − U

c2− V 2

2c2+ L, (5)

where V is coordinate velocity of that point in SSBframe of reference. Scaling constant L is supposedto be order of 1/c2. When the point of interestis on the geoid, proper time τ become the Terres-trial Time (TT). Coordinate time T with the samerate with TT in average is realized by choosing thescale factor L appropriately. Supposing that longtime average of equation (5) equals to unity whenscaling constant L = LB,

<dτ

dT>= 1− <

U

c2+

V 2

2c2> +LB = 1. (6)

Then scaling factor LB is defined by

LB =1c2

< U +V 2

2>, (7)

where brackets <> means long time average.Currently, LB = 1.55051976772×10−8±2×10−17 isused as scaling factor [McCarthy and Petit, 2003].The coordinate time scaled by l = 1 + LB is

July 2004 13

the TDB and corresponding Barycentric Dynam-ical Frame of reference is defined by scaled metricby this factor.

By using gravitational potential at the geocen-ter UE =

∑J �=E

GMJ

rJand the scaling factor LB, a

new coordinates parameter of infinitesimal trans-formation can be defined.

dT ′ = (1 + LB)

√1 − 2

UE

c2dT (8-a)

d�X′ = (1 + LB)

√1 + 2γ

UE

c2d�X. (8-b)

By substituting equation (8) to (3), infinitesimalline element between events is expressed by

ds2 = c2dT ′2 −3∑

i=1

dX ′i2.

This means that the new parameters (dT ′, d�X′)represent local Minkowskian flat coordinates sys-tem around the geocenter at that moment.

Now, geocentric local inertia coordinate system(dt, d�x ) co-moving with geocenter and small por-tion of SSB frame around the geocenter expressedby (dT ′, d�X′) can be transformed each other byLorentz transformation, since both systems are lo-cal inertia frames.

cdt = γscdT ′ − γs

�VE · d�X′

c(9-a)

d�x = d�X′ + (γs − 1)�VE · d�X′

V 2E

�VE

−γs�VEdT ′, (9-b)

where VE is coordinate velocity of earth evolution

with respect to the SSB. And γs = 1/

√1 − V 2

E

c2 isLorentz factor. Substituting equation (8) to (9),expanding, and retaining up to order of (1/c2) be-comes

dt = γs(1 + LB)�1 − UE

c2

�dT

−γs(1 + LB)(1 + γ UEc2

)�VE ·d�X

c2

∼=�

1 − UE

c2+

V 2E

2c2+ LB

�dT −

�VE · d�X

c2

(10-a)

d�x = (1 + LB)�1 + γ UE

c2

�d�X

+(1 + LB)(γs − 1)(1 + γUE

c2)�VE · d�X

V 2E

�VE

−(1 + LB)�1 − UE

c2

�γs

�VEdT

∼=�

1 + γUE

c2+ LB

�d�X +

�VE · d�X

2c2�VE

−�

1 − UE

c2+

V 2E

2c2+ LB

��VEdT.

(10-b)

These equations are the infinitesimal transfor-mation between the Barycentric Dynamical Frameof reference (TDB-frame) and Geocentric Coordi-nates Frame of reference (TCG-frame). InverseLorentz transformation of equation (9) is

cdT ′ = γscdt + γs�VE ·d�x

c(11-a)

d�X′ = d�x + (γ − 1)�VE ·d�x

V 2E

�VE + γs�VEdt. (11-b)

Inverting equations. (8) by expanding and retain-ing terms in order of 1/c2 is

dT =(

1 +UE

c2− LB

)dT ′ (12-a)

d�X =(

1 − γUE

c2− LB

)d�X′. (12-b)

Then infinitesimal inverse transformation fromTCG-frame to TDB-frame in vicinity of the earthis given in order of c−2 as

dT =

�1 +

UE

c2+

V 2E

2c2− LB

�dt +

�VE · d�x

c2

(13-a)

d�X =

�1 − γ

UE

c2− LB

�d�x +

�VE · d�X

2c2�VE

+

�1 − γ

UE

c2+

V 2E

2c2− LB

��VEdt (13-b)

The scaling relation between TCG-frame (t, �x)and local reference frame on the geoid (hereafterreferred as TT-frame) (τ, �ξ) is given by

dτ = (1 − LG)dt (14-a)

d�ξ = (1 − LG)d�x, (14-b)

14 IVS NICT-TDC News No.24

where LG = Wg

c2 is scaling constant defined bygravitational potential Wg on the geoid, and itsnumerical value is defined as LG = 6.969290134 ×10−10 [McCarthy and Petit, 2003]. Using equations(10), (13), and (14), and retaining terms in order of1/c2 yields infinitesimal transformation from TDB-frame to TT-frame as

dτ =�1 − UE

c2+

V 2E

2c2+ LB − LG

�dT

−(1 − LG)�VE ·d�X

c2

∼=�1 − UE

c2+

V 2E

2c2+ LC

�dT − �VE ·d�X

c2(15-a)

d�ξ =�1 + γ UE

c2+ LB − LG

�d�X +

�VE ·d�X2c2

�VE

−�1 − UE

c2+

V 2E

c2+ LB − LG

��VEc

dT

∼=�1 + γ UE

c2+ LC

�d�X +

�VE ·d�X2c2

�VE

−�1 − UE

c2+

V 2E

2c2+ LC

��VEc

dT (15-b)

and its inverse transformation

dT =(1 + UE

c2 + V 2E

2c2 − LB + LG

)dτ

+(1 + UE

c2 + V 2E

2c2 − LB + LG

)�VE ·d�ξ

c2

∼=(1 + UE

c2 + V 2E

2c2 − LG

)dτ +

�VE ·d�ξc2

(16-a)

d�X =(1 − γ UE

c2 − LB + LG

)d�ξ +

�VE ·d�ξ2c2

�VE

+(1 − γ UE

c2 + V 2E

2c2 − LB + LG

)�VEdτ

∼= (1 − γ UE

c2 − LC

)d�ξ +

�VE ·d�ξ2c2

�VE

+(1 − γ UE

c2 + V 2E

2c2 − LC

)�VEdτ,

(16-b)

where LC = LB −LG is used. In the same way,the relation between TCB-frame and TT-frame iseasily obtained by placing LB = 0. Actually re-placement of LC =⇒ −LG in equations. (15) and(16) give the infinitesimal transformations betweenTCB-frame and TT-frame. The TDB-frame is sup-posed as the SSB frame in the discussion in thefollowing sections, however, the same discussion isvalid for TCB-frame by the simple replacement ofthe scaling factor.

3. VLBI delay expression with Halley’s for-mula

Let us suppose radio signal departed from ra-dio source 0 at T0 and arrive at observer 1 and 2 atepoch T1, and T2, respectively. Relative positionvector from observer 2 at T2 to the radio source 0

at T0 is approximately expressed by relative vector�R02(T1) and velocity vector �V2 in the TDB-frameas follows:

�R02(T2) = �R02(T1) − �V2(T2 − T1), (17)

where acceleration of station 2 was eliminated. Thetime interval T2 − T1 is less than 42 milli-secondson the ground baseline and acceleration contribu-tion due to earth spin and evolution around the sunare 2.09× 10−2m/s2 and 5.95× 10−3, respectively.Thus error of this approximation is less than 20 mi-cro meters and negligible for our purpose. Squareof this vector is

R202(T2) = R2

02(T1) − 2�R02(T1) · �V2(T2 − T1)+V 2

2 (T2 − T1)2

= R202

�1 − 2

��R02·�V2(T2−T1)R02

+V 22 (T2−T1)2

R202

�,

(18)

where �R02(T1) is simply express by �R02 by elimi-nating the epoch in the second line. Taking squareroot and expanding it by Taylor series

√1 + x =

1 + 12x − 1

8x2 + 116x3 + · · · gives

R02(T2) = R02(T1)

�1 − ��R02 ·

�V2(T2 − T1)

R02

+V 2

2 − (��R02 · �V2)

2

2R202

(T2 − T1)2

+V 2

2 − (��R02 · �V2)

2

2R302

(��R02 · �V2)(T2 − T1)

3 + · · ·

(19)

Retaining terms up to the 2nd order of V2(T2−T1)becomes

R02(T2) = R02(T1)

{1 − �R02 ·

�V2(T2 − T1)R02

+V 2

2 − ( �R02 · �V2)2

2R202

(T2 − T1)2

⎫⎬⎭ . (20)

Truncation error of this approximation is order of

R02

(V2(T2−T1)

R02

)3

and this term increases as thedistance R02 decreases. Magnitude of this termis less than 0.15 milli-meters in any spacecraft ob-servations, even for low earth orbit satellite with100 km altitude, for instance. In other words, thisform has 1 pico second precision for any spacecraftin ground based interferometric observation. Timeinterval T2−T1 can be expressed by using equation(20) as follows:

c(T2 − T1) = R02(T2) − R01(T1) + c∆tg (21)

= c∆tg − �K · �B − ��R02 · �V2(T2 − T1)

+V 22 −(

��R02·�V2)2

2R02(T2 − T1)

2, (22)

July 2004 15

where �K and �B is pseudo-source vector, whichwas introduced by Fukushima [1994] and baselinevector, which are defined in TDB-frame as

�K =�R01(T1) + �R02(T1)R01(T1) + R02(T1)

(23-a)

�B = �X2(T1) − �X1(T1). (23-b)

The pseudo-source �K vector correspond to thesource vector in normal (infinite) VLBI model. Butformer is neither unit vector nor constant vector,whereas latter is constant unit vector. ∆tg is grav-itational delay due to ray path bending. It is givenby

∆tg = (1 + γ)∑

J

GMJ

c3ln[

(R0J + R2J + R20)(R0J + R2J − R20)

(R0J + R1J − R10)(R0J + R1J + R10)

].

