11
1 INTRODUCTION
An uninterrupted information about the ship’s
positionisoneofthemostimportantelementsofthe
safetyofnavigationintheseatransportinrestricted
and coastal areas, recommended by International
Maritime Organization – IMO (imo.org). The
information about userʹs position is obtained
generally from specialized electronic posit
ion–fixing
systems, in particular, satellite navigation systems
(SNS) as the American GPS system (Januszewski J.
2010,Hofmann‐WellenhofB.etal.2008,Kaplan,E.D.
& Hegarty, C.J. 2006). Nowadays (March 2014) this
system is fully operational with very robust
constellation31satellites(www.gpsworld.com).
FormarineandnavigationusersGPSpositionfix
canbeobtainedin2Dor3Dmode,tha
tincludesonly
horizontal coordinates (no GPS elevation) or
horizontal coordinatesplus elevation and requires a
minimum at three or four visible satellites, respec‐
tively.Inmode2Dtheusermustmanuallyintroduce
therealvalue ofantenna height(abovegeoide –sea
level).
Information on several hundred GPS receivers
designed for ma
rine and/or navigation users and
positionaccuracywhichcanbeobtainedcanbefound
inannualreceiversurveypublishedinGPSWorld.
Oneachship’sbridgeoneGPSstationaryreceiver
isinstalledat leastbut on many ships there are
twoorevenmoreGPSreceivers.Asinthema
jorcases
the coordinates of the position obtained from these
receiversdifferthefollowingquestionscanbeposed:
whatisthecauseofthisdivergence?
Nominal and Real Accuracy of the GPS Position
Indicated by Different Maritime Receivers in
Different Modes
J
.Januszewski
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT:Nowadaysontheship’sbridgetwoorevenmoreGPSreceiversareinstalled.Asinthemajorcases
thecoordinatesofthepositionobtainedfromthesereceiversdifferthefollowingquestionscanbeposed–what
isthecauseofthisdivergence,whichreceiverinthefirstmustbeta
kenintoaccountetc.Basedoninformation
publishedinannualGPSandGNSSreceiversurveyitwasestimatedthepercentageofGPSreceiversdesigned
formarineand/ornavigationusers.ThemeasurementsofGPSpositionbasedonthefourdifferentstationary
GPSreceiverswererealizedinthelaboratoryofGdyni
aMaritimeUniversityinPolandinthesummer2012.
Thecoordinatesofthepositionofallthesereceiverswereregisteredatthesametime.Themeasurementsin
mode3Dweremadefordifferentinputdata,thesameforallreceivers.Thedistancesbetweentheindividual
unit’s antenna were considered also. Next measurements in mode 3D also were realized on two ships in
differentEuropeanports.Additionalmeasurementswerema
deinmode2Dwiththreereceiversfordifferent
their’santennaheights.Theresults showedthattheGPSpositionaccuracydependsonthetypeofthereceiver
anditstechnicalparameterspart
icularly.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 1
March 2014
DOI:10.12716/1001.08.01.01
12
which receiver in the first must be taken into
accountandwhy?
which input data has the biggest influence on
position’saccuracy?
2 GPSRECEIVERSURVEY
The most known and at the same time the most
comprehensive GPS and GNSS receiver survey is
published each January
in GPS World monthly
(gpsworld.com). The survey 2014 provides the
informationon380receiversfrom 47manufacturers.
Thesereceiversaredesignedfor15differentkindsof
user environment and applications. In the table 1 it
was showed the number of receivers for marine,
navigation and both marine and navigation. More
than 80% of these receivers can be used in marine
or/andnavigationapplications.
About each receiver the reader can find
information on 19 parameters,among them
informationconcerningposition:
autonomous(code),
real‐timedifferential(code),
real‐timekinematic,
post‐processed,or
note: na – not applicable
(in the case of some
models of Hemisphere, Rockwell Collins and
Trimblemanufacturers),or
lack of information, e.g. all models Furuno
manufacturer,or
note: data available upon request (e.g. Interstate
ElectronicsCorporation).
Table1.ThenumberofGPSreceivers designedformarine
andnavigationuserenvironmentandapplications.
_______________________________________________
UserNumberofreceivers Percentage
_______________________________________________
Marine102.6
Navigation5313.9
Marineandnavigation24664.7
Total30981.2
_______________________________________________
Dependingonthemanufacturerandthereceiverit
canbegiventhefirstvalueamongmentionedabove,
the first two, three or the most frequently cases the
firstfour.
For marine and land navigation users with the
receivers L1, C/A, the most important is the first
magnitude, position accuracy,
and in the case of
DGPS receiver second also. The first magnitude is
givenalwaysinmeters,asprecisevalue(e.g.2.5),as
value bracket (e.g. 2 –3) or as approximated value
(e.g.≈5).
Somemanufacturersaddinformationaboutgiven
values,e.g.CEP(CircularErrorProbable),RMS(Root
MeanSquare) or
confidence level in percentage, e.g.
