381
1 INTRODUCTION
In early 1980s, when the first satellite navigation
system (SNS), Transit in USA and Cikada in Soviet
Union were already operational, China began
actively study the satellite systems in line with
Chinas’sconditions.Thisnewsystem,calledBeiDou
(Big Dippler), earlier Compass, as all other SNSs,
consists of three ma
jor components: the space
constellation, the ground control segment and the
user segment. In 2000, the BeiDou Navigation
Satellite Demonstration System (BDS) was
established.(Report...2013,www.insidegnss.com).
Thefunctionsandperformanceparametersatthis
stepareasfollows(Report…2013):
positionaccuracy:betterthan10m(95%);
velocityaccuracy:bettertha
n0.2m/s;
timeaccuracy:50ns;
short message communications: 120 Chinese
characterspermessage.
Global services BeiDou will provide by around
2019/2020 (Munich 2016, imo.org). The final space
constellation of this system will consist of 35
satellites:
5 GEO (058.75
O
E, 080
O
E, 110.5
O
E, 140
O
E and
160
O
E),altitude35,786km;
BeiDou and Galileo, Two Global Satellite Navigation
Systems in Final Phase of the Construction, Visibility
and Geometry
J
.Januszewski
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT:Spatialsegmentisoneof threesegmentsof eachsatellitenavigation systems (SNS).Nowadays
twoSNSs,GPSandGLONASS,arefullyoperational,twonextSNSs,BeiDouinChinaandGalileoinEurope,
areinfinalphaseoftheconstruction.InthecaseofChinasystemthi
ssegmentwillconsistof35satelliteswith
threetypesoforbits−medium(MEO),geostationary(GEO)andinclinedgeosynchronous(IGSO).AsGEOand
IGSO satellites can be used in China and Asia‐Pacific region only, BeiDou MEO constellation with 27 fully
operationalsatelliteswillbetakenintoaccountinthispaper.Theorbitalpla
nesoftheGalileoconstellationwill
bedividedin“slots”thatcontainsatleastoneoperationalsatellite.TheGalileoreferenceconstellationhas24
nominalorbitalpositionsoroperationalslotsinMEOhomogeneouslydistributedin3orbitalplanes;i.e.8slots
equallyspacedperplane.As the error of user’s position obtained from both systems depends ongeometry
fact
orDOP(DilutionOfPrecision)amongotherthingstheknowledgeofthenumberofsatellitesvisiblebythe
user above given masking elevation angle H
min and the distributions of DOP coefficient values, GDOP in
particular, is very important. The lowest and the greatest number of satellites visible in open area by the
observeratdifferentlatitudesfordifferentH
min,thepercentageofsatellitesvisibleaboveangleH,distributions
(in per cent) of satellites azimuths and GDOP coefficient values for different H
min for BeiDou and Galileo
systemsatdifferentlatitudesarepresentedinthepaper.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 10
Number 3
September 2016
DOI:10.12716/1001.10.03.01
382
27 MEO (altitude 21,500 km, inclination 55
O
, 3
evenlydistributedorbitalplanes,oneach9evenly
distributedsatellites).The phase isselectedfrom
the Walker 24/3/1 constellation, and the right
ascensionofascendingnodeofthesatellitesinthe
firstorbitalplaneis0
O
;
3IGSO(altitude36,000km,inclination55
O
,evenly
distributedin3orbitalplanes).Thetracksofsub‐
satellite points for thoseIGSO satellites are
coincided while the longitude of the intersection
point is 118
O
E, with a phase difference of 120
O
.
The sub‐satellite tracks for the current (August
2016) other two operational IGSO satellites are
coincided while the longitude of the intersection
pointisat095
O
E.Thesetwosatelliteswillnotbe
infinalconstellation.
It means that the final number of operational
satellites(35)willbethegreatestamongallcurrently
operational (GPS – 32, GLONASS – 24) or under
construction (Galileo – 30) SNSs. BeiDou
constellation,astheonlySNS,usesthreementioned
abovetypesoforbits,whileallothersuseMEOorbits
only(JanuszewskiJ.2010,MartinH.2013).
The most important parameters of all BeiDou
satellitesarepresentedinthetable1.