(24)

An attention have to be paid to that radiosource coordinates used in relative position vector�R0i in above formulae are at the epoch T0, whenthe radio signal departed. Writing explicitly,

�R0i(T1) = �X0(T0) − �Xi(T1), (i=1,2) (25)

is used in following discussion in this paper. Theepoch T0 is obtained by solution of the followinglight time equation

T1 − T0 =

∣∣∣�X0(T0) − �XE(T1) − �R1E(T1)∣∣∣

c

+(1 + γ)∑J

GMJ

c3

(R0J + R1J + R10

R0J + R1J − R10

).

(26)

Predicted orbit (position) of the radio source is sup-posed to be given as function of time. Positionvector of station 1 �X1 = �XE(T1) + �R1E(T1). Geo-centric position vector �R1E in TDB-frame is ex-pressed by geocentric vector �ρ1E in TT-frame withequation (16) as

�R1E =(

1 − γUE

c2− LC

)�ρ1E +

�VE · �ρ1E

2c2�VE

+(

1 − γUE

c2+

V 2E

c2− LC

)�VEd∆τ∗

1

=(

1 − γUE

c2− LC

)�ρ1E −

�VE · �ρ1E

2c2�VE .

(27)

The second term of right hand side of the first lineis due to difference of simultaneity between TDB-frame and TT-frame. Placing dT = 0, d�X = �R1E

in equation (15-a), and retaining terms of 1/c2 or-der becomes

∆τ∗1 = −

�VE · �R1E

c2= −

�VE · �ρ1E

c2.

Relative vector �R1E is computed with �ρ1E withequation (27). Position vector �X0 and �XE is givenas function of time from predicted orbit and plane-tary ephemeris. Equation (26) can be solved by it-erative procedure such as Newton-Raphson methodand initial value T

(0)0 = T1.

To solve the equation (22) regarding T2 − T1,re-writing it by the order of T2 − T1 becomes

V 22 − ( �R02 · �V2)2

2R02(T2 − T1)2

− (c + �R02 · �V2)(T2 − T1)

+ c∆tg − �K · �B = 0. (28)

In general, when second order equation is given

12f ′′x2 + f ′x + f0 = 0, (29)

approximation solution of it is known as

x =−f0

f ′(1 − f0f ′′

2f ′2

) , (30)

which is named Halley’s formula. It be-comes good approximation solution especiallywhen f ′′f0 << f ′2, and this is the case. The othersolution of the equation x = −2f ′

f ′′ is rejected, sinceit is not obviously the solution of our interest.

Solution of equation (28) is expressed with Hal-ley’s formula as

T2 − T1 =∆tg − �K·�B

c

(1 + �R02 · �V2c ){

1 +�K·�B{V 2

2 −(��R02·�V2)2}

2c2R02(1+��R02·

�V2c )2

} ,

(31)

where term of ∆τg in the denominator was elimi-nated because it is in order of c−4. The solution isre-written by using β02 = �R02 · �V2

c and β2 = V2/cas

T2 − T1 =∆tg − �K·�B

c

(1 + β02){

1 +�K·�B(β2

2−β202)

2R02(1+β02)2

} (32)

Approximation error of Halley’s formula is evalu-ated by (f0)3f ′′2

4f ′5 � B4c ( B

R02)2β4. This is in order of

c−4, thus it is safely negligible.

16 IVS NICT-TDC News No.24

By the way, the relation of time interval T2−T1

in TDB and τ2−τ1 in TT is derived by using equa-tion (16-a) as follows:

T2 − T1 =(

1 +UE

c2+

V 2E

2c2− LC

)(τ2 − τ1)

+�VE · ( �ξ2(τ2) − ξ1(τ1))

c2

∼=(

1 +UE

c2+

V 2E

2c2− LC

)(τ2 − τ1)

+�VE · [�b + �w2(τ2 − τ1)]

c2

=

(1 +

UE

c2+

V 2E

2c2+

�VE · �w2

c2− LC

)×(τ2 − τ1) +

�VE · �bc2

,

(33)

where �b = �ξ2(τ1) − �ξ1(τ1) is baseline vector inTT-frame. �ξ2(τ2) is approximated as �ξ2(τ2) ∼=�ξ2(τ1) + �w2(τ2 − τ1), where �w2 is velocity vectorin TCG-frame. Error of this approximation is lessthan 20 micro meters and negligible.