95%,butmostreceiversiswithout.Inallthesecases
we must suppose that given meters concern
horizontal accuracy with 95% confidence level. The
greatest (1.2 m) and the smallest (10 m) accuracy
provide the models OEM (NovAtel manufacturer)
and the models SIRP (CSR manufacturer),
respectively.Positionautonomous(code)information
about accuracy for several dozen selected receivers
designed for marine and/or navigation users is
showedinthetable2(gpsworld.com).
3 GPSPOSITIONINDIFFERENTMODES
TheGPSpositionfixcanbeobtainedinmode2Dor
3D,thechoicemadebytheuserwaspossible
firstof
allinthecaseofprofessionalGPSreceiversproduced
in 1990s when the number of fully operational
satellites was 24 sometimes one or two more. With
then constellation the damage or failure of two and
sometimesone satelliteonly can signify the increase
of DOP coefficient value considerable.
At that time
thesolutionwasthechoiceofmode2D.
ThecurrentvaluesofHDOP,VDOP(inmode3D
only) coefficients were indicated by almost all
receivers,PDOPorGDOPcoefficientsrarely.
AsnowadaysthenumberofGPSsatellitesis30or
31alwaysthenumberofsatellitesvisibleby
receiver’s
antennaabovemaskingangleH
min=5
O
oreven10
O
is
atanymomentandatanypointontheEarthgreater
than minimal number 4 considerably. Therefore the
currently produced GPS receivers (e.g. MX 512
Simrad)determinepositionin3Dmodeonly.
Inthe case of some receivers, as Furuno GP33, if
the number of satellites which can be
used for
position determination is for any reason equal 3,
position is obtained in mode 2D automatically, but
the user cannot introduce the real value of antenna
height.ThesereceiversindicateDOPvaluewhichcan
berecognizedasPDOPorHDOPifthepositionwas
determinedinmode3Dor2D
respectively.
4 GPSPOSITIONACCURACY
The accuracy of the user’s position solution
determined by SNS is ultimately expressed as the
productofageometryfactorandapseudorangeerror
factor(Kaplan,E.D.&Hegarty,C.J.2006):
(errorinSNSsolution)=(geometryfactor)x
(pseudorangeerrorfactor) (1)
Asthe
errorsolutioncanbeexpressedbyM –the
standard deviation of the positioning accuracy,
geometryfactorbythe dilution of precision
(DOP) coefficient and pseudorange error factor by
σ
UERE (UERE – User Equivalent Range Error), these
rela‐tioncanbedefinedas:
M
=DOP∙σUERE (2)
Ifwecanobtainallfourcoordinatesoftheobser‐
ver’s position (latitude, longitude, altitude above
givenellipsoid,time–φ,λ,h,t),factorDOPisexpres‐
sed by GDOP (Geometric Dilution of Precision)
coefficient,ifwewantobtainhorizontalcoordina‐tes,
only, geometry factor DOP is expressed by HDOP
(Horizontal Dilution of Precision) coefficient. In this
situation the horizontalaccuracy with 95%
confidencelevel
M
%95
,
canbeapproximatedby:
13
M
%95
,
≈2∙HDOP∙σUERE (3)
Specializing the equation giving the functional
relationship between the errors in the pseudorange
values and the induced errors in the computedposi
tionandtimebiasfortheverticaldimensionwecan
saythatthe95%pointforthedistributionoftheho‐
rizontalerror (2б) can be estimated by the doubled
productofHDOPcoefficientandtheuserequiva‐lent
rangeerror(б
UERE).
Table2. Position autonomous (code) information about
position accuracy of selected receivers for marine (M)
and/ornavigation(N)users.
_______________________________________________
ManufacturermodelUser Value[m]
_______________________________________________
AltusPositioningSystems M,N 1.3
(APS)
Ashtech/Boards&Sensors M, N 3
(MB800Board)
BasebandTechnologies,Inc. M,N≈5
(BTI‐2800LP)
CSRN10
(GSD4e)
FetchRadioFrequencySystem M,N 3CEP
Corporation(FM11)
GlobalTopTechnologyM,N withoutaid3
(Gmm‐u2p) (50%CEP)
IF
ENGmbHN≈10(95%)
(SX‐NSR)
JacksonLabsTechnologies,Inc. M,N <2RMS
(SAASMCSAS)
JAVADGNSSM,N <2
(TRIUMPH‐1)
LeicaGeosystemsAGM,N 2−3
(VivaGS10)
NovAtelM,N 1.2
(OEM615)
NVSTechnologiesAGM,N RMS:<1.5
(NV08C‐CSM)
ORCATechnologies,LLC
Position <990%
(GS‐101)
RockwellCollins M,N <4CEP
(MPE‐S)
Septentrio M,N 1.3(1s)
(AsteRx‐mOEM)
SpectrumInstruments M2.5
(TM‐4MR)
SurreySatelliteTechnology N<10
(SGR‐10)
THALES–AvionicsDivision M,N <5(95%)
(GNSS1000C)
Topcon M
2−3
(MR‐1)
Trimble M,N 1−5
(BD920GNSSReceiver)
u‐blox M,N 2CEP
(UBX‐M8030‐KA/KT)
_______________________________________________
GlobalGPScivilserviceperformancecommitment
met continuously since December 1993. Root Mean
Square(RMS)Signal‐in‐Space(SiS)UserRangeError
(URE)was equal1.6 metresin2001,1.1 in2006 and
finally0.8in2013(Gruber,B.2012),MartinH.2013).
Signal in Space User Range Error is the difference
between a GPS sat
ellite’s navigation data (position
andclock)andthetruthprojectedonthelineofsight
totheuser.
TheHDOP coefficient value depends on the SNS
geometry, the user’s coordinates, time and the
number of satellites fully operational in given
moment, in particular. At the beginning of XXI
century for GPS system thi
s value was about 1.5, at
present(March2014)isabout1.0becauseveryrobust
GPS constellation consists of 31 space vehicles
currentlyinoperation(www.navcen.uscg.gov).
5 THEMEASUREMENTSOFGPSPOSITIONIN
MODE3D
The measurements of GPS position based on
stationaryreceiverswererealizedinthelaboratory of
University and on two ships in different ports in
Europe.
5.1 Themeasurementsinthelaboratory
The measurements of GPS positions ba
sed on four
different stationary receivers were realized in the
laboratoryofGdyniaMaritimeUniversityinGdynia
inPolandinthesummer2012.Thesereceiverswere:
MX 200 Professional Navigator, ma
nufacturer
Magnavox,calledlaterMX200,
ap Mk10 Professional, manufacturer Leica, called
laterMK10,
MX512SimradNavigationSystem,manufactu‐rer
Simrad,calledlaterSimrad,
NR–N124 Marine Navigator, manufacturer MAN
Technologies,calledlaterMAN.
The three coordinates of positions (latitude,
longit
ude,heightaboveellipsoidWGS–84)ofallfour
receivers,thepositions ofantennas ofthesesreceivers
inreality,obtainedfromgeodeticmeasurements(Real
Time Kinematic – RTK) and production year are
presented in the table 3. The antennas of these
receivers were installed on the masts on the roof of
theuniversitybuilding.Allpositionsweremea
sured
andpresentedinWGS–84datum.
Themeasurements weremade for differentinput
data,thesameforallfourreceivers:
two different masking elevation angles H
min, 5
O
and 25
O
, the most frequently used angle in the
receiversinopenarea(e.g.oceannavigation)and
typical angle for restricted area (e.g. coastal
navigation),respectively,
two different datums, WGS–84 and Timbolaia
1948,datumofficiallyappliedforGPSsystemand
thedatumforwhichthepositionoffsetrelativeto
WGS–84issignificant,respectively.ForTimbolaia
datum(ellipsoidEverest)thi
soffsetisS0
O
00.2696’;
W0
O
00.81’.
The days of measurements, the registration
duration and the number of positions registered by
each receiver in mode 3D for different datums and
angles H
min are given in the table 4. In each series
duringabout24hoursselecteddata:
– three coordinates of position: latitude, longitude
andheight(aboveselectedellipsoid),
– HorizontalDilutionofPrecisionHDOPcoefficient,
– thenumberof satellitesls usedin the receiver in
positioncalculation
14
Table3.Themeasurementsinthelaboratory–thecoordinatesoftheGPSreceiversinstalledinGdyniaMaritimeUniversity
inPoland(RTKposition),datumWGS–84.
__________________________________________________________________________________________________
ReceiverCoordinates
__________________________________________________________________________________________________
Model ProductionyearLatitudeLongitudeHeightaboveellipsoidWGS–84[m]
__________________________________________________________________________________________________
MX2001991 54
O
31’5.04922”N 018
O
33’16.36049”E 57.48
Mk10 1995 54
O
31’5.04918”N 018
O
33’16.39215”E 57.48
Simrad2011 54
O
31’5.18485”N 018
O
33’16.50982”E 54.21
MAN200154
O
31’5.07664”N 018
O
33’16.38120”E54.65
__________________________________________________________________________________________________
Table4. The measurements in the laboratory – the days of measurements, the registration duration and the number of
positionsfordifferentreceivers,datumsandanglesH
min.
__________________________________________________________________________________________________
Hmin[
O
] Datum DayReceiverStartofmeasurements Duration Numberofpositions
__________________________________________________________________________________________________
5WGS84 12.07.2012 MX200 10:03:03 24h36min39513
Mk1010:02:29 24h19min8686
Simrad 10:04:26 24h34min8851
MAN10:01:4024h37min8868
__________________________________________________________________________________________________
25WGS84 31.07.2012 MX200 11:50:23 23h02min36879
Mk1011:52:27 23h01min8247
Simrad 11:51:16 23h24min8429
MAN11:51:0123h41min8506
__________________________________________________________________________________________________
5Timbolaia 01.08.2012 MX200 11:33:56 24h05min38576
1948 Mk1011:35:17 24h01min8644
Simrad 11:50:56 23h46min8560
MAN11:52:5123h43min8545
__________________________________________________________________________________________________
were registered by PC with sampling int
erval of 10
second(Mk10,SimradandMAN)and2or3second
(MX 200). If any data has been incomplete, this
measurementwas rejected.That’s why forthe given
periodofthemeasurementsthenumberofpositions
obtainedfromdifferentreceiversisnotthesame.
In the case of all receivers if we change the
ma
sking angle the coordinates of the position
determinedforthenewvalueofthisanglesignalized
on the screen and registered by PC are the same.
MeanwhileifwechangethedatumfromWGS–84for
Timbolaia the coordinates on the screen can differ
from coordinated registered. In the case of MX 200,
MK10andMANreceiversthecoordinatessignalized
onthescreenaredeterminedin“t
henew”Timbolaia
datum while registered by PC are still in “the old”
WGS–84 datum. Only in Simrad receiver all
coordinatesareinTimbolaiadatumineachcase.
InMX200,Mk10andSimradreceiversthevertica
l
separationbetweenthegeoidandreferenceellipsoid
WGS–84,calledgeoidundulation, was+34.3 m(the
value for Gdansk Bay). In these three receivers in
mode3Dthecurrentvalueofthegeoidalheight(the
receiver’s antenna height above geoide), and no
ellipsoidalheight,issignalizedonthescreen,whilein
MAN receiver the ellipsoidal height is signalized
only.
Thetota
lnumberofpositionsregisteredbyallfour
receiverswas192314:MX200–114968,Mk10–25577,
Simrad–25840,MAN–25929.
For each series of measurements and for each
receiverwerecalculated:
three coordinates (lat
itude, longitude and height
abovegivenellipsoid)ofmeanposition,
2D–twodimensional(horizontal)distancefrom
the known position of the receiver (RTK) to the
meanreceiverposition,
3D– threedimensional distance from the known
positionofthereceiver(RTK)tothemea
nreceiver
position,
latitudeerrorσ
φandlongitudeerrorσλ,
heighterrorσ
H,
horizontalpositionerrorσ
φ,λ,(σ2Dwithconfidence
level95%),
three dimensional position errorσ
φ,λ,H (σ3D with
confidencelevel95%),
meanvalueofHDOPcoefficient.
Positionfix in mode“3D” can be calculated only
from these satellites, which elevation angle in
observer’sreceiveratthemomentofmeasurementis
higher than masking elevation angle H
min. At any
momenttheuser’sreceiverneedstoseeatleastfour
satellites.
5.2 Themeasurementsontheships
The measurements were realized on the ship DP3
EddaFides(thefirstfloatinghotelandservicevessel
to be built exclusively for the offshore oil and gas
industry(www.marinetraffic.com)equippedwith:
two identical SAAB R4 GPS/DGPS Navigation
System (www.saab
group.com) receivers, called
laterSAABAandB,portHaugesundinNorway,
November2011,adozenorsoone‐hoursessions,
This receiver L1, C/A consists of 12 channels (2
dedicated to SBAS and DGPS by SBAS or
externallyRTCMcorrections).SAABR4isreceiver
a
pproved for SOLAS and any other precision
navigation application. The actual distance
betweenreceiver’santennaswas1.5m;
two identical Kongsberg DPS 232 (GPS L1/L2 +
GLONASS L1/L2 + SBAS) receivers, called later
Konsgberg A and B, in the region of the port
CastelloninSpain,NovemberandDecember2011,
adozenorsoone‐hoursessions.DPS232isanall‐
in‐one DP new generation GNSS‐ba
sed position
reference system, which takes positioning to the
nextlevelforsecureandrobustsolutionsexerting
GPS and GLONASS. SBAS or DGPS horizontal
user’s position accuracy is less than 1 m (95%)
15
(www.km.kongberg.com). The actual distance
betweenreceiver’santennaswas7.0m.
Ineachseriesofthemeasurementsthegeographic
coordinates of two receivers were registered at the
sametimewithsamplingintervalof60second,mode
3D, datum WGS–84 for different input data
introduced in receiver A or in receiver B or both
receivers.
Thenextmeasurementsofpositionsba
sedontwo
GPS receivers installed on the generalcargo ship
SMT Bontrup (length overall 200.5 m) were realized
inthreeEuropeanportsin2012year,ineachporttwo
onehoursessions.Ineachcaseastherealpositionit
was assumed the position coordinates red from the
chart which datum was WG
S–84. These receivers
were Furuno GPS Navigator GP–90, called later
FurunoandSAABR4GPS/DGPSNavigationSystem,
usedasGPSonly,calledlaterSAAB.Thecoordinates
ofthereceivers wereregisteredatthesametimewith
samplingintervalof60second,modewas3D,datum
WG
S–84andmaskingangleH
min=5
O
.
6 THEMEASUREMENTSOFGPSPOSITIONIN
MODE2D
The measurements of GPS position based on
stationaryreceiverswererealizedinthelaboratory of
Universityin2005year(JanuszewskiJ.2005)and2014
year.Thesereceiverswere:
MLRFX412,manufacturerMLRElectronic,cal‐led
laterMLR,and
two receivers MX 200 and MK10 used in the
measurementsinmode“3D”(p.3).
In each receiverma
sking elevation angle was 5
O
,
datumWGS−84.Ineachyearthemeasurementswere
realizedin tens series, the period ofeach series was
one hour. The data, latitude and longitude, for real
valueofantennaheightH
ant=27m,thesameforall
threereceivers,andfivedifferentvaluesH
ant=0
m,50
m, 100 m, 200 m and 500 m, were registered by
personalcomputer(PC)withdifferentintervalof1or
2seconds.
7 THERESULTS
The distances between the two positions on the
ellipsoid WGS–84 were calculated from the relation
(AdmiraltyManualofNavigation2008):
1’=1852.22–9.32cos2φ
m (4)
whereφ
m=middlelatitudeoftwopositions.
Table5.Themeasurementsinthelaboratoryinmod
e3D–thecoordinatesofthemeanposition,themeanellipsoidalheight
andthedifferenceΔHbetweenmeanellipsoidalheightandRTK heightfordifferentreceivers,anglesH minanddatums.
__________________________________________________________________________________________________
ReceiverDatumHmin[
O
] MeanpositionMeanheight[m] ΔH[m]
LatitudeLongitude
__________________________________________________________________________________________________
MX200 WGS845 54
O
31’5.07213”N 018
O
33’16.39668”E 54.84 – 2.64
25 54
O
31’5.06263”N 018
O
33’16.40463”E 57.28 – 0.20
Timbolaia1948 554
O
30’48.88686”N 018
O
32’27.80670”E56.62–0.86
__________________________________________________________________________________________________
Mk10 WGS845 54
O
31’5.10862”N 018
O
33’16.39753”E 60.36 +2.88
25 54
O
31’5.13099”N 018
O
33’16.40908”E 62.23 +4.75
Timbolaia1948 554
O
30’48.94974”N 018
O
32’27.75545”E61.92+4.44
__________________________________________________________________________________________________
Simrad WGS845 54
O
31’5.21343”N 018
O
33’16.52619”E 53.75 – 0.46
25 54
O
31’5.21831”N 018
O
33’16.52328”E 54.31 +0.10
Timbolaia1948 554
O
30’49.03898”N 018
O
32’27.92994”E54.210
__________________________________________________________________________________________________
MANWGS845 54
O
31’5.08449”N 018
O
33’16.41743”E 52.09 – 2.56
25 54
O
31’5.10673”N 018
O
33’16.42334”E 54.12 – 0.53
Timbolaia1948 554
O
30’48.91694”N 018
O
32’27.82025”E53.95–0.70
__________________________________________________________________________________________________
Table6.Themeasurementsinthelaboratoryinmode3D–thedistances[m]betweenRTKpositionsandbetweenreceiver‘s
antennasforall6pairsofreceivers.
__________________________________________________________________________________________________
ReceiverMXMk10SimradMAN
RTK antenna RTK antenna RTK antenna RTK antenna
__________________________________________________________________________________________________
MX–– 0.57 0.504.98 4.790.93 0.90
Mk10 0.57 0.50–– 4.70 4.920.87 0.85
Simrad 4.98 4.794.70 4.92–– 3.96 4.13
MAN0.93 0.900.87 0.853.96 4.13––
__________________________________________________________________________________________________
Table7.Themeasurementsinthelaboratoryinmode3D–thedistancedbetweenRTKpositionandmeanpositionofthe
receiverandthebearingαbetweenthemfromRTKpositionfordifferentreceivers,anglesH
minanddatums.
__________________________________________________________________________________________________
DatumHmin[
O
]MX200MK10SimradMAN
_______________________________________________________________________
d[m]α[
O
] d[m]α[
O
] d[m]α[
O
] d[m]α[
O
]
__________________________________________________________________________________________________
WGS84 5 0.86 421.84 30.92 160.694 69
25 0.89 622.55 831.06 770.862 61
Timbolaia1948 51004.56 240 1004.89 240 1004.72 240 1003.46 240
__________________________________________________________________________________________________
16
7.1 Themeasurementsinthelaboratoryinmode3D
The coordinates of the mean position, the mean
ellipsoidalheightandthedifferenceΔHbetweenthe
mean height and RTK height for all four receivers,
differentanglesH
minanddatumsarepresentedinthe
table 5. For Mk 10 the mean height is greater than
RTK height considerably (almost 5 m), for MX 200
andMANthemeanheightisless(–2.78m)thanRTK
height for all H
min and datums, and for Simrad the
differenceΔHis the least, itsabsolute value doesn’t
exceed0.5m.
ThedistancesbetweenRTKpositionsandbetween
receiver‘s antennas for all 6 pairs of receivers are
showedinthe table 6.After the comparison of RTK
distance with the actual antennas distance for each
pa
ir we can say that the smallest and the greatest
differenceΔDof these distances is in the case of
pair Mk10 & MAN receivers (2 cm) and of the pair
MK10 & Simrad receivers (22 cm) respectively. The
differenceΔD doesn’t exceed 13% of the bigger
distancethatti
me.
The distance d between RTK position and mean
position of the receiver and the bearingαbetween
themfromRTKpositionfordifferentreceivers,angles
H
min and datums are presented in the table 7. For
datum WGS–84 and for all receivers because of
smaller number of satellites used in position
calculationthedistancedisforH
min=25
O
greaterthan
H
min = 5
O
but this increase is little. For datum
Timbolaia for all receivers distance d increases
considerably, until almost 1005 m. It’s because the
positionoffsetrelativeisforthisdatumsignificant.
The minimal ls
min and maximal lsmax number of
satellitesusedinthepositioncalculationfordifferent
anglesH
min,datumsandreceiversareshowedinthe
table 8. For all receivers the numbers ls
min and lsmax
dependonthenumberofreceiver’schannelslc.Inthe
caseMX200andMk10receiversaslc=6thenumber
ls
max is for Hmin = 5
O
and independently of datum
equal 6 only, it means that the number ls
max is less
than the number of satellites visible by the antenna
considerably.ForthesamereceiversifH
min=25
O
the
numberls
maxisthesame(6)butlsmindecreasesupto3,
it means that the position was determined in mode
2D.ForSimradandMANreceiversthenumberls
max
is for H
min = 5
O
equal the number lc, 10 and 12
respectively. For these receivers the number ls
min, 8
and7,respectively,isgreaterthanthenumberls
max(6)
forMX200andMk10receivers.
Table8.Themeasurementsinthelaboratory–minimallsmin
andmaximalls
maxnumberofsatellitesusedintheposition
calculation for different angles H
min and datums and for
differentreceivers.
_______________________________________________
WGS84Timbolaia1948
ReceiverH
min=5
O 
Hmin=25
O
Hmin=5
O
ls
min lsmax lsmin lsmax lsmin lsmax
_______________________________________________
MX200 5 6 3 6 5 6
Mk10 4 6 3 6 4 6
Simrad 8 10 4 8 6 10
MAN7 12  4 8 8 12
_______________________________________________
The errorsσ
φ,σλ,σ2D,σH,σ3D and HDOP
coefficient value for different receivers, angles H
min
and datums are showed in the table 9. We can say
that:
foreachreceiverandindependentlyofdatumthe
errorsσ
φ,σλ,σHareforHmin
=25
O
greaterthanfor
H
min=5
O
,
forall3seriesofmeasurementsthe errorsσ
φ,σλ,
σ
HareforSimradandMANreceiverssmallerthan
for MX 200 and MK10 receivers considerably,
twiceorevenmore,
forall3seriesofmeasurementstheerrorσ
Hisfor
all receivers greater thanσ
φ as well asσλ. This
difference is particularly evident if H
min = 25
O
, at
least twice. It’s because the number of satellites
used in position calculation is that time less
considerably,
theerrorσ
2D(95%)isforallreceiverslessthan10
m,alsoforangleH
min=25
O
,
ifH
min=5
O
,independentlyofdatum,theerrorσ3D
(95%)isthesmallestforSimradreceiver,ifH
min=
25
O
thiserroristhesmallestforMANreceiver.It’s
becauseofthegreaternumberofsatellitesusedin
positioncalculation,MAN–12,Simrad–10only,
if H
min = 5
O
, independently of datum, HDOP
coefficientvalueisforSimradandMANreceivers
lessthanforMX200andMK10receivers,ifH
min=
25
O
this coefficient is almost the same for all
receivers.It’sbecause forthisanglethenumberof
satelliteswhichcanbeusedforcalculateHDOPis
forallreceiversalmostthesame(6or8)whilefor
H
min=5
O
thisnumberisforMAN(12)andSimrad
(10)greaterthanfortwoothers(6)considerably.
7.2 Themeasurementsontheshipsinmode3D
The latitude errorσ
φ, longitude errorσλ, horizontal
positionerrorσ
2D(95%)andthedistanceDABbetween
mean positions of two SAAB receivers for different
inputdata(6one‐hoursessions)andtwoKongsberg
receivers for different daytimes and the
measurements conditions (4 one‐hour sessions) are
showedinthetable10andtable11respectively. We
canconcludethat:
inthe caseof two identical receivers, errorσ
2D is
not the same, but the difference is few per cent
only,
the errorσ
2D of position determined 23 h 56 min
laterthanthefirstpositionwiththesamesatellite
constellation is not the same because the
measurements conditions (signal in space in
particular)changewithtime,
for different daytimes and the measurements
conditions the position’s accuracy is almost the
same,about1morless,
if ma
sking angle of the receiver increases few
times,allerrorsincreasesconsiderablyalso,
the distance between mean positions of two
identical SAAB receivers and two identical
Kongsbergreceivers(D
AB)isnotgreaterthan4.7 m
and2.3m,respectively.
17
Table9. The measurements in the laboratory – the errorsσφ,σλ,σ2D,σH,σ3D and HDOP coefficient value for different
receivers,anglesH
minanddatums.
__________________________________________________________________________________________________
Hmin[
O
] Datum Receiverσφ[m] σλ[m] σ2D[m] σ2D(95%)[m] σH[m] σ3D(95%)[m] HDOP
__________________________________________________________________________________________________
5WGS84 MX200 1.74 1.07 2.04 4.08 3.43 7.98 1.74
Mk102.51 1.88 3.14 6.28 3.51 9.42 1.27
Simrad 0.60 0.45 0.75 1.50 0.81 2.43 0.92
MAN0.71 0.44 0.83 1.66 2.00 4.33 0.89
25WGS84 MX200 4.03 1.20 4.20 8.40 9.23 20.29 2.04
Mk103.43 2.36 4.16 8.32 8.09 18.20 2.01
Simrad 1.71 0.74 1.86 3.72 3.52 7.96 2.00
MAN
1.66 0.70 1.80 3.60 3.22 7.38 2.06
5Timbolaia MX200 1.87 1.34 2.30 4.60 3.81 8.90 1.73
948 Mk103.25 2.71 4.23 8.46 5.52 13.91 1.31
Simrad 0.59 0.52 0.79 1.58 1.21 2.89 0.92
MAN
0.72 0.68 0.99 1.982.03 4.520.89
__________________________________________________________________________________________________
Table10.ThemeasurementsontheshipDP3EddaFides–latitudeerrorσφ,longitudeerrorσλ,horizontalpositionerrorσ2D
(95%),distanceD
ABbetweenmeanpositionsoftwoSAABR4GPS/DGPSreceiversfordifferentinputdata.
__________________________________________________________________________________________________
No InputdataReceiverAReceiverBDAB[m]
ReceiverA ReceiverBσ
φ[m] σλ[m]σ2D[m](95%)σφ[m]σλ[m]σ2D[m](95%)
__________________________________________________________________________________________________
1 GPS/SBAS, GPS/SBAS,Hmin=5
O
 0.17 0.19 0.510.22 0.14 0.52 0.75
2 H
min=5
O
23h56minlaterthan 0.17 0.19 0.510.17 0.14 0.44 0.60
themeasurements
number1,thesame
satelliteconstellation
3 GPS/SBAS, GPS/SBAS,H
min=20
O
 0.18 0.15 0.471.72 0.62 3.66 1.02
H
min=5
O
4 GPS/SBAS,H
min=5
O
,differentGPS 0.52 0.48 1.421.48 0.60 3.19 4.64
satelliteconstellationforAandB
5 GPS/SBAS, GPS/DGPS,H
min=5
O
 0.15 0.32 0.710.27 0.16 0.63 1.20
H
min=5
O
6 GPS/SBAS, GPSonly,H
min=5
O
0.21 0.27 0.681.45 1.38 4.00 1.88
 H
min=5
O
__________________________________________________________________________________________________
Table11.ThemeasurementsontheshipDP3EddaFides–latitudeerrorσφ,longitudeerrorσλ,horizontalpositionerrorσ2D
(95%), distance D
AB between mean positions of two Kongsberg DPS 232 receivers for different daytimes and the
measurementsconditions.
__________________________________________________________________________________________________
No MeasurementsconditionsReceiverAReceiverBDAB[m]
ReceiverA
ReceiverBσφ[m]σλ[m]σ2D[m](95%)σφ[m]σλ[m]σ2D[m](95%)
__________________________________________________________________________________________________
1 GPS/GLONASS,sunset 0.25 0.17 0.600.33 0.21 0.78 0.16
2 GPS/GLONASS,sunrise 0.37 0.31 0.970.24 0.48 1.07 0.56
3 GPS/GLONASS,trans‐shipment 0.30 0.19 0.710.24 0.30 0.77 2.21
4 changeofGPSandGLONASSsatellites 2.16 2.97 7.340.37 3.23 6.55 1.69
usedinbothreceiversinpositioncalcu
lation
__________________________________________________________________________________________________
Table12.ThemeasurementsontheshipSMTBontrup–latitudeerrorσφ,longitudeerrorσλ,horizontalpositionerrorσ2D
(95%),distanceDbetweenmeanpositionandrealposition,maximaldistancebetweenGPSpositionandrealpositionfor
differentreceiversindifferentdaysandports.
__________________________________________________________________________________________________
PortDayReceiverσφ[m] σλ[m] σ2D[m](95%) D[m]Dmax[m]
__________________________________________________________________________________________________
Amsterdam 22.02.2012 Furuno 1.25 2.12 4.90 8.17 13.05
(Netherlands) Saab1.48 2.36 5.58 7.50 13.00
23.02.2012 Furuno 1.37 1.79 4.50 6.78 11.34
Saab1.60 1.96 4.928.85 16.67
__________________________________________________________________________________________________
Antwerp21.01.2012 Furuno 1.98 1.84 5.40 5.60 10.98
(Belgium) Saab1.63 1.46 4.36 7.88 11.58
02.03.2012 Furuno 1.63 2.44 5.86 4.18 9.23
Saab1.28 1.87 4.544.98 9.83
__________________________________________________________________________________________________
Bremanger01.01.2012 Furuno 1.80 2.54 6.22 7.19 15.17
(Norway) Saab1.35 1.60 4.16 7.30 13.14
18.02.2012 Furuno 1.89 2.30 5.96 5.53 13.53
Saab1.35 2.26 5.267.66 13.68
__________________________________________________________________________________________________
18
Table13.GPSSystem,position“2D”;meandifferencesbetweenmaximumandminimumvaluesoflatitudeandlongitude,
respectivelyΔφandΔλ[m], horizontal position error M with 95% confidence level [m] for different receiver’s antenna
heightsH
antandfordifferentyearsofmeasurementsinGdynia.
__________________________________________________________________________________________________
Hant[m] YearMX 200 MLRMk10

Δφ Δλ MΔφ Δλ MΔφ Δλ M
__________________________________________________________________________________________________
0200519.5 16.8 9.618.5 10.6 20.033.5 20.8 11.8

2014 11.1 6.26.110.4 6.36.142.4 18.7 11.3
27
200514.4 10.5 3.818.5 10.5 19.69.911.1 4.8

20146.3 3.9 2.98.55.8 3.69.67.3 3.9
50
200536.5 22.8 12.418.6 10.7 18.634.5 18.6 11.8

201413.9 2.89.012.6 7.57.960.7 58.3 22.6
100
2005103.0 58.4 32.692.6 53.1 34.894.3 58.0 31.4

201432.6 20.0 25.0 45.6 16.0 32.066.2 40.0 32.5
200
2005229.5 135.473.6203.7127.475.2192.2 106.984.2

201491.1 57.9 72.464.6 61.3 65.8129.9134.3 64.2
500
2005615.0 403.0349.2481.5 339.9239.2554.8 288.6242.8

2014155.9 171.0130.2237.4 85.5 175.0484.6261.3263.6
__________________________________________________________________________________________________
Inthe case of the measurementbased on Furuno
andSaabreceiversontheshipSMTBontrupwecan
saythattheerrorsσ
φ,σλandσ2Darealmostthesame
forthesereceivers,errorσ
2Disabout4.1÷6.2m(table
10).For bothFuruno andSaab thedistance between
mean position and real position is from interval
4.1÷8.9 m while maximal distance between GPS
position and real position from interval 9.2÷16.7 m.
These values are typical for GPS accuracy in real
conditions.
7.3
Themeasurementsinthelaboratoryinmode2D
Foreachseries ofmeasurementsandforeachreceiver
werecalculated:thecoordinatesofmeanpositionP
m,
latitude error (m
φ), longitude error (mλ), mean
differencesbetweenmaximum andminimum values
of latitude, longitude and altitude, respectivelyΔφ,
Δλ,andhorizontalpositionerrorMofP
matthe95%
confidencelevel.
Forallthesethreereceivers,foreachyearandfor
eachH
ant the mean values of the differencesΔφ,Δλ
and error M are presented in the table 13.We can
recapitulatethat:
thelowestvaluesofthedifferencesΔφ,Δλandthe
errorMareforrealvaluesofH
antforallreceivers
andforallyears
for real value of H
ant the differencesΔφ,Δλand
theerrorMareforthemeasurementsin2014less,
insome casesconsiderably, than in2005 year for
all receivers. For all other values of H
ant the both
differencesandtheerror Marein2014yearless,in
many cases considerably, than 9 years earlier for
thereceiversMX200andMLR.
the differencesΔφ,Δλand the error M increase
withthedifferencebetweenH
antanditsrealvalue
forallreceiversandforallyears.
foreachreceiver,forallyearsandforeachH
antthe
differencesΔφandΔλ(in degrees) are in almost
all cases practicallythe same, but asΔλdepends
onlatitude,itsvalueinmetersisusuallyless.
8 CONCLUSIONS
thechoiceoftheSNSreceiverandthemodeofits
usedependonthetypeoftheshipanditsregion
of navigation. The accuracy of the position GPS
stand‐alone (e.g. SAAB GPS only) for the cargo
ship during ocean and coastal navigation is
sufficient while the same receiver SAAB on
specialized ship where high accuracy is needed
determines the position using SBAS or DGPS
augmentation.
accordingtoFederalAdministration
andmaritime
receivers producers the GPS system makes
possible the determination of horizontal user’s
position(95%confidencelevel) withtheaccuracy
fewmetres.Themeasurementsbasedondifferent
stationary GPS stand‐alone receivers realized in
the laboratory and on the ships confirm it. With
augmentation DGPS or SBAS this accuracy
increasesto1mandless.
the accuracy of the user’s positionobtained from
the GPS system depends on the number of
channels(lc)ofuser’sreceiverandthenumberof
the GPS satellites visible at given moment by
receiver’s antenna above masking angle. That’s
why the knowledge of technical
performances of
the receiver and the total number of the GPS
satellitesfullyoperational(ls)isveryimportantfor
theusers. There isno direct relation between the
numberlc,thenumberlsandthepositionerrorM,
but we can say the following “when lc and ls
greater,M
isless”andinversely“whenlcandlsis
less,Misgreater”.
errorMofthepositionfixedinmode“2D”forreal
value of H
ant is less than error M of the same
positionfixedinmode“3D”forallreceivers.
theaccuracyofSNSpositionindicatedbydifferent
maritime receivers differ because these units use
differentmethodsandalgorithmswhichenableto
change the results of pseudorