Hindawi Publishing CorporationInternational Journal of Navigation and ObservationVolume 2013 Article ID 371450 5 pageshttpdxdoiorg1011552013371450
Research ArticleTime Synchronization and Performance ofBeiDou Satellite Clocks in Orbit
Han Chunhao Cai Zhiwu Lin Yuting Liu Li Xiao ShenghongZhu Lingfeng and Wang Xianglei
Beijing Satellite Navigation Center Beijing 100094 China
Correspondence should be addressed to Lin Yuting lyt1108163com
Received 24 March 2013 Revised 3 July 2013 Accepted 31 July 2013
Academic Editor Sandro Radicella
Copyright copy 2013 Han Chunhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The time model of Beidou satellite clocks is analyzed The general relations of satellite clocks with the system time are studiedThe error sources of two-way radio time transfer between satellites and uplink stations are analyzed The uncertainty of type A isabout 03 ns in Beidou system All the satellite clocks in orbit of Beidou satellite navigation system are evaluated by the clock offsetsobserved by the two-way radio time transferThe frequency stabilities at a sample time of 10000 s and 1 day for all the satellite clocksare better than 10 times 10
minus13 It means that the performance of Beidou satellite clocks in orbit is consistent with the ground test andthe results in orbit are a little better than those in ground vacuum
1 Introduction
Beidou satellite navigation system began to provide regionalservice since December 2012 The constellation of Beidousystem is constituted of 14 satellites in orbit 5GEO satellites5IGSO satellites and 4MEO satellites Table 1 shows the basicinformation of the Beidou satellites Service area now coverslatitude 55
∘S sim 55∘N and longitude 55
∘E sim 180∘E Practical
operational accuracy of Beidou system is better than 10m(95) in horizontal and 15m (95) in vertical [1]
As we all know that time synchronization of satelliteclock plays a significant role in satellite navigations accurateand reliable satellite clock offset parameters are the base ofPNT service Time synchronization error of satellite clock ismainly caused by the time transfer from the master stationand its offset prediction The clock prediction error dependson its frequency instability Then the measurement predic-tion and evaluation of satellite clocks are very important fora satellite navigation system
GPS operates a worldwide monitoring stations networkand includes sixUSAF stations elevenNGA stations and twoIGS stations Geodetic receivers are equipped in these stationsto monitor the performance of satellite clocks On 28 May2010 the first Block IIF satellite designated SVN62PRN25was launched containing three atomic frequency standards
one DCBFS serial number 1010 (Cs 1010) and two RFSserial numbers 27 and 14 (Rb 27 and Rb 14) The frequencystabilities of SVN62 Cs 1010 and Rb 27 are respectively 5 times
10minus14 and 7times10
minus15 at 1 day in orbit And the frequency stabilityof GPS Block IIR Rb is about 9 times 10
minus15 at 1 day for October2010 (all using NGA data) [2ndash4] while the frequency stabilityat 1 day for Galileo satellite clock is about 5times10
minus14 for GIOVEA Rb clocks and 8 times 10
minus15 for GIOVE B PHM [5 6]How about the performance of Beidou clocks in orbits
It is a very concerned question for many GNSS users Thesystem signals and observations of Beidou regional systemare analyzed by Deutsches Zentrum fur Luft-und Raumfahrt(DLR) using a local monitoring network in March 2012The short-term stability and middle-term stability of Beidousatellite clocks are analyzed and compared to other systemsFrequency stability of Beidou RAFS is about 7 times 10
minus12
sim
1 times 10minus11 at 1 second Frequency stability of the best Beidou
satellite clock is about 1 times 10minus13 at 1000 seconds and GPS
Block IIF is not worse than 1times10minus13 [7] In the following sec-
tions the timemodel of satellite clocks used by Beidou systemis described then the error source and uncertainty of the two-way radio time transfer (TWTT) are analyzed which is usedtomeasure clock differences between satellites and the uplinkstations Finally the results and conclusions are detailed
2 International Journal of Navigation and Observation
Table 1 Basic information of Beidou satellite clocks
Num Type (Num) Date03 GEO-1 201011704 GEO-3 20106205 IGSO-1 20108106 GEO-4 201011107 IGSO-2 2010121808 IGSO-3 201141009 IGSO-4 201172710 IGSO-5 201112211 GEO-5 201222512 MEO-3 201243013 MEO-4 201243014 MEO-5 201291915 MEO-6 201291916 GEO-6 20121025
2 Time Model of Satellite Clocks
Considering the large-scale spacetime involved (about 1 times
105 km in space and several days even several months or
years in time) and the precision requirements (1m even 1 cm1mm level) the GNSS data process must be dealt with underthe framework of relativity and quantum theory Two kindsof conceptually different time scales are concerned in GNSSproper times and coordinate times Essentially for any twoevents the observed space interval and time interval betweenthem are dependent on the observer The time readingsgiven directly by ideal clocks located in satellites stations orobservers are proper times They are related to the observeror to the spacetime environments of the clocks This meansthat different observer has different clock due to its relativevelocity and position in the gravitation field In order to havea common time reference for all observers we must choose aspecial observer and construct a reference systemA referencesystem contains a 3-dimensional space reference frame anda time reference The former determines the spatial position(3 space coordinates) of an event and the latter gives thehappening time which is called coordinate time For Earthsatellites a nonrotating geocentric reference system is used todescribe their orbits The reference time is usually TCG (thegeocentric coordinate time) or TT (the terrestrial time) [8 9]