Relation between baseline vector in TDB-frameand TT-frame is derived with equation (16-b) asfollows:

�B = �X2(T1) − �X1(T1)

=

�1 − γ

UE

c2− LC

�[�ξ2(τ

∗1 ) − �ξ1(τ1)]

+�VE · [�ξ2(τ

∗1 ) − �ξ1(τ1)]

2c2�VE

+

�1 − γ

UE

c2+

V 2E

2c2− LC

��VE(τ∗

1 − τ1)

=

�1 − γ

UE

c2− LC

�[�b + �w2(τ

∗1 − τ1)]

+�VE · [�b + �w2(τ

∗1 − τ1)]

2c2�VE

+

�1 − γ

UE

c2+

V 2E

2c2− LC

��VE(τ∗

1 − τ1)

∼=�

1 − γUE

c2− LC

��b −

�VE · �bc2

�VE

2+ �w2

�,

(34)

where terms in order of c−2 were retained. Timeinterval τ∗

1 − τ1 is due to difference of simultaneitybetween TDB-frame and TT-frame. Event at sta-tion 1 corresponds (T1, �X1) ⇔ (τ1, �ξ1), and eventat station 2 does (T1, �X2) ⇔ (τ∗

1 , �ξ2). Thus τ∗1 − τ1

is given by substituting dT = 0 in the equation(15-a) as

τ∗1 − τ1 = −

�VE · �Bc2

∼= −�VE · �b

c2(35)

Substituting equation (34) into (32) and retain-ing terms in order of c−2 becomes

T2 − T1 =

∆tg −�1 − γ UE

c2− LC

��K·�b

c+

�VE ·�bc3

��VE2

+ �w2

�· �K

(1 + β02)(1 + α),

(36)

where following replacement of notation wereused:

βijdef= �Rij ·

�Vj

c(37-a)

αdef=

�K · �b(β22 − β2

02)2R02(1 + β02)2

(37-b)

β2def= V2/c. (37-c)

Equating time interval of equations (36) and (33),solution of it with respect to τ2 − τ1 is

τ2 − τ1 =∆tg −

[1 − (γ + 1)UE

c2 − V 2E+2�VE ·�w2

2c2

]�K·�bc − �VE ·�b

c2 [1 + β02 − (�VE+2�w2)·�K2c ]

(1 + β02)(1 + α), (38)

where pseudo-source vector �K is given by

�K =�R01(T1) + �R02(T1)R01(T1) + R02(T1)

. (39)

And these can be computed from observation station coordinates (�ρ1E(τ1), �ρ2E(τ1)) in TT-frame by

July 2004 17

means of

�R0i(T1) = �X0(T0) − �X1(T1)

= �X0(T0) − �XE(T1) − �RiE(T1) (40-a)

�RiE(T1) =(

1 − γUE

c2− LC

)�ρiE(τ1) −

�VE · �ρiE

2c2�VE . (40-b)

, where (i=1,2).

Prediction orbit (position) of radio source (�X0(T0)) and geocenter (�XE(T1)) in TDB-frame are sup-posed to be given as function of time.

Equation (38) gives geometrical delay of VLBImeasured by atomic clock on the geoid for finitedistance radio source, when �X0 and �XE is given inTDB-frame.

If radio source coordinates and earth ephemerisis given in TCB-frame, formula corresponding toequation (40-b) is obtained by replacing the scal-ing factor with LB =⇒ 0 as

�RiE(T1) =

�1 − γ

UE

c2+ LG

��ρiE(τ1) −

�VE · �ρiE

2c2�VE ,

(41)

where i = 1, 2.Time derivative of delay (delay rate) and partial

derivative with respect to radio source coordinatesand station coordinates will be derived in the nextpaper (part II) in the next issue.

References

Eubanks, T. M., A Consensus Model for Relativistic Ef-fects in Geodetic VLBI, Proc. of the USNO workshopon Relativistic Models for Use in Space Geodesy, 60–82, 1991.

Fukushima, T., Lunar VLBI observation model, As-tron. Astrophys., 291, 320–323, 1994.

Hellings, R. W., Relativistic effects in astronomicaltiming measurements, Astron. J., 91, 650–659, 1986.

McCarthy, D. D. and G. Petit, IERS Conventions2003, IERS Technical Note, No. 32, 2003

Moyer, T. D., Formulation for Observed and ComputedValues of Deep Space Network Data Types for Nav-igation, JPL Monograph 2 (JPL Publication 00-7).This is published from JPL Deep Space Communi-cations and Navigation Series, John Wiley & Sons.Inc., Hoboken New Jersey ISBN 0-471-44535-5, 2000

Sekido M. and T. Fukushima, Relativistic VLBI delaymodel for finite distance radio source, Proceedingof IUGG 2003 in Sapporo, Special issued of J. ofGeodesy, 2004 (in printing).

Shahid-Saless, B. and R. W. Hellings, A Picosecond Ac-curacy Relativistic VLBI Model via Fermi NormalCoordinates, Geophys. Res. Lett., 18, 1139–1142,1991.

Sovers, O. J. and C. S. Jacobs, Observation Model andParameter Partials for the JPL VLBI Parameter Es-timation Software “MODEST”-1996”, JPL Publica-tion 83-39, Rev. 6: 6–8, 1996.

18 IVS NICT-TDC News No.24

The Australian experience with

the PC-EVN recorder

Dodson, R1,2, S. Tingay3, C. West3,A. Hotan3, C. Phillips4, J. Ritakari5,F. Briggs6, G. Torr6, J. Quick7,Y. Koyama8, W. Brisken9, B. Reid2,and D. Lewis4

1 Institute of Space and Astronautical Science,JAXA, 3-1-1 Yoshinodai, Sagamihara,Kanagawa 229-8510, Japan

2 University of Tasmania, Hobart, 70003 Swinburne University of Technology,

PO Box 218, Hawthorn 3122, Melbourne,Australia

4 Australia Telescope National Facility,Commonwealth Scientific and IndustrialResearch Organization, P. O. Box 76,Epping NSW 2122, Australia

5 Metsahovi Radio Observatory,Metsahovintie 114, 02540 Kylmala, Finland

6 RSAA, The Australian National University,Mount Stromlo Observatory, Cotter Road,ACT 2611, Australia

7 Hartebeesthoek Radio Astronomy Observatory,P.O. Box 443, Krugersdorp 1740, South Africa

8 Kashima Space Research Center, NICT,893-1 Hirai, Kashima, Ibaraki 314-8501,Japan

9 National Radio Astronomy Observatory,P.O. Box 0, Socorro, NM 87801, USA

Abstract: We report on our experiences usingthe Metsahovi Radio Observatory’s (MRO) VLBIStandard Interface (VSI, Whitney 2002) recorderin a number of astronomical applications. ThePC-EVN device is a direct memory access (DMA)interface which allows 512 megabit per second(Mbps) or better recording to “off the shelf” PCcomponents. We have used this setup to recordat 640 Mbps for a pulsar coherent dispersion sys-tem and at 256 Mpbs for a global VLBI session.We have also demonstrated recording at 512 Mbpsand will form cross correlations between the CPSR-II and the PC-EVN systems.

1. Introduction

Astronomy has always battled against the ex-tremely weak signals received from objects impos-sibly far away. We can improve the situation byrecording the signals with cooler feeds, observingfor longer, or by collecting wider bandwidths, as ex-pressed by the radiometer equation (see e.g. Kraus1986).

With modern digital technology it is possibleto sample increasingly wider bandwidths with ahigher number of bits. Furthermore by record-ing to consumer electronic hardware (the so called“Commercial off the Shelf” or COTS approach(e.g. Whitney 2003)) the equipment is cheap, reli-able and easy to repair, replace and upgrade.

The potential downside of this is that everyonebuilds their own machine, with the equipment thatwas available at that moment (a particular problemwith motherboards, which seem to have a lifetimeof six months) and compatibility issues could arise.These, however, have not affected us and we havefour very different configurations in use.

2. PC-EVN Hardware

The boards purchased from MRO were their twoVSI boards; VSIB (a DMA card) and VSIC (a con-verter card). The VSIB card allows data to bewritten to or read from the hard drives on the PC.The provided operating system was debian linux(the stable woody series with kernel 2.4.19 and thebig physical area patch). The recommended PCmotherboard is the K7 series from MSI with anAMD processor. With these we run four IDE disks(200 GBytes in size) from the motherboard. A bootdisk (and CD) is run from a PCI IDE card, mak-ing the total disk capacity one terabyte. The datadisks are mounted in a (software) RAID0 array.We have also used the Dell 1600C server machine,because with these the data disks can be externalApple Xraid disks on a 64 bit PCI bus. These wererun using SuSe 8.2 linux OS. Using alternate moth-erboards and OS versions caused no problems.

The cards cost 565 each, the PC the order ofAU$2000 and about the same for four 200 Gbytehard drives. Therefore the total cost of the systemwas around AU$5500.

3. The Mt. Pleasant Pulsar backend

Hobart has been monitoring the Vela pulsar’spulse time of arrival (TOA) for over twenty years.The original system (which caught a glitch in thefirst week of operation (McCulloch et al., 1983))has been upgraded over the years to one that;

• monitors Vela for 18 hours a day (and a secondglitching pulsar for the remaining 6 hours).

• collects two minute averaged profiles at threefrequencies (635, 990 and 1390 MHz). Thebandwidth is matched to the dispersion timefor a dispersion measure (DM) of 69 pc cm−3.The automatically generated fit to these datais available on the web1 .

1http://www-ra.phys.utas.edu.au/∼rdodson/0835-4510.par

July 2004 19

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Figure 2. Profile of Vela from 0.7 second of dataat 619 to 644 MHz.

• collects continuously sampled data at 990 MHz(incoherently dedispersed to increase thebandwidth by a factor of eight). From thissingle pulse system 10 second profiles are con-stantly formed and checked for the occurrenceof a glitch. These data are saved for 3 daysfor deep analysis of immediate post (and pre)glitch behaviour (Dodson, McCulloch & Lewis2002).

• now also collects continous sampled data at635 MHz across a 25 MHz bandpass offset frombaseband by 10 MHz, increasing the band-width one hundred fold. This data is bufferedfor 2.5 hours, after which it is overwritten.Once a glitch is detected by the single pulsesystem the data is saved for off-line coherentdedispersion and profile forming.

Figure 3. The VLBI system with 4 demountable200GB IDE drives.

The last Vela glitch (January 2000) spun-up thepulsar within the detection time of the single pulsesystem (i.e. less than 30 seconds) and also showeda previously undetected decaying spin-down termwith a time constant of 1 minute (Dodson et al.,2002). Our new system will produce TOA’s withaccuracy of the order of 0.1 msec every second (asopposed to every 10 seconds with the single pulseor 120 seconds with the multi-frequency systems).

The IF (baseband to 40 MHz) was fed in to aMAXIM 1448 A/D mounted on an evaluation card(AU$330 each), along with a 80 MHz clock. Twoof these provide the two polarisations. The outputof these are TTL, so the four most significant bits(of the 10 bits provided by the MAX1448 card) arebuffered to LVDS along with the clock signal, andcombined with an external 1PPS signal. These arefed directly into the VSIB. The recovered band-pass is shown in Figure 1. In running the VSIBat 80 MHz we are clocking the data at two and ahalf times the VSI standard, nevertheless this pro-duced no complications. The recording software isthat provided (wr), with minor modifications to al-low continous looped recording and shared memorycontrol. This system is now running and recordingdata, and we are just waiting for the next glitch.

Once we have data covering the glitch eventwe will excise the interference, coherently dedis-perse the signal, form 1 second profiles and mea-sure the TOAs. This will be done with theATNF/Swinburne software package PSRCHIVE(Hotan et al., 2004). The profile from a short sec-tion of data is shown in Figure 2.

4. The VLBI system

The VSIC card converts many “legacy” VLBIdigital signals into the ordering and levels (LVDS)

20 IVS NICT-TDC News No.24

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Figure 4. Autocorrelation of four 16MHz bandpasses (LHC and RHC at 4792-4808 and 4808-4824 MHz)from the ATNF DAS recorded on to the PC-EVN system. A LHC tone at 4797 MHz was injected.

of the VSI standard required by the VSIB DMAcard. In the Hobart system the VSIC card ismounted and powered inside the PC case (see Fig-ure 3, the connector is on the right under the harddrives). For the Swinburne systems the VSIC cardwas enclosed in its own box. The card will handleup to 32 channels of data, plus the required signalclocks and 1PPS signals.

The VSIC card will format data with S2 pin out-puts (as well as VLBA, Mk3 and Mk4 formats), soit was a trivial task to connect the VSIC to thecable normally going to the S2 recorder. Onceagain the provided program wr was used to col-lect the data. wr reads a minimum of 8 chan-nels, whilst the maximum rate S2 recording modes(32x4-2) records two IFs of 16 MHz of data at 2bits into 4 channels. The DAS modes used (VSOPand MP16S), however, encode four IFs of 16 MHzof data at 2 bits into 8 channels. Therefore wecould record double the usual LBA bandwidth us-ing the PC-EVN system. Four 16 MHz bandpassesare shown in Figure 4. More details can be foundin Dodson 2004.

The experiment performed was a global eVLBIobservation. Most Australian telescopes (ATCA,Mopra, Parkes, Tidbinbilla and Ceduna)recorded on PC-EVN machines, and Hobart

recorded to their Mk5a system. Also recordingon Mk5 systems were Hartebeesthoek (SA) andPietown (USA). Data was recorded to the K5 sys-tem at Kashima in Japan.

During the experiment small sections of therecorded data from Ceduna, Mopra, Parkes, Tid-binbilla and Narrabri were transfered to varioussoftware correlators to perform near real timefringe checking. Various approaches to correla-tion have been developed; a XF and then fringerotate correlator running on the Swinburne super-computer, this is the correlator which we are plan-ning to use for stage one VLBI data production.We also have test correlators running on a con-ventional PC which take various other approaches;FX then fringe rotate, XF then fringe rotate anda fringe rotate and XF correlator. For a 1 kHzchannel width (which is equivalent to 0.2 km s−1

for 1.4 GHz) the fringe rotation needs to be lessthan 28 Hz to keep the phase change to less than10o in a single integration period. This conditionis fulfilled (so we can correlate then rotate) for theATNF antennae (i.e. Parkes, Mopra and ATCA),but not for the more distant ones. However for con-tinuum observations with a limited field of view thechannel widths can be a thousand times greater,and the condition is met for all non-space base-

July 2004 21

Figure 5. 0.1 second integrated cross correlation of four telescopes with PC-EVN systems on the strongcontinuum source J0006-0623 using 16 MHz centred at 2282 MHz. The fringes for Parkes to ATCA arein the cross hands (therefore in different colours) showing that the polarisations were swapped (Left andRight, rather than Right and Left) at that telescope.

lines. The major advantage of the XF then rotatemode is that we perform both the bit decodingand correlation calculation in a single lookup ta-ble operation. These rapid integer operations areseven times faster than the rotate and XF correlatemethod.

We observed the strong continuum sourcesJ0006-0623, J1037-2934 and the pulsar Vela.

Fringes were found only two minutes after thewavefront reached the antennae using the Swin-burne correlator. Figure 5 shows the delays foundfor Parkes to the ATCA, Ceduna and Mopra onJ0006-0623 from the single processor correlator (inthe XF & fringe rotate mode).

The data has now been transported on externaldisks to Swinburne to be correlated on the super-

22 IVS NICT-TDC News No.24

computer. A full report on the software correlator,the experiments and the results is in preparation.Of particular note is that this is the first mixedformat global eVLBI experiment.

5. The Stromlo Streamer

For radio astronomers, the radio frequency inter-ference (RFI) environment continues to get worse,and has become a critically important issue in thedevelopment of the next generation of radio tele-scopes, including the Square Kilometre Array. Forthe SKA site evaluations and interference miti-gation investigations Mount Stromlo Observatory(Australian National University) has used a nearidentical setup to the pulsar system as a flexibletest bed for emulating radio astronomy backendsin software. The system is portable, carrying withit a low-precision 64 MHz clock and 4 MAXIM 1448A/D cards for accepting 4 IFs as input. The flexi-bility provided by the MRO wr routine allows theA/Ds to deliver different numbers of bits precisionand different sampling rates without reconfiguringthe hardware.

The most often used application has been in thearea of RFI mitigation to further the program de-scribed in Briggs, Bell and Kesteven (2000). Thefour input channels can record, for example, thesignals from two polarizations of a telescope aswell as the signals from RFI sensors that are op-timized to provide gain directed at broadcast tow-ers. The ‘Streamer’ has seen action at Molonglo at843 MHz, where the phased signals from East andWest arms are recorded separately, along with RFIreference signals from both polarizations of a 6 mparabola. In these experiments, we recorded four8 MHz bands with 8 bit precision and computed thecross-power spectra as well as total power spectrafrom all channels as a step toward RFI characteri-zation and cancellation. We are exploring the im-plementation of similar techniques with the Swin-burne CPSR-II system at Parkes, which can recordtwice the bandwidth of the PC-EVN system (i.e.four 64 MHz bandwidths). CPSR-II has the greatadditional benefit of 30 dual CPU processors, sothat it is a production machine capable of doing thesignal processing in real time, while the Streamer’sstrong points are its portability, low cost and avail-ability.

6. The future

Using the PC-EVN systems in place we will col-lect the data from the S2 formatter output port(C2a), and fringe check the data on the fly dur-ing all VLBI observations. Automation of the datacollection is being organised.

We have collected the data from the DAS correla-tor port rather than the S2 connector port, whichallows us to record 2 IFs of 64 MHz (at 2 bits).At Parkes we will use coincident data recorded onthe CPSR-II system to produce the zero baselinecross correlations. We will shortly attempt to cor-relate CPSR-II data (from Parkes) with data fromtwo PC-EVN machines (at ATCA) to demonstrate1 Gbps VLBI in Australia. We are also investigat-ing the possibility of using the system as a databuffer on the to-be-upgraded ATNF network (i.e.on the 10 Gbps links between antenna).

The recording rate limitations are from that sus-tainable by the hard drives (about 800 MBs), how-ever when greater speeds are possible (with SerialIDE drives or just general improvements) we willbe at the PCI maximum rate (1056 Mbs). Alreadywe’d like to be able to read and write over the samebus at the same time, in which case developing theVSIB card to run on the faster, emerging, technolo-gies would be of great priority. The estimated costfor this is 3 man months, and if sufficient interestis generated this will be undertaken at Metsahovi.

7. Conclusions

We have demonstrated the adaptability of thePC-EVN system, and its low cost of setup in bothhardware and manpower. We have used it for ana-log RF recording systems and as a digital recorderfor the Australian VLBI system.

References

Briggs, F. H., J. F. Bell, and M. J. Kesteven , Astron.J., 120, pp.3351–3361, 2000.

Dodson, R., eLBA memo series, 1, 2004.

Dodson, R. G., P. M. McCulloch, and D. R. Lewis,Astrophys. J., 564, pp.L85–L88, 2002.

Hotan, A. W., W. van Straten, and R. N. Manchester,astro-ph/0404549, 2004.

Kraus, J. D., Radio astronomy, Powell, Ohio: Cygnus-Quasar Books, 1986.

McCulloch, P. M., P. A. Hamilton, G. W. R. Royle, andR. N. Manchester, Nature, 302, pp.319-321, 1983

Whitney, A., in e-VLBI workshop at JIVE, Parsley S.,Whitney A., eds, Mark 5 and e-VLBI, 2003.

Whitney, A., in e-VLBI workshop at Haystack, ParsleyS., Whitney A., eds, VSI-H, 2003.

July 2004 23

- News - News - News - News - News - News - News - News - News - News - News -

CARAVAN-35, Small Radio Telescope Package Released

Junichi Nakajima (nakaji@nict.go.jp)

Kashima Space Research CenterNational Institute of Information and Communications Technology

893-1 Hirai, Kashima, Ibaraki 314-8501, Japan

CARAVAN 35 is a new portable educational radio telescope package (Figure 1). The minimumsize 35-cm dish aperture is mainly targeting daytime Sun radio emission and users can understandradio telescope function from the simplified system. NICT (former CRL) had been held summer sciencecourse for high-school students. In this course, students can build their own radio telescope from scratch.Though we received strong demands to carry out this radio telescope education in high-school, oftenthere is difficulty in school facility where they does not have microwave and electronic instruments.

For such educational purpose, we have designed RFD-1500 (Figure 2). The pocket sized total-powertelescope backend includes microwave IF amplifier, splitter, detector and DC amplifier. Since the in-tegrated RFD1500 succeeded to eliminate unstable behavior in high-Gain system, simply hook up theRFD1500 unit between satellite dish and DVM, student and teacher without microwave electronics back-ground can perform experiment in short time. Starting from measuring antenna temperature, studentslearn Y-factor method, Solar temperature in satellite-band (10GHz), and telescope efficiency. Find fixedsatellite in GSO orbit and following Sun in the sky help understanding of celetial coordinate system.

CARAVAN is named after our small VLBI telescope research project CARAVAN (Compact Antennaof Radio Astronomy VLBI Adapted Network). These VLBI dishes are 65-cm and 2.4m. In future wehope interferometric connection to the 35-cm little brothers in educational field.

CARAVAN-35 package include TDK TA-352 prime focused satellite dish, RFD-1500 radio telescopebackend, high precision SANWA DVM, calibration blackbody absorber and accessories. The basicpackage is priced from 400USD. These are distributed from Electro Design Corporation (EDC). Forfurther information please contact (Electro Design Co.Ltd., Nakane 169-2 Noda-city CHIBA JAPAN278-0031 TEL81-4-7123-9511 FAX81-4-7123-9513, skinoshita@edco.jp)

Figure 1. CARAVAN-35 package is being distributedfrom EDC. 35- cm dish, RFD-1500 backend andDVM are the key components. By using RS-232 /USB readout of DVM, students can experience pen-recorder type basic observation essential in radio-astronomy.

Figure 2. RFD1500, compact total-powerbackend. RF amplifier, detector and DC am-plifier are packed into a small package. Stu-dent hook up satellite dish and RFD1500.Then the dish is transform into their own ra-dio telescope.

“IVS NICT Technology Development Center News” (IVS NICT-TDC News) published by theNational Institute of Information and Communications Technology (NICT) (former the Commu-nications Research Laboratory (CRL)) is the continuation of “IVS CRL Technology DevelopmentCenter News” (IVS CRL-TDC News). (On April 1, 2004, Communications Research Laboratory(CRL) and Telecommunications Advancement Organization of JAPAN (TAO) were reorganizedas “National Institute of Information and Communications Technology (NICT)”.)

VLBI Technology Development Center (TDC) at NICT is supposed

1) to develop new observation techniques and new systems for advanced Earth’s rotation ob-servations by VLBI and other space techniques,

2) to promote research in Earth rotation using VLBI,3) to distribute new VLBI technology,4) to contribute the standardization of VLBI interface, and5) to deploy the real-time VLBI technique.

The NICT TDC newsletter (IVS NICT-TDC News) is published biannually by NICT.

This news was edited by Tetsuro Kondo and Yasuhiro Koyama, Kashima Space Research Center,who are editorial staff members of TDC at the National Institute of Information and Commu-nications Technology, Japan. Inquires on this issue should be addressed to T. Kondo, KashimaSpace Research Center, National Institute of Information and Communications Technology, 893-1 Hirai, Kashima, Ibaraki 314-8501, Japan, TEL : +81-299-84-7137, FAX : +81-299-84-7159,e-mail : kondo@nict.go.jp.

Summaries of VLBI and related activities at the National Institute of Information andCommunications Technology are on the Web. The URL to view the home page ofthe Radio Astronomy Applications Section of the Kashima Space Research Center is :“http://www.nict.go.jp/ka/radioastro/”.

IVS NICT TECHNOLOGY DEVELOPMENT CENTER NEWS No.24, July 2004

International VLBI Service for Geodesy and AstrometryNICT Technology Development Center News

published byNational Institute of Information and Communications Technology, 4-2-1 Nukui-kita, Koganei,

Tokyo 184-8795, Japan