Table 1. BeiDou system, parameters of GEO, IGSO and
MEOsatellites(www.isg.org)
_______________________________________________
ParameterSatellite
GEO IGSO MEO
_______________________________________________
SatellitebusDFH−3BDFH−3BNavigation
satellitebus
LaunchvehicleCZ−3C CZ−3A CZ−3B
Launchmass[kg] 4600 4200 800
Drymass[kg]1550 1900 nodetails
Bodysize[m]1.8x2.2x2.5
Solararraysize[m]3x2.2x1.7(twopieces)
Span
width[m]17.7 17.7 17.7
Crosssection[m2] 272727
Poweroutput[kW] 6.86.21.5
Spacedesignline[years] 885
_______________________________________________
The satellites are and will be launched from the
XSLC (Xichang Satellite Launch Center) in the
southwestern province Sichuan of China, using
China’s Long March 3 CZ launch vehicles
(www.beidou.gov.cn).
The BeiDou navigation (NAV) messages are
formatted in D1 and D2 based on their rate and
structure in superframe, frame and
subframe. The
firstformatwillbetransmittedbyall35satellites,the
secondisalreadybyGEOsatellitesonly.Therateof
these messages is 50 bps and 500 bps respectively
(www.beidou.gov.cn).
D1 NAV message contains basic, named
sometimes fundamental also, information about
broadcasting27MEOand3IGSOsatellites,
almanac
information offsets from other global SNSs (GPS,
GLONASSandGalileo).
D2NAVmessagecontainsmentionedabovebasic
NAV information of the broadcasting satellite and
additionally augmentation service information –
integrity and differential correction information,
ionospheric grid information. In the case of this
formatthedefinitionofbasicNAVinformationis
the
same as that in format D1 except the page number
(Pnum) and seconds of week (SOW), which are
different from these in format D1 (BeiDou, Signal.
2013,BeiDou,Open.2013).
In Europe the development of initial design
concepts for a new own satellite navigation system
beganinthe1990s,
withselectionofaninitialsystem
design in 2002. In March 2002 the European Union
andtheEuropeanSpaceAgencyagreedtofundthe
project, named Galileo, pending a review in 2003.
The Galileo constellation design was originally
plannedbasedonathree‐planeWalkerconstellation
withaminimumofnine
operationalsatellitesineach
planeandthreeactivespares,oneperorbitalplane;
totalnumberofsatellites–30.
Over the course of time the planned Galileo
constellation changed and in 2014 these changes
becameevident.Thereferencespacesegmenthas24
operationalsatellitesonlyinaWalker24/3/1design
alongwithuptosixoperatingspares–twoineach
plane. The eight satellites in each plane are equally
spaced; locations of the spares will be determined.
The MEO planes, altitude 23,222 km, have 120
O
separation with inclination 56
O
. Galileo satellites
nominallyhaveamassof700kg,measuring2.7mx
1.1mx1.2m,withdeployedsolararraysspanning
18.7m(BeitzJ.W.2016,www.gsc.europa.eu).
AllGalileosatelliteswerelaunched,twosatellites
at once, from the Guiana Space Centre, French and
Europeanspaceport nearKourouin
FrenchGuiana,
using carrier Soyuz‐STB/Fregat‐MT. Currently
(August2016)spatialsegmentconsistsof9satellites,
one partially unavailable, four with status in
commissioning(twolastsatelliteslaunchedMay24,
2016 will be operational soon). Next launch is
scheduledforNovember17,2016fromKouroualso
but using new carrier
Ariane 5ES. This dispenser
allows for a launch of four satellites at once. The
subsequent eight satellites will be launched in 2017
and2018,thelastonein2019.
2 BEIDOUANDGALILEOCONSTELLATIONS
The nominal values of geographical longitude of
ascending node and argument of latitude of all 27
BeiDou
MEOsatellitesandall24Galileoareshowed
inthetable2andtable3,respectively.
Table2. BeiDou system, geographical longitude of
ascendingnode(An)andargumentoflatitude(Al)ofall27
MEOsatellites
_______________________________________________
OrbitI,OrbitII,OrbitIIII,
An=0
O
An=120
O
An=240
O
_______________________________________________
Noof Al Noof Al NoofAl
satellite [deg] satellite [deg] satellite [deg]
_______________________________________________
10 1013  1926
240  1153  2066
380  1293  21106
4120 13133 22146
5160 14173 23186
6200 15213 24226
7240 16253 25266
8280 17293 26306
9320 18
333 27346
_______________________________________________
383
Table 3. Galileo system, geographical longitude of
ascendingnode(An)andargumentoflatitude(Al)ofall24
satellites
_______________________________________________
OrbitI,OrbitII,OrbitIIII,
An=0
O
An=120
O
An=240
O
_______________________________________________
Noof Al Noof Al NoofAl
satellite [deg] satellite [deg] satellite [deg]
_______________________________________________
10 915  1730
245  1060  1875
390  11105 19120
4135 12150 20165
5180 13195 21210
6225 14240 22255
7270 15285 23300
8315 16330 24345
_______________________________________________
3 TESTMETHODS
AllcalculationsbasedonreferenceellipsoidWGS–84
were made on author’s simulating program. The
interval of the latitude of the observer between 0
O
and90
O
wasdividedinto9zones,each10
O
wide.In
theobserver’sreceivermaskingelevationangleH
min
was assumed to be 0
O
(horizon), 5
O
(the most
frequentlyusedvalueofH
min),10
O
,15
O
,20
O
and25
O
.
Theangle25
O
isrepresentativeforthepositioningin
restrictedareawherethevisibilityofsatellitescanbe
limited. This problem is very important in road
transport (urban canyon) and in maritime transport
in restricted area where the visibility of satellites is
limited. The calculations were made for 27 BeiDou
MEOand24
Galileosatellitesconstellations.
For each zone of latitude and for each ma sking
elevationangle(H
min)onethousand(1000)
geographic–time coordinates of the observer were
generated by random–number generator with
uniformdistribution:
latitudeinterval0–600minutes(10
O
),
longitudeinterval0−21600minutes(360
O
),
timeintervalinminutes,Galileo:0−14,360.75,(17
orbitalperiods,each14h4min45sec),BeiDou:0
– 10,091.48 minutes (13 MEO satellite orbital
periods,each12h,56min16.05sec).
For each geographic–time coordinates: the
satelliteelevation(H),thesatelliteazimuth(Az),the
number of
visible satellites (ls) and GDOP
(Geometric Dilution of Precision) coefficient values
were calculated. Elevation H was divided into 9
intervals,each10
O
wide, azimuth(Az)was divided
into8intervals,each45
O
andGDOPvalue(w)into8
intervals:w<2,2≤w<3,3≤w<4,4≤w<5,5≤w<6,6≤w<8,
8≤w<20,w≥20.
4 VISIBILITYOFBEIDOUMEOSATELLITESAND
GALILEOSATELLITES
Thelowest(ls
min)andthegreatest(lsmax)numberlsof
satellitesvisiblebythe observerinopenareaabove
different H
min in all 9 zones of latitudes for both
systemsarepresentedinthetable4.AsforH
min≤25
O
thenumber lsisinthecaseofBeiDougreaterthan3
foralluser’slatitudesitmeansthat3Dpositioncan
be obtained always and anywhere in the world. In
the case of Galileo the number ls can be equal 3 in
zone 0–10
O
and at latitudes 40–60
O
; it means 2D
positiononly.Wecansayalsothat:
for both systems the number ls depends on
observer’slatitude,independentlyofH
minvalue;
forH
min=0
O
thenumberlsminisforBeiDousystem
thelowest(6)inzone20−30
O
andthegreatest(9)
inzone0−10
O
andatlatitudes60−90
O
,forGalileo
system this number is the lowest (6 also) at
latitudes 20–60
O
and the greatest (9 also) at
latitudes 70–90
O
; the number lsmax (12 always) is
for BeiDou in all 9 latitude zones, for Galileo at
latitudes10–40
O
and60–90
O
.
Ifthenumberlsisequal4theusermustbevery
carefulbecausethenumberofsatelliteswhichcanbe
used in position determination can decrease at any
moment and for any reason. That’s why the
additional calculations were made for both systems
fordifferentH
mininorderto determine thegreatest
elevation H for which the number ls of satellites
visibleat differentlatitudesinopenareaabovethis
angleisequal4(ls4)or3(ls3)(table5).
Table4. System BeiDou, the lowest and the greatest
numberofMEOsatellitesvisibleinopenareaaboveH
minat
differentobserver’slatitudes.
_______________________________________________
LatitudeHmin
[
O
]0
O
5
O
10
O
15
O
20
O
25
O
_______________________________________________
0−10 BeiDou 9−12 8–12 7−10 5−10 4−8 4–7

Galileo8−118−11 6−10 4−8 4−8 3−7
10−20 BeiDou 8–12 6–12 6−10 5−9 4–9 4–8

Galileo7–12 6–11 5–9 4–9 4–8 4–8
20–30 BeiDou 6–12 6–11 6–10 5–9 4–9 4–7

Galileo6–10 6–10 5–9 4–9 4–8 4–7
30–40 BeiDou 7–12 6–12 6–10 5–9 5–9 4–7

Galileo6–12 6–11 5–9 4–9 4–9 4–7
40–50 BeiDou 7–12 6–12 6–10 5–10 4–8 4–7

Galileo6–11 6–11 5–9 4–9 4–8 3–7
50–60 BeiDou 8–12 6–11 6–10 5–10 4–9 4–7

Galileo6–10 6–10 5–9 4–9 4–7 3–7
60–70 BeiDou 9–12 8–12 7−11 6–9 5–9 4–7

Galileo8–12 8–11 6−9 5–9 4–8 4–7
70–80 BeiDou 9–12 8–12 8–11 6–9 5–8 4–8

Galileo9–12 8–11 7–10 5–9 5–8 4–7
80–90 BeiDou 9−12 9–12 8−10 7−9 6−9 4–8

Galileo9−12 8–11 7−9 6−8 6−8 4–7
_______________________________________________
Table5. BeiDou system(MEO satellites only) and Galileo
system,thegreatestelevationH[
O
]forwhichthenumber
lsofsatellitesvisibleatdifferentlatitudesbytheobserver
inopenareaabovethisangleisequal4or3
_______________________________________________
LatitudeNumberlsofsatellites
[
O
]43
BeiDou Galileo BeiDou Galileo
_______________________________________________
0–1026233229
10–2028253329
20–3030263533
30–4028263330
40–5028243332
50–6028243233
60–7028253232
70–
8029273229
80–9033323435
_______________________________________________
Ifthenumberlsisequal4theusermustbevery
carefulbecausethenumberofsatelliteswhichcanbe
used in position determination can decrease at any
moment and for any reason. That’s why the
additional calculations were made for both systems
384
fordifferentH
mininorderto determine thegreatest
elevation H for which the number ls of satellites
visibleat differentlatitudesinopenareaabovethis
angleisequal4(ls4)or3(ls3)(table5).
InthecaseofBeiDousystemandls4theelevation
Histhelowest(26)in
zone0–10
O
,thegreatest(33)in
zone80–90
O
.Inthecaseofls3thelowestelevationH
(32) is in zone 0−10
O
and at latitudes 50–80
O
, the
greatest (34) in zone 20–30
O
. In the case of Galileo
and ls4 the H is the lowest (23) in zone 0–10
O
, the
greatest (32) in zone 80–90
O
, and for ls3 the lowest
(29) at latitudes 0–20
O
and in zone 70–80
O
, the
greatest(35)inzone80–90
O
.
The weightedmeannumberls
mofBeiDouMEO
satellitesandGalileosatellitesvisibleabovehorizon
and the percentage of satellites visible by the
observer in open area above given angle H in all 9
latitude zones for both systems are showed in the
table6.SupplementarycalculationsweremadeforH
=5
O
,15
O
and25
O
inallthesezones.Becauseofgreater
number of satellites (BeiDou – 27, Galileo−24) the
ls
m is for China system greater than for European
systemirrespectiveoflatitude.
Additionallywecansaythatforbothsystems:
thepercentageofsatellitesvisibledecreaseswith
angle H in each zone, if this angle is equal 20
O
thispercentagedecreasestoabout60%ormore,if
itis40
O
toabout30%ormore;
at latitudes equal or greater than 70
O
the
percentage of satellites visible above H≤20
O
is
greaterthaninallotherlatitudes;
at latitudes less than 70
O
the percentage of
satellitesvisibleabove20
O
≤H≤50
O
isthegreatest
inzone30−40
O
;
becauseofaltitudeandorbitinclinationvaluesof
bothsystemsandgeometricalfigureoftheEarth
in zone 70−80
O
any BeiDou and Galileo satellite
cannot be visible by the observer above 70
O
and
80
O
respectively, in zone 80−90
O
any satellite of
bothsystemsabove60
O
.
Distribution(inpercent)ofsatellitesazimuthsin
openareaforH
min=5
O
and25
O
inall9latitudeszones
ofhemispherenorthforbothsystemsispresentedin
thetable7.Wecanresumethatforbothsystems:
foreachH
minandeachzonebothdistributionsare
almostthesame;
distribution of satellites azimuths depends on
observer’slatitudeandangleH
min;
atlatitudes0−20
O
thepercentageofsatelliteswith
azimuthsfromintervals045−135
O
and225−315
O
is
forH
min=5
O
lessthaninallotherintervals;
at latitudes30−50
O
the percentage of satellites in
interval45−90
O
andinterval270−315
O
isforboth
H
min values greater than in all other intervals
considerably;
at latitudes 50−70
O
in all 6 intervals of azimuths
45−315
O
thepercentageofsatellitesincreaseswith
H
min whereas in two other intervals (azimuth
315−045
O
)decreasessignificantly;
atlatitudes40–70
O
thepercentageofsatellites
inintervals45−90
O
and270−315
O
isforHmin=25
O
several dozen times greater than in interval
315−045
O
,
at latitudes80−90
O
the percentage of satellites in
allintervalsisforbothH
minalmostthesame.
the percentage of satellitesis almostthesamein
all 9 zones however for Galileo system for each
H≤60
O
itisgreaterthanforBeiDousystem;
atlatitudes70−80
O
thenumberofsatellitesisinall
intervalsalmostthesame,butforH
min=5
O
only.
Thepercentage ofsatellitesazimuthsindifferent
intervalsdependsonobserver’slatitude.Thegreatest
diversifications are at latitudes 30−70
O
for both
systems. That’s why the knowledge of these
distributionsareveryimportantfortheusers,inroad
transportinurbancanyoninparticular.
Table 6. Percentage of BeiDou MEO satellites and Galileo satellites visible in open area above angle (H) at different
observer’slatitudes(φ),ls
m–weightedmeannumberofsatellitesvisibleabovehorizon(H=0
O
)
__________________________________________________________________________________________________
Latitude System lsmElevationangleH[
O
]
[
O
]0 10  20  30  40  50 60  70 80
__________________________________________________________________________________________________
0−10 BeiDou 10.9 100 81.0 59.7 39.7 25.8 15.5 8.23.70.9
Galileo 9.8100 80.8 59.4 39.7 25.8 15.7 8.03.40.9
10−20 BeiDou 10.7 100 77.0 58.7 43.7 29.0 16.9 9.04.01.0
Galileo 9.6100 76.9 58.4 43.4 29.5 17.0 8.93.91.0
20–
30 BeiDou 10.0 100 78.1 61.5 46.9 34.4 21.6 11.4 3.71.3
Galileo 9.1100 78.3 61.2 46.9 34.3 21.7 11.1 4.91.2
30–40 BeiDou 9.7100 79.1 62.3 48.0 35.6 25.0 15.2 6.21.5
Galileo 8.8100 79.5 63.1 48.3 35.4 25.0 15.1 6.31.6
40
–50 BeiDou 9.9100 77.7 60.1 45.9 34.2 24.5 15.7 8.22.3
Galileo 9.0100 77.4 60.7 46.5 34.3 24.0 15.9 8.72.1
50–60 BeiDou 10.6 100 75.9 56.4 42.3 30.7 21.2 13.1 6.72.0
Galileo 9.6100 76.6 56.9 43.3 30.7 21.2 13.4 7.22.6
60
–70 BeiDou 10.9 100 77.6 60.0 40.5 27.6 17.6 9.23.00.2
Galileo 9.8100 81.6 57.4 42.0 28.7 18.4 9.73.90.4
70–80 BeiDou 11.0 100 82.9 64.5 42.5 27.7 12.4 3,10 0
Galileo 10.0 100 83.2 66.0 45.3 26.7 13.6 4.30.20
80−90 BeiDou 11.0 100 83.5 66.6 48.6 25.1 3.40 0 0
Galileo 10.0 100 83.7 67.6 50.4 29.2 5.60 0 0
__________________________________________________________________________________________________
385
Table 7. Distribution (in per cent) of BeiDou MEO satellites and Galileo satellites azimuths in open area for different
maskingelevationangles(H
min)atdifferentobserver’slatitudes(φ), lsm–weightedmeannumberofsatellitesvisibleabove
H
min
__________________________________________________________________________________________________
φ NSystem Hmin lmAzimuth[
O
]
[
O
][
O
] 0−4545−90 90−135 135−180 180−225 225–270 270−315 315–360
__________________________________________________________________________________________________
0−10 BeiDou 5 9.915.2 10.0 10.0 15.0 14.7 10.1 10.3 14.7
25 5.417.3 10.1 10.4 12.7 11.7 10.0 10.5 17.3
Galileo 5 8.914.5 10.3 9.815.1 15.3 9.810.3 14.9
25 4.816.5 11.0 10.0 12.3 12.2 9.710.8 17.5
10−20 BeiDou 5 9.514.8 11.2 10.2 14.1 13.6 10.3 11.5 14.3
25 5.518.7 10.5 10.5 10.7 10.4 9.911.0 18.3
Galileo 5 8.614.6 11.3 9.814.0 14.0 9.911.4 15.0
25 4.918.2 10.9 9.910.5 10.5 11.7 11.7 18.6
20–30 BeiDou 5 8.913.3 13.7 10.8 12.2 11.8 10.6 13.9 13.7
25 5.416.9 12.7 10.5 9.810.2 10.0 13.3 16.6
Galileo 5 8.014.1 13.2 10.6 11.8 11.8 10.6 13.8 14.1
25 4.917.0 12.3 10.2 10.2 10.3 10.0 13.2 16.8
30–40 BeiDou 5 8.79.618.0 11.1 11.4 11.2 11.0 18.1 9.8
25 5.310.4 18.2 11.0 10.0 10.6 10.6 18.7 10.5
Galileo 5 7.810.6 17.2 10.9 11.1 11.4 10.9 16.8 11.1
25 4.911.5 17.4 10.9 9.710.5 10.6 17.3 12.1
40–50 BeiDou 5 8.75.721.2 11.6 11.4 11.2 11.9 21.4 5.6
25 5.22.923.5 11.9 11.6 10.7 12.8 23.7 2.9
Galileo 5 7.96.620.8 11.4 10.9 11.3 11.6 20.4 7.0
25 4.83.823.5 11.8 10.5 11.0 12.3 23.0 4.1
50–60 BeiDou 5 9.37.418.3 12.8 11.5 11.3 13.1 17.8 7.8
25 5.10.321.4 14.9 13.3 12.6 16.3 20.8 0.4
Galileo 5 8.58.718.3 12.3 10.8 11.2 12.3 17.8 8.6
25 4.80.822.3 14.1 12.0 12.7 15.4 21.7 1.0
60–70 BeiDou 5 9.810.1 14.3 13.7 12.0 12.0 13.3 14.2 10.4
25 5.31.516.0 17.5 15.0 14.8 17.7 16.1 1.4
Galileo 5 9.010.8 14.6 12.8 11.8 12.2 12.8 14.3 10.7
25 4.92.016.8 16.1 14.6 15.1 16.4 16.6 2.4
70–80 BeiDou 5 10.0 11.3 13.1 12.9 12.7 12.4 12.7 13.1 11.8
25 6.07.713.2 14.6 14.4 14.4 14.3 13.5 7.9
Galileo 5 9.111.8 13.1 12.7 12.2 12.7 12.5 13.1 11.9
25 5.68.913.5 14.2 13.3 14.0 14.0 13.3 8.8
80–90 BeiDou 5 10.1 12.1 12.8 12.6 12.4 12.8 12.1 13.0 12.2
25 6.411.4 12.6 12.9 13.0 13.4 12.2 13.0 11.5
Galileo 5 9.212.3 12.5 12.5 12.4 13.0 12.4 12.5 12.4
25 5.912.5 11.8 13.3 12.8 13.0 13.1 11.8 11.7
__________________________________________________________________________________________________
5 GEOMETRYOFBEIDOUMEOSATELLITES
ANDGALILEOSATELLITES
Distribution(inpercent)ofGDOPcoefficientvalues
inopen areaforH
min= 5
O
and25
O
inall9latitudes
zones for both systems is presented in the table 8.
Additional calculations were made in zone 50−60
O
(latitude of Poland) for four other H
min values (0
O
,
10
O
,15
O
and20
O
).WecansaythatGDOPcoefficient
value:
depends on angle H
min and observer’s latitudes
anditsdistributionsarealmostthesameforboth
systems;
increaseswithH
mininall9zonesforbothsystems,
but the greatest values and growths are at high
latitudes;
canbelessthan2forBeiDousystemandH
min=5
O
atlatitudes0−20
O
only;
for H
min= 5
O
isalwayslessthan4 for BeiDouin
zone0−10
O
andforGalileoinzone20−40
O
;
for H
min = 5
O
for both systems is always greater
than3inzone70−80
O
andgreaterthan4inzone
80−90
O
;
forH
min=25
O
canbelessthan3forGalileoinzone
10−20
O
onlyandforBeiDouinzone60−70
O
only;
forH
min=25
O
canbeequalorgreaterthan20inall
9zonesforbothsystems;
for H
min = 25
O
and for both systems is equal at
least4orgreaterinzone70−80
O
andequal6or
greaterinzone80−90
O
.
Aswasshowedinthetable4inthecaseofGalileo
inthree latitude zones,0−10
O
,40−50
O
and50−60
O
,if
H
min = 25
O
3D position cannot be obtained always.
Whenthenumberofsatellitesvisiblebytheobserver
decreasestothreethenumberoffixwithoutposition
(Nofix)isgreaterthanzero.
Distribution (in per cent) of GDOP coefficient
values for the observer at latitudes 50–60
O
, if the
numberofvisiblesatelliteslsisknown,forH
min=25
O
and5
O
,forbothsystemsispresentedrespectivelyin
thetable9andthetable10.Wecanshowedthat:
forBeiDousystemifH
min=5
O
GDOPvalueisless
than3ifls=11andcanbelessthan3ifls=8,9or
10.Ifls=6 thiscoefficientisequalorgreaterthan
3andlessthan5;
forGalileosystemifH
min=5
O
GDOPvalueisless
than3ifls=10,canbelessthan3ifls=7,8or9.If
ls=6thiscoefficientisequalorgreaterthan3and
lessthan4;
386
for BeiDou system if H
min = 25
O
GDOP value is
lessthan4ifls=7andcanbelessthan4ifls=6 
or5.Ifls=4thiscoefficientisequalatleast8;
forGalileosystemifH
min=25
O
lscanbeequal3
(0.3 %) and then the position 3D cannot be
obtained.GDOPvalueis less than 4ifls =7 and
can be less than 4 if ls = 5 or 6. If ls = 4 this
coefficientisequalatleast5.
thereis
notadirectrelationbetweenanumberls
of satellites visible above H
min and GDOP
coefficientvalue,butinthe caseofbothsystems
wecanrealize”whenlsisgreater,GDOPcanbe
less”andviceversa“whenlsisless,GDOPcanbe
greater”.
Table 8. BeiDou MEO satellites and Galileo satellites distribution (in per cent) of GDOP coefficient values and No Fix
(withoutposition)fordifferentmaskingelevationangles(H
min)atdifferentobserver’slatitudes(φ)
__________________________________________________________________________________________________
Latitude System Hmin NoFixGDOPcoefficientvalue−w
[
O
][
O
]w<2 2≤w<3 3≤w<4 4≤w<5 5≤w<6 6≤w<8 8≤w<20 w≥20
__________________________________________________________________________________________________
0−10 BeiDou 5−0.691.3 8.1−−−−−
25−−−25.8 37.7 15.0 7.09.45.1
Galileo 5−−93.5 5.21.3−−−−
25  0.9−−17.6 27.5 5.610.1 25.5 12.8
10−20 BeiDou 5−0.486.3 12.4 0.9−−−−
25−−−16.0 41.3 14.7 8.316.9 2.8
Galileo 5−−89.7 9.90.4−−−−
25−−0.78.532.7 8.211.6 27.5 10.8
20–30 BeiDou 5−−76.1 17.4 6.5−−−−
25−−−18.7 34.4 16.8 8.213.5 8.4
Galileo 5−−69.2 30.8−−−−−
25−−−2.247.0 7.511.2 24.7 7.4
30–40 BeiDou 5−−95.8 2.71.5−−−−
25−−−11.2 44.7 36.7 1.65.60.2
Galileo 5−−54.7 45.3−−−−−
25−−−10.8 46.1 2.25.717.5 17.7
40–50 BeiDou 5−−86.4 7.85.8−−−−
25−−−24.5 27.2 28.5−14.9 4.9
Galileo 5−−51.5 47.3 1.2−−−−
25  0.1−−27.5 18.4 1.64.718.4 29.3
50–60 BeiDou 5−−70.4 27.8 1.8−−−−
25−−−13.6 39.0 22.4 0.114.7 10.2
Galileo 5−−69.6 30.1 0.3−−−−
25  0.3−−17.7 45.0 0.32.811.1 22.8
60–70 BeiDou 5−−28.1 69.3 2.6−−−−
25−−0.11.829.9 49.2 5.78.44.9
Galileo 5−−19.2 79.5 1.3−−−−
25−−−1.937.7 15.9 13.5 15.5 15.5
70–80 BeiDou 5−−−35.7 49.1 14.4 0.8−−
25−−−−8.827.1 27.0 35.5 1.6
Galileo 5−−−31.1 54.4 14.2 0.3−−
25−−−−9.423.1 24.6 41.5 1.4
80–90 BeiDou 5−−−−0.813.1 27.2 37.1 21.8
25−−−−−−10.8 60.6 28.6
Galileo 5−−−−0.611.5 26.6 39.0 22.3
25−−−−−−7.261.8 31.0
__________________________________________________________________________________________________
Table9. BeiDouMEOsatellites andGalileo satellites, distribution(in percent) ofGDOP coefficientvalues at observer’s
latitudes50–60
O
,ifthenumberofvisiblesatelliteslsisknown,Hmin=25
O
,Nofix–thepercentageoffixwithoutposition
__________________________________________________________________________________________________
SystemandsatellitesGDOPcoefficientvalue–w
ls System % 3≤w<4 4≤w<5 5≤w<6 6≤w<8 8≤w<20 w≥20
__________________________________________________________________________________________________
ls<4 BeiDou−−−−−−−
NoFix Galileo 0.3−−−−−−
4 BeiDou 24.7−−−−14.6 10.1
Galileo 36.1−−0.22.111.0 22.8
5 BeiDou 39.3 0.116.5 22.4 0.10.10.1
Galileo 47.9 3.044.0 0.10.70.1−
6 BeiDou 32.7 10.2 22.5−−−−
Galileo 13.7 12.7 1.0−−−−
7 BeiDou 3.33.3−−−−−
Galileo 2.02.0−−−−−
__________________________________________________________________________________________________
BeiDou 100 13.6 39.0 22.4 0.114.7 10.2
Galileo 100 17.7 45.0 0.32.811.7 22.8
__________________________________________________________________________________________________
387
Table 10. BeiDou MEO satellites, Galileo satellites,
distribution (in per cent) of GDOP coefficient values at
observer’s latitudes 50 – 60
O
, Hmin = 5
O
, if the number of
visiblesatelliteslsisknown
_______________________________________________
System VisibleGDOPcoefficientvalue−w
satellites
l
s % 2≤w<3 3≤w<4 4≤w<5
_______________________________________________
BeiDou 6 2.1−0.31.8
Galileo 2.0−2.0−
BeiDou 7 3.5−3.5−
Galileo 7.71.06.40.3
BeiDou 8 14.9 3.311.6−
Galileo 36.2 15.121.1−
BeiDou 9 28.1 16.811.3−
Galileo 44.5 43.80.7−
BeiDou 10 45.0 43.91.1−
Galileo 9.69.6−−
BeiDou 11 6.46.4−−
Galileo−−−−
_______________________________________________
100 70.427.81.8
100 69.630.10.3
_______________________________________________
As the longitudes of two extreme BeiDou GEO
satellitesare058.75
O
Eand160
O
E,thetrucksofsub‐
satellitepointsfor3IGSOsatellitesarecoincidedand
thelongitudeoftheintersectionpointsis118
O
E,this
system currently provides positioning data between
longitude055
O
Eto180
O
Eandfromlatitude55
O
Sto
55
O
N.ThisareaincludesChinaterritoryentirely.
6 BEIDOUANDGALILEOSTATUS
Currently(August2016)thereare20BeiDousatellites
in orbit and healthy and one with status in
commissioningand9Galileooperationalsatellites,4
with status in commissioning and one partially
unavailable. By 2020 or earlier BeiDou would
reach
fulloperationalcapability(FOC)with35satellites.In
thecaseofGalileo12nextsatellitesareplannedtobe
launchedintheyears2016−2018,thelastin2019.FOC
of this system is planned in 2020 (European GNSS
Service Centre, www.gpsworld.com,
www.gsc.europa.eu).
7 CONCLUSIONS
Full Operational Capability (FOC)
of BeiDou
system will made China the third nation in
possession of independent, global navigation
system following the United States and Russia.
FOC of Galileo will made the first in history
international institution (European Union) in
possessionofglobalsystem.
BeiDouMEOconstellationwith27 fully
operationalsatelliteswill
provideglobalcoverage
and the possibility of user’s 3D position
determination at any moment and any point on
theEarthaswellasinthecasewhenthesatellites
arevisiblebytheuserbelow25
O
only.Inthecase
ofGalileo24satellitesconstellationthispossibility
will be the same except for zone 0−10
O
and
latitudes40−60
O
.
The percentage of satellites visible in open area
above given angle and the distributions of
satellitesazimuthsfordifferentelevationangleare
atdifferentlatitudesalmostthesame.
The number of BeiDou MEO satellites (27) is
greater than the number of Galileo satellites of
nominal constellation (24) but
orbit altitude of
European system (23,222 km) is greater than in
China system (21,500 km). That’s why the
distributions of GDOP coefficient values is for
both systems at different latitudes almost the
same.
BeiDousystemwillmeetthedemandsofChina’s
national security, economic development. One of
themost
importantaimsofGalileoistoprovidean
indigenous alternative high precision positioning
system upon which European nations can rely.
Galileo is intended to provide horizontal and
vertical position measurements within one‐metre
precision (95%). Both these new SNSs will be
committedtoprovidingstable,reliableandquality
satellitenavigationservices
forglobalusers.
Whereas the constellation of 27 BeiDou MEO
satellites will provide global coverage at any
moment, the constellation of 3 IGSO and 5 GEO
satelliteswill can beusedin limited area only. It
means that the advantages of D2 NAV message,
integrity information in particular will
be
accessible to users in China and the Asia−Pacific
regiononly.
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BeitzJ.W.2016.EngineeringSatellite‐BasedNavigationand
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www.beidou.gov.cn
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