The relationship between the proper time 120591 of satellite andthe coordinate time TT (here noted by 119905) can be modeled as[8]
119905 = [1 minus(1198820
minus (32) (120583119886))
1198882
] (120591 minus 1205910
)
+2
1198882
radic120583119886 sdot 119890 (sin 119864 minus sin 1198640
)
(1)
where 120583 = GM119864
is the geocentric gravitation constant 1198820
the gravity potential of the geoid 119886 the orbit main axis 119890
the eccentricity 119864 the real eccentric anomaly and 119888 the speedof light respectively Then
120591 minus 119905 = [1198820
minus ((32) (GM119864
119886))
1198882
] (119905 minus 1199050
)
minus2
1198882
radic119886GM119864
sdot 119890 sin119864
(2)
If the satellite clock 119879(119905) is modeled as
119879 (119905) = 120591 (119905) + 1198860
+ 1198861
(119905 minus 1199050
) + 1198862
(119905 minus 1199050
)2
+ 120585 (119905) (3)
in which 1198860
1198861
and 1198862
are clock offset parameters and 120585(119905) isthe clock phase noise the offset of satellite clock reffered toBDT can be written as
119909 (119905) equiv 119879 (119905) minus BDT (119905)
= 1198860
+ 1198861
(119905 minus 1199050
) + 1198862
(119905 minus 1199050
)2
+ Δ119905119901
grav + 120585 (119905)
(4)
HereΔ119905119901
grav is the periodic term of relativistic effect as follows
Δ119905119901
grav = minus2
1198882
radic120583119886 119890 sin 119864 = minus2119878
sdot 119878
1198882
(5)
The relativistic effect must be taken into account for the eval-uation of clock performance If not the stability of frequencywill be influenced The quasi-half-day periodical terms inAllan deviations of GPS clocks and Galileo clocks [2 5] weguess may be caused by this term
3 Two-Way Satellite TimeTransfer and Error Analysis
In Beidou system TWTT between satellites and uplink sta-tions is used for the satellitetime synchronization The basicprinciple of TWTT is as follows The satellites and stationsgenerate and transmit pseudo-range signals controlled bytheir local clocks then the uplink pseudo-range 120588
119906
anddownlink pseudo-range 120588
119889
are measured by the satellitesand the stations respectively The uplink pseudo-range anddownlink pseudo-range can be written as
120588119906
(119879119903
119878
) =1003816100381610038161003816119878 (119905119903
119878
) minus 119877
(119905119890
119877
)1003816100381610038161003816 sdot
1
119888minus Δ119879119877
(119905119890
119877
) + Δ119879119878
(119905119903
119878
)
+ 120591119890
119877
+ 120591119903
119878
+ 120591tro + 120591ion (119891119906) + 120591grav
120588119889
(119879119903
119877
) =1003816100381610038161003816119877 (119905119903
119877
) minus 119878
(119905119890
119878
)1003816100381610038161003816 sdot
1
119888+ Δ119879119877
(119905119903
119877
) minus Δ119879119878
(119905119890
119878
)
+ 120591119903
119877
+ 120591119890
119878
+ 120591tro + 120591ion (119891119889) + 120591grav
(6)
where 119905119903
119878
and 119905119890
119878
are time of reception and emission of thesatellite signal 119905119903
119877
and 119905119890
119877
are time of reception and emission ofthe station signalΔ119879
119878
andΔ119879119877
are satellite and stationrsquos clockoffset 120591119903
119877
and 120591119890
119877
are time delay of reception and emission ofthe station equipment 120591119890
119878
and 120591119903
119878
are time delay of receptionand emission of the satellite equipment 120591tro and 120591ion are
International Journal of Navigation and Observation 3
troposphere delay and ionosphere delay119891119906
and119891119889
are uplinkfrequency and downlink frequency 120591grav relativistic timedelay caused by Earth gravitation
The clock differences between satellites and stations arecomputed in the master station by using the uplink pseudo-ranges and the downlink pseudo-ranges The satellite clockoffset can be given by the observed uplink pseudo-range anddownlink pseudo-range as follows
Δ119879119878
(119905119894
) = Δ119879119877
(119905119894
) +1
2
times [120588119906
(119879119894
119878
) minus 120588119889
(119879119894
119877
)]
minus1
119888( 119878
minus 119877
) sdot 119899119877119878
(Δ119879119878
minus Δ119879119877
minus 120591119877119878
)
+ Δ120591119877
minus Δ120591119878
minus Δ120591ion + sdot sdot sdot
(7)
where
Δ120591119877
equiv 120591119903
119877
minus 120591119890
119877
Δ120591119878
equiv 120591119903
119878
minus 120591119890
119878
Δ120591ion equiv 120591ion (119891119906) minus 120591ion (119891119889)
119899119877119878
equiv(119878
minus 119877
)
1003816100381610038161003816119878 minus 119877
1003816100381610038161003816
(8)
The random error of satellite clock difference includes thenoise of pseudo-range observable and the satellite clock phasenoise In short term (le1000 s) the influence of the frequencydrift and phase noise of satellite clock to clock offset can beneglected So the uncertainty of typeAof satellite-board clockoffset measurement can be calculated by the fluctuation ofclock difference Analysis shows that the uncertainty of typeA is less than 03 ns [10] In middle or long term (ge10000 s)the influence of the pseudo-range noise can be neglected andthe results of the Allan variance of satellite clocks are reliable
4 Performance Evaluation ofBeidou Satellite Clocks in Orbit
Satellites that include GEO satellites of serial number 03 0406 and 11 IGSO satellites of serial number 07 08 09 and 10andMEOsatellites of serial number 13 and 14 are evaluated Inorder to ensure the reliability of the evaluation result the timeinterval of satellite clock data is no less than 15 daysThe timescale reference for analysis is the high performance hydrogenclock in ground
Figures 1 2 and 3 show the linear residuals and second-order polynomial residuals of the observed satellite clock off-sets
The green curves are plots of the linear residuals of satel-lite clocks All of the linear residual of GEO-3 GEO-4 andIGSO-2 are smooth which mean that the rubidium clockshave significant frequency drifts The blue curves are thesecond-order polynomial residuals of satellite clocks which
0
100
200
0
2000
0 10 20 30 40 50 60minus200
minus100
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Time (days)
Second-order polynomial
minus4000
minus2000 Line
ar re
sidua
ls (n
s)
Residual errors of GEO-3 satellite fromJanuary 1 2012 to February 21 2012
minus90644e minus 010t2 + 0016545t minus 9246854626
Figure 1 Residual of GEO-3 satellite clock
2205 2210 2215 2220 2225 2230 2235 2240
0
500
1000
Time (days)
0
10
20
minus1500
minus1000
minus500
minus30
minus20
minus10
1058t2 + 012814t + 4745457275
Residual errors of GEO-4 satellite fromJanuary 15 2012 to February 14 2012
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Second-order polynomial
Line
ar re
sidua
ls (n
s)
Figure 2 Residual of GEO-4 satellite clock
0 10 20 30 40 50 60 70 80
0
100
200
300
400
Time (days)
0
1000
2000
minus200
minus100
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Second-order polynomial
Line
ar re
sidua
ls (n
s)Residual errors of IGSO-2 satellite from
January 13 2012 to March 31 2012
minus1000
minus2000
minus3000
minus4000
minus42549e minus 010t2 + 0010565t minus 1240635676
Figure 3 Residual of IGSO-2 satellite clock
4 International Journal of Navigation and Observation
Table 2 Frequency stability of Beidou system satellite clocks
GEO-1 GEO-3 GEO-4 GEO-5 IGSO-1 IGSO-2 IGSO-3 IGSO-4 IGSO-5Stability(10000 s) 731 times 10minus14 552 times 10minus14 758 times 10minus14 917 times 10minus14 813 times 10minus14 595 times 10minus14 794 times 10minus14 853 times 10minus14 898 times 10minus14
Stability(1 day) 671 times 10minus14 290 times 10minus14 383 times 10minus14 566 times 10minus14 938 times 10minus14 307 times 10minus14 253 times 10minus14 391 times 10minus14 445 times 10minus14
100 101 102 103 104 105 106
Averaging time (s)
Alla
n fre
quen
cy st
abili
ty120590y(120591)
10minus15
10minus14
10minus13
10minus12
10minus11
10minus10
GEO-1GEO-3GEO-4GEO-5IGSO-1IGSO-2
IGSO-3IGSO-4IGSO-5MEO-3MEO-4
Figure 4 Frequency stability of Beidou system satellite clocks
demonstrate that the frequency drafts are changing slowlyand the rubidium clocks in orbit have high-level noise char-acteristic such as flick and random walk
The frequency stability of Beidou satellite clocks is evalu-ated by use of the overlappingAllan deviation Figure 4 showsplots of the frequency stability of Beidou system satelliteclocks Table 2 shows the frequency stability at a sample timeof 10000 seconds and 1 day
The frequency stability of Beidou satellite clocks is of thelevel of 10minus14 at a sample time of 10000 seconds and 1 dayThefrequency stability at a sample time of 10000 seconds is about595 sim 917times10
minus14 and that at a sample time of 1 day is about253 sim 938 times 10
minus14Figure 5 gives the comparison of the clock performances
in orbit and in the ground vacuumThe results show that theperformances in orbits are conformable with those in groundAs a whole the results in orbit are a little better than those inground
5 Conclusion
The long-term evaluation for Beidou satellite clocks has beendone using TWTT between satellites and stationsThe results
1 2 3 4 5 6 7 8 9
Allan stability
In orbitIn ground vacuum
Alla
n fre
quen
cy st
abili
ty120590y(86400)
10minus13
Figure 5 Clock day stabilities in orbit and in ground vacuum pots
show that the performance of satellite clock is steady and ingood condition The frequency stabilities at a sample time of10000 s and 1 day for all the satellite clocks are better than 10times
10minus13 Itmeans that the performance of Beidou satellite clocks
in orbit is consistent with the ground test and the results inorbit are a little better than those in ground vacuum
Acknowledgments
Theauthors wish to thank the Editor SandroM Radicella theEditorial AssistantMs Joanna and the anonymous reviewerswhose comments helped improve this paper enormously
References
[1] H Qiaohua ldquoDevelopment of Beidou navigation satellite sys-temrdquo in Proceedings of the 5th Meeting of International Commit-tee on GNSS (ICG-5 rsquo12) Beijing China 2012
[2] F Vannicola R Beard J White and K Senior ldquoGPS Block IIFatomic frequency standard analysisrdquo in Proceedings of the 42thAnnual Precise Time and Time Interval (PTTI) Meeting pp 181ndash196 2010
[3] J Oaks J A Buisson andMM Largay ldquoA summary of theGPSconstellation clock performancerdquo in Proceedings of the 39thAnnual Precise Time and Time Interval (PTTI) Meeting pp 119ndash130 2007
[4] D M Manning and C P Petersen ldquoAFNGA GPS monitorstation high-performance cesium frequency standard stability
International Journal of Navigation and Observation 5
20072008 from NGA kalman filter clock estimatesrdquo in Pro-ceedings of the 40th Annual Precise Time and Time Interval(PTTI) Meeting pp 335ndash348 2008
[5] P Waller F Gonzalez S Binda et al ldquoThe in-orbit performan-ces of GIOVE clocksrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 57 no 3 pp 738ndash745 2010
[6] P Waller F Gonzalez and S Binda ldquoLong-term performanceanalysis of giove clocksrdquo in Proceedings of the 42th Annual Pre-cise Time and Time Interval (PTTI) Meeting pp 171ndash180 2010
[7] O Montenbruck A Hauschild P Steigenberger U Hugento-bler P Teunissen and S Nakamura ldquoInitial assessment of thecompassbeidou-2 regional navigation satellite systemrdquo GPSSolutions vol 17 no 2 pp 211ndash222 2013
[8] H Chunhao ldquoTime measurement within the frame of relativ-ityrdquo Progress in Astronomy vol 20 no 2 pp 107ndash113 2002
[9] H Chunhao C Zhiwu L Yuting L Li et al ldquoTime synchroni-zation and performance evaluation of beidou satellite clocksrdquoin Proceedings of the 3rd China Satellite Navigation Conference2012
[10] L Liu L-F Zhu C-H Han X-P Liu and C Li ldquoThe modelof radio two-way time comparison between satellite and stationand experimental analysisrdquo Chinese Astronomy and Astrophys-ics vol 33 no 4 pp 431ndash439 2009
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2 International Journal of Navigation and Observation
Table 1 Basic information of Beidou satellite clocks
Num Type (Num) Date03 GEO-1 201011704 GEO-3 20106205 IGSO-1 20108106 GEO-4 201011107 IGSO-2 2010121808 IGSO-3 201141009 IGSO-4 201172710 IGSO-5 201112211 GEO-5 201222512 MEO-3 201243013 MEO-4 201243014 MEO-5 201291915 MEO-6 201291916 GEO-6 20121025
2 Time Model of Satellite Clocks
Considering the large-scale spacetime involved (about 1 times
105 km in space and several days even several months or
years in time) and the precision requirements (1m even 1 cm1mm level) the GNSS data process must be dealt with underthe framework of relativity and quantum theory Two kindsof conceptually different time scales are concerned in GNSSproper times and coordinate times Essentially for any twoevents the observed space interval and time interval betweenthem are dependent on the observer The time readingsgiven directly by ideal clocks located in satellites stations orobservers are proper times They are related to the observeror to the spacetime environments of the clocks This meansthat different observer has different clock due to its relativevelocity and position in the gravitation field In order to havea common time reference for all observers we must choose aspecial observer and construct a reference systemA referencesystem contains a 3-dimensional space reference frame anda time reference The former determines the spatial position(3 space coordinates) of an event and the latter gives thehappening time which is called coordinate time For Earthsatellites a nonrotating geocentric reference system is used todescribe their orbits The reference time is usually TCG (thegeocentric coordinate time) or TT (the terrestrial time) [8 9]
The relationship between the proper time 120591 of satellite andthe coordinate time TT (here noted by 119905) can be modeled as[8]
119905 = [1 minus(1198820
minus (32) (120583119886))
1198882
] (120591 minus 1205910
)
+2
1198882
radic120583119886 sdot 119890 (sin 119864 minus sin 1198640
)
(1)
where 120583 = GM119864
is the geocentric gravitation constant 1198820
the gravity potential of the geoid 119886 the orbit main axis 119890
the eccentricity 119864 the real eccentric anomaly and 119888 the speedof light respectively Then
120591 minus 119905 = [1198820
minus ((32) (GM119864
119886))
1198882
] (119905 minus 1199050
)
minus2
1198882
radic119886GM119864
sdot 119890 sin119864
(2)
If the satellite clock 119879(119905) is modeled as
119879 (119905) = 120591 (119905) + 1198860
+ 1198861
(119905 minus 1199050
) + 1198862
(119905 minus 1199050
)2
+ 120585 (119905) (3)
in which 1198860
1198861
and 1198862
are clock offset parameters and 120585(119905) isthe clock phase noise the offset of satellite clock reffered toBDT can be written as
119909 (119905) equiv 119879 (119905) minus BDT (119905)
= 1198860
+ 1198861
(119905 minus 1199050
) + 1198862
(119905 minus 1199050
)2
+ Δ119905119901
grav + 120585 (119905)
(4)
HereΔ119905119901
grav is the periodic term of relativistic effect as follows
Δ119905119901
grav = minus2
1198882
radic120583119886 119890 sin 119864 = minus2119878
sdot 119878
1198882
(5)
The relativistic effect must be taken into account for the eval-uation of clock performance If not the stability of frequencywill be influenced The quasi-half-day periodical terms inAllan deviations of GPS clocks and Galileo clocks [2 5] weguess may be caused by this term
3 Two-Way Satellite TimeTransfer and Error Analysis
In Beidou system TWTT between satellites and uplink sta-tions is used for the satellitetime synchronization The basicprinciple of TWTT is as follows The satellites and stationsgenerate and transmit pseudo-range signals controlled bytheir local clocks then the uplink pseudo-range 120588
119906
anddownlink pseudo-range 120588
119889
are measured by the satellitesand the stations respectively The uplink pseudo-range anddownlink pseudo-range can be written as
120588119906
(119879119903
119878
) =1003816100381610038161003816119878 (119905119903
119878
) minus 119877
(119905119890
119877
)1003816100381610038161003816 sdot
1
119888minus Δ119879119877
(119905119890
119877
) + Δ119879119878
(119905119903
119878
)
+ 120591119890
119877
+ 120591119903
119878
+ 120591tro + 120591ion (119891119906) + 120591grav
120588119889
(119879119903
119877
) =1003816100381610038161003816119877 (119905119903
119877
) minus 119878
(119905119890
119878
)1003816100381610038161003816 sdot
1
119888+ Δ119879119877
(119905119903
119877
) minus Δ119879119878
(119905119890
119878
)
+ 120591119903
119877
+ 120591119890
119878
+ 120591tro + 120591ion (119891119889) + 120591grav
(6)
where 119905119903
119878
and 119905119890
119878
are time of reception and emission of thesatellite signal 119905119903
119877
and 119905119890
119877
are time of reception and emission ofthe station signalΔ119879
119878
andΔ119879119877
are satellite and stationrsquos clockoffset 120591119903
119877
and 120591119890
119877
are time delay of reception and emission ofthe station equipment 120591119890
119878
and 120591119903
119878
are time delay of receptionand emission of the satellite equipment 120591tro and 120591ion are
International Journal of Navigation and Observation 3
troposphere delay and ionosphere delay119891119906
and119891119889
are uplinkfrequency and downlink frequency 120591grav relativistic timedelay caused by Earth gravitation
The clock differences between satellites and stations arecomputed in the master station by using the uplink pseudo-ranges and the downlink pseudo-ranges The satellite clockoffset can be given by the observed uplink pseudo-range anddownlink pseudo-range as follows
Δ119879119878
(119905119894
) = Δ119879119877
(119905119894
) +1
2
times [120588119906
(119879119894
119878
) minus 120588119889
(119879119894
119877
)]
minus1
119888( 119878
minus 119877
) sdot 119899119877119878
(Δ119879119878
minus Δ119879119877
minus 120591119877119878
)
+ Δ120591119877
minus Δ120591119878
minus Δ120591ion + sdot sdot sdot
(7)
where
Δ120591119877
equiv 120591119903
119877
minus 120591119890
119877
Δ120591119878
equiv 120591119903
119878
minus 120591119890
119878
Δ120591ion equiv 120591ion (119891119906) minus 120591ion (119891119889)
119899119877119878
equiv(119878
minus 119877
)
1003816100381610038161003816119878 minus 119877
1003816100381610038161003816
(8)
The random error of satellite clock difference includes thenoise of pseudo-range observable and the satellite clock phasenoise In short term (le1000 s) the influence of the frequencydrift and phase noise of satellite clock to clock offset can beneglected So the uncertainty of typeAof satellite-board clockoffset measurement can be calculated by the fluctuation ofclock difference Analysis shows that the uncertainty of typeA is less than 03 ns [10] In middle or long term (ge10000 s)the influence of the pseudo-range noise can be neglected andthe results of the Allan variance of satellite clocks are reliable
4 Performance Evaluation ofBeidou Satellite Clocks in Orbit
Satellites that include GEO satellites of serial number 03 0406 and 11 IGSO satellites of serial number 07 08 09 and 10andMEOsatellites of serial number 13 and 14 are evaluated Inorder to ensure the reliability of the evaluation result the timeinterval of satellite clock data is no less than 15 daysThe timescale reference for analysis is the high performance hydrogenclock in ground
Figures 1 2 and 3 show the linear residuals and second-order polynomial residuals of the observed satellite clock off-sets
The green curves are plots of the linear residuals of satel-lite clocks All of the linear residual of GEO-3 GEO-4 andIGSO-2 are smooth which mean that the rubidium clockshave significant frequency drifts The blue curves are thesecond-order polynomial residuals of satellite clocks which
0
100
200
0
2000
0 10 20 30 40 50 60minus200
minus100
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Time (days)
Second-order polynomial
minus4000
minus2000 Line
ar re
sidua
ls (n
s)
Residual errors of GEO-3 satellite fromJanuary 1 2012 to February 21 2012
minus90644e minus 010t2 + 0016545t minus 9246854626
Figure 1 Residual of GEO-3 satellite clock
2205 2210 2215 2220 2225 2230 2235 2240
0
500
1000
Time (days)
0
10
20
minus1500
minus1000
minus500
minus30
minus20
minus10
1058t2 + 012814t + 4745457275
Residual errors of GEO-4 satellite fromJanuary 15 2012 to February 14 2012
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Second-order polynomial
Line
ar re
sidua
ls (n
s)
Figure 2 Residual of GEO-4 satellite clock
0 10 20 30 40 50 60 70 80
0
100
200
300
400
Time (days)
0
1000
2000
minus200
minus100
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Second-order polynomial
Line
ar re
sidua
ls (n
s)Residual errors of IGSO-2 satellite from
January 13 2012 to March 31 2012
minus1000
minus2000
minus3000
minus4000
minus42549e minus 010t2 + 0010565t minus 1240635676
Figure 3 Residual of IGSO-2 satellite clock
4 International Journal of Navigation and Observation
Table 2 Frequency stability of Beidou system satellite clocks
GEO-1 GEO-3 GEO-4 GEO-5 IGSO-1 IGSO-2 IGSO-3 IGSO-4 IGSO-5Stability(10000 s) 731 times 10minus14 552 times 10minus14 758 times 10minus14 917 times 10minus14 813 times 10minus14 595 times 10minus14 794 times 10minus14 853 times 10minus14 898 times 10minus14
Stability(1 day) 671 times 10minus14 290 times 10minus14 383 times 10minus14 566 times 10minus14 938 times 10minus14 307 times 10minus14 253 times 10minus14 391 times 10minus14 445 times 10minus14
100 101 102 103 104 105 106
Averaging time (s)
Alla
n fre
quen
cy st
abili
ty120590y(120591)
10minus15
10minus14
10minus13
10minus12
10minus11
10minus10
GEO-1GEO-3GEO-4GEO-5IGSO-1IGSO-2
IGSO-3IGSO-4IGSO-5MEO-3MEO-4
Figure 4 Frequency stability of Beidou system satellite clocks
demonstrate that the frequency drafts are changing slowlyand the rubidium clocks in orbit have high-level noise char-acteristic such as flick and random walk
The frequency stability of Beidou satellite clocks is evalu-ated by use of the overlappingAllan deviation Figure 4 showsplots of the frequency stability of Beidou system satelliteclocks Table 2 shows the frequency stability at a sample timeof 10000 seconds and 1 day
The frequency stability of Beidou satellite clocks is of thelevel of 10minus14 at a sample time of 10000 seconds and 1 dayThefrequency stability at a sample time of 10000 seconds is about595 sim 917times10
minus14 and that at a sample time of 1 day is about253 sim 938 times 10
minus14Figure 5 gives the comparison of the clock performances
in orbit and in the ground vacuumThe results show that theperformances in orbits are conformable with those in groundAs a whole the results in orbit are a little better than those inground
5 Conclusion
The long-term evaluation for Beidou satellite clocks has beendone using TWTT between satellites and stationsThe results
1 2 3 4 5 6 7 8 9
Allan stability
In orbitIn ground vacuum
Alla
n fre
quen
cy st
abili
ty120590y(86400)
10minus13
Figure 5 Clock day stabilities in orbit and in ground vacuum pots
show that the performance of satellite clock is steady and ingood condition The frequency stabilities at a sample time of10000 s and 1 day for all the satellite clocks are better than 10times
10minus13 Itmeans that the performance of Beidou satellite clocks
in orbit is consistent with the ground test and the results inorbit are a little better than those in ground vacuum
Acknowledgments
Theauthors wish to thank the Editor SandroM Radicella theEditorial AssistantMs Joanna and the anonymous reviewerswhose comments helped improve this paper enormously
References
[1] H Qiaohua ldquoDevelopment of Beidou navigation satellite sys-temrdquo in Proceedings of the 5th Meeting of International Commit-tee on GNSS (ICG-5 rsquo12) Beijing China 2012
[2] F Vannicola R Beard J White and K Senior ldquoGPS Block IIFatomic frequency standard analysisrdquo in Proceedings of the 42thAnnual Precise Time and Time Interval (PTTI) Meeting pp 181ndash196 2010
[3] J Oaks J A Buisson andMM Largay ldquoA summary of theGPSconstellation clock performancerdquo in Proceedings of the 39thAnnual Precise Time and Time Interval (PTTI) Meeting pp 119ndash130 2007
[4] D M Manning and C P Petersen ldquoAFNGA GPS monitorstation high-performance cesium frequency standard stability
International Journal of Navigation and Observation 5
20072008 from NGA kalman filter clock estimatesrdquo in Pro-ceedings of the 40th Annual Precise Time and Time Interval(PTTI) Meeting pp 335ndash348 2008
[5] P Waller F Gonzalez S Binda et al ldquoThe in-orbit performan-ces of GIOVE clocksrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 57 no 3 pp 738ndash745 2010
[6] P Waller F Gonzalez and S Binda ldquoLong-term performanceanalysis of giove clocksrdquo in Proceedings of the 42th Annual Pre-cise Time and Time Interval (PTTI) Meeting pp 171ndash180 2010
[7] O Montenbruck A Hauschild P Steigenberger U Hugento-bler P Teunissen and S Nakamura ldquoInitial assessment of thecompassbeidou-2 regional navigation satellite systemrdquo GPSSolutions vol 17 no 2 pp 211ndash222 2013
[8] H Chunhao ldquoTime measurement within the frame of relativ-ityrdquo Progress in Astronomy vol 20 no 2 pp 107ndash113 2002
[9] H Chunhao C Zhiwu L Yuting L Li et al ldquoTime synchroni-zation and performance evaluation of beidou satellite clocksrdquoin Proceedings of the 3rd China Satellite Navigation Conference2012
[10] L Liu L-F Zhu C-H Han X-P Liu and C Li ldquoThe modelof radio two-way time comparison between satellite and stationand experimental analysisrdquo Chinese Astronomy and Astrophys-ics vol 33 no 4 pp 431ndash439 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Navigation and Observation 3
troposphere delay and ionosphere delay119891119906
and119891119889
are uplinkfrequency and downlink frequency 120591grav relativistic timedelay caused by Earth gravitation
The clock differences between satellites and stations arecomputed in the master station by using the uplink pseudo-ranges and the downlink pseudo-ranges The satellite clockoffset can be given by the observed uplink pseudo-range anddownlink pseudo-range as follows
Δ119879119878
(119905119894
) = Δ119879119877
(119905119894
) +1
2
times [120588119906
(119879119894
119878
) minus 120588119889
(119879119894
119877
)]
minus1
119888( 119878
minus 119877
) sdot 119899119877119878
(Δ119879119878
minus Δ119879119877
minus 120591119877119878
)
+ Δ120591119877
minus Δ120591119878
minus Δ120591ion + sdot sdot sdot
(7)
where
Δ120591119877
equiv 120591119903
119877
minus 120591119890
119877
Δ120591119878
equiv 120591119903
119878
minus 120591119890
119878
Δ120591ion equiv 120591ion (119891119906) minus 120591ion (119891119889)
119899119877119878
equiv(119878
minus 119877
)
1003816100381610038161003816119878 minus 119877
1003816100381610038161003816
(8)
The random error of satellite clock difference includes thenoise of pseudo-range observable and the satellite clock phasenoise In short term (le1000 s) the influence of the frequencydrift and phase noise of satellite clock to clock offset can beneglected So the uncertainty of typeAof satellite-board clockoffset measurement can be calculated by the fluctuation ofclock difference Analysis shows that the uncertainty of typeA is less than 03 ns [10] In middle or long term (ge10000 s)the influence of the pseudo-range noise can be neglected andthe results of the Allan variance of satellite clocks are reliable
4 Performance Evaluation ofBeidou Satellite Clocks in Orbit
Satellites that include GEO satellites of serial number 03 0406 and 11 IGSO satellites of serial number 07 08 09 and 10andMEOsatellites of serial number 13 and 14 are evaluated Inorder to ensure the reliability of the evaluation result the timeinterval of satellite clock data is no less than 15 daysThe timescale reference for analysis is the high performance hydrogenclock in ground
Figures 1 2 and 3 show the linear residuals and second-order polynomial residuals of the observed satellite clock off-sets
The green curves are plots of the linear residuals of satel-lite clocks All of the linear residual of GEO-3 GEO-4 andIGSO-2 are smooth which mean that the rubidium clockshave significant frequency drifts The blue curves are thesecond-order polynomial residuals of satellite clocks which
0
100
200
0
2000
0 10 20 30 40 50 60minus200
minus100
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Time (days)
Second-order polynomial
minus4000
minus2000 Line
ar re
sidua
ls (n
s)
Residual errors of GEO-3 satellite fromJanuary 1 2012 to February 21 2012
minus90644e minus 010t2 + 0016545t minus 9246854626
Figure 1 Residual of GEO-3 satellite clock
2205 2210 2215 2220 2225 2230 2235 2240
0
500
1000
Time (days)
0
10
20
minus1500
minus1000
minus500
minus30
minus20
minus10
1058t2 + 012814t + 4745457275
Residual errors of GEO-4 satellite fromJanuary 15 2012 to February 14 2012
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Second-order polynomial
Line
ar re
sidua
ls (n
s)
Figure 2 Residual of GEO-4 satellite clock
0 10 20 30 40 50 60 70 80
0
100
200
300
400
Time (days)
0
1000
2000
minus200
minus100
Seco
nd-o
rder
pol
ynom
ial r
esid
uals
(ns)
Second-order polynomial
Line
ar re
sidua
ls (n
s)Residual errors of IGSO-2 satellite from
January 13 2012 to March 31 2012
minus1000
minus2000
minus3000
minus4000
minus42549e minus 010t2 + 0010565t minus 1240635676
Figure 3 Residual of IGSO-2 satellite clock
4 International Journal of Navigation and Observation
Table 2 Frequency stability of Beidou system satellite clocks
GEO-1 GEO-3 GEO-4 GEO-5 IGSO-1 IGSO-2 IGSO-3 IGSO-4 IGSO-5Stability(10000 s) 731 times 10minus14 552 times 10minus14 758 times 10minus14 917 times 10minus14 813 times 10minus14 595 times 10minus14 794 times 10minus14 853 times 10minus14 898 times 10minus14
Stability(1 day) 671 times 10minus14 290 times 10minus14 383 times 10minus14 566 times 10minus14 938 times 10minus14 307 times 10minus14 253 times 10minus14 391 times 10minus14 445 times 10minus14
100 101 102 103 104 105 106
Averaging time (s)
Alla
n fre
quen
cy st
abili
ty120590y(120591)
10minus15
10minus14
10minus13
10minus12
10minus11
10minus10
GEO-1GEO-3GEO-4GEO-5IGSO-1IGSO-2
IGSO-3IGSO-4IGSO-5MEO-3MEO-4
Figure 4 Frequency stability of Beidou system satellite clocks
demonstrate that the frequency drafts are changing slowlyand the rubidium clocks in orbit have high-level noise char-acteristic such as flick and random walk
The frequency stability of Beidou satellite clocks is evalu-ated by use of the overlappingAllan deviation Figure 4 showsplots of the frequency stability of Beidou system satelliteclocks Table 2 shows the frequency stability at a sample timeof 10000 seconds and 1 day
The frequency stability of Beidou satellite clocks is of thelevel of 10minus14 at a sample time of 10000 seconds and 1 dayThefrequency stability at a sample time of 10000 seconds is about595 sim 917times10
minus14 and that at a sample time of 1 day is about253 sim 938 times 10
minus14Figure 5 gives the comparison of the clock performances
in orbit and in the ground vacuumThe results show that theperformances in orbits are conformable with those in groundAs a whole the results in orbit are a little better than those inground
5 Conclusion
The long-term evaluation for Beidou satellite clocks has beendone using TWTT between satellites and stationsThe results
1 2 3 4 5 6 7 8 9
Allan stability
In orbitIn ground vacuum
Alla
n fre
quen
cy st
abili
ty120590y(86400)
10minus13
Figure 5 Clock day stabilities in orbit and in ground vacuum pots
show that the performance of satellite clock is steady and ingood condition The frequency stabilities at a sample time of10000 s and 1 day for all the satellite clocks are better than 10times
10minus13 Itmeans that the performance of Beidou satellite clocks
in orbit is consistent with the ground test and the results inorbit are a little better than those in ground vacuum
Acknowledgments
Theauthors wish to thank the Editor SandroM Radicella theEditorial AssistantMs Joanna and the anonymous reviewerswhose comments helped improve this paper enormously
References
[1] H Qiaohua ldquoDevelopment of Beidou navigation satellite sys-temrdquo in Proceedings of the 5th Meeting of International Commit-tee on GNSS (ICG-5 rsquo12) Beijing China 2012
[2] F Vannicola R Beard J White and K Senior ldquoGPS Block IIFatomic frequency standard analysisrdquo in Proceedings of the 42thAnnual Precise Time and Time Interval (PTTI) Meeting pp 181ndash196 2010
[3] J Oaks J A Buisson andMM Largay ldquoA summary of theGPSconstellation clock performancerdquo in Proceedings of the 39thAnnual Precise Time and Time Interval (PTTI) Meeting pp 119ndash130 2007
[4] D M Manning and C P Petersen ldquoAFNGA GPS monitorstation high-performance cesium frequency standard stability
International Journal of Navigation and Observation 5
20072008 from NGA kalman filter clock estimatesrdquo in Pro-ceedings of the 40th Annual Precise Time and Time Interval(PTTI) Meeting pp 335ndash348 2008
[5] P Waller F Gonzalez S Binda et al ldquoThe in-orbit performan-ces of GIOVE clocksrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 57 no 3 pp 738ndash745 2010
[6] P Waller F Gonzalez and S Binda ldquoLong-term performanceanalysis of giove clocksrdquo in Proceedings of the 42th Annual Pre-cise Time and Time Interval (PTTI) Meeting pp 171ndash180 2010
[7] O Montenbruck A Hauschild P Steigenberger U Hugento-bler P Teunissen and S Nakamura ldquoInitial assessment of thecompassbeidou-2 regional navigation satellite systemrdquo GPSSolutions vol 17 no 2 pp 211ndash222 2013
[8] H Chunhao ldquoTime measurement within the frame of relativ-ityrdquo Progress in Astronomy vol 20 no 2 pp 107ndash113 2002
[9] H Chunhao C Zhiwu L Yuting L Li et al ldquoTime synchroni-zation and performance evaluation of beidou satellite clocksrdquoin Proceedings of the 3rd China Satellite Navigation Conference2012
[10] L Liu L-F Zhu C-H Han X-P Liu and C Li ldquoThe modelof radio two-way time comparison between satellite and stationand experimental analysisrdquo Chinese Astronomy and Astrophys-ics vol 33 no 4 pp 431ndash439 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
4 International Journal of Navigation and Observation
Table 2 Frequency stability of Beidou system satellite clocks
GEO-1 GEO-3 GEO-4 GEO-5 IGSO-1 IGSO-2 IGSO-3 IGSO-4 IGSO-5Stability(10000 s) 731 times 10minus14 552 times 10minus14 758 times 10minus14 917 times 10minus14 813 times 10minus14 595 times 10minus14 794 times 10minus14 853 times 10minus14 898 times 10minus14
Stability(1 day) 671 times 10minus14 290 times 10minus14 383 times 10minus14 566 times 10minus14 938 times 10minus14 307 times 10minus14 253 times 10minus14 391 times 10minus14 445 times 10minus14
100 101 102 103 104 105 106
Averaging time (s)
Alla
n fre
quen
cy st
abili
ty120590y(120591)
10minus15
10minus14
10minus13
10minus12
10minus11
10minus10
GEO-1GEO-3GEO-4GEO-5IGSO-1IGSO-2
IGSO-3IGSO-4IGSO-5MEO-3MEO-4
Figure 4 Frequency stability of Beidou system satellite clocks
demonstrate that the frequency drafts are changing slowlyand the rubidium clocks in orbit have high-level noise char-acteristic such as flick and random walk
The frequency stability of Beidou satellite clocks is evalu-ated by use of the overlappingAllan deviation Figure 4 showsplots of the frequency stability of Beidou system satelliteclocks Table 2 shows the frequency stability at a sample timeof 10000 seconds and 1 day
The frequency stability of Beidou satellite clocks is of thelevel of 10minus14 at a sample time of 10000 seconds and 1 dayThefrequency stability at a sample time of 10000 seconds is about595 sim 917times10
minus14 and that at a sample time of 1 day is about253 sim 938 times 10
minus14Figure 5 gives the comparison of the clock performances
in orbit and in the ground vacuumThe results show that theperformances in orbits are conformable with those in groundAs a whole the results in orbit are a little better than those inground
5 Conclusion
The long-term evaluation for Beidou satellite clocks has beendone using TWTT between satellites and stationsThe results
1 2 3 4 5 6 7 8 9
Allan stability
In orbitIn ground vacuum
Alla
n fre
quen
cy st
abili
ty120590y(86400)
10minus13
Figure 5 Clock day stabilities in orbit and in ground vacuum pots
show that the performance of satellite clock is steady and ingood condition The frequency stabilities at a sample time of10000 s and 1 day for all the satellite clocks are better than 10times
10minus13 Itmeans that the performance of Beidou satellite clocks
in orbit is consistent with the ground test and the results inorbit are a little better than those in ground vacuum
Acknowledgments
Theauthors wish to thank the Editor SandroM Radicella theEditorial AssistantMs Joanna and the anonymous reviewerswhose comments helped improve this paper enormously
References
[1] H Qiaohua ldquoDevelopment of Beidou navigation satellite sys-temrdquo in Proceedings of the 5th Meeting of International Commit-tee on GNSS (ICG-5 rsquo12) Beijing China 2012
[2] F Vannicola R Beard J White and K Senior ldquoGPS Block IIFatomic frequency standard analysisrdquo in Proceedings of the 42thAnnual Precise Time and Time Interval (PTTI) Meeting pp 181ndash196 2010
[3] J Oaks J A Buisson andMM Largay ldquoA summary of theGPSconstellation clock performancerdquo in Proceedings of the 39thAnnual Precise Time and Time Interval (PTTI) Meeting pp 119ndash130 2007
[4] D M Manning and C P Petersen ldquoAFNGA GPS monitorstation high-performance cesium frequency standard stability
International Journal of Navigation and Observation 5
20072008 from NGA kalman filter clock estimatesrdquo in Pro-ceedings of the 40th Annual Precise Time and Time Interval(PTTI) Meeting pp 335ndash348 2008
[5] P Waller F Gonzalez S Binda et al ldquoThe in-orbit performan-ces of GIOVE clocksrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 57 no 3 pp 738ndash745 2010
[6] P Waller F Gonzalez and S Binda ldquoLong-term performanceanalysis of giove clocksrdquo in Proceedings of the 42th Annual Pre-cise Time and Time Interval (PTTI) Meeting pp 171ndash180 2010
[7] O Montenbruck A Hauschild P Steigenberger U Hugento-bler P Teunissen and S Nakamura ldquoInitial assessment of thecompassbeidou-2 regional navigation satellite systemrdquo GPSSolutions vol 17 no 2 pp 211ndash222 2013
[8] H Chunhao ldquoTime measurement within the frame of relativ-ityrdquo Progress in Astronomy vol 20 no 2 pp 107ndash113 2002
[9] H Chunhao C Zhiwu L Yuting L Li et al ldquoTime synchroni-zation and performance evaluation of beidou satellite clocksrdquoin Proceedings of the 3rd China Satellite Navigation Conference2012
[10] L Liu L-F Zhu C-H Han X-P Liu and C Li ldquoThe modelof radio two-way time comparison between satellite and stationand experimental analysisrdquo Chinese Astronomy and Astrophys-ics vol 33 no 4 pp 431ndash439 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Navigation and Observation 5
20072008 from NGA kalman filter clock estimatesrdquo in Pro-ceedings of the 40th Annual Precise Time and Time Interval(PTTI) Meeting pp 335ndash348 2008
[5] P Waller F Gonzalez S Binda et al ldquoThe in-orbit performan-ces of GIOVE clocksrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 57 no 3 pp 738ndash745 2010
[6] P Waller F Gonzalez and S Binda ldquoLong-term performanceanalysis of giove clocksrdquo in Proceedings of the 42th Annual Pre-cise Time and Time Interval (PTTI) Meeting pp 171ndash180 2010
[7] O Montenbruck A Hauschild P Steigenberger U Hugento-bler P Teunissen and S Nakamura ldquoInitial assessment of thecompassbeidou-2 regional navigation satellite systemrdquo GPSSolutions vol 17 no 2 pp 211ndash222 2013
[8] H Chunhao ldquoTime measurement within the frame of relativ-ityrdquo Progress in Astronomy vol 20 no 2 pp 107ndash113 2002
[9] H Chunhao C Zhiwu L Yuting L Li et al ldquoTime synchroni-zation and performance evaluation of beidou satellite clocksrdquoin Proceedings of the 3rd China Satellite Navigation Conference2012
[10] L Liu L-F Zhu C-H Han X-P Liu and C Li ldquoThe modelof radio two-way time comparison between satellite and stationand experimental analysisrdquo Chinese Astronomy and Astrophys-ics vol 33 no 4 pp 431ndash439 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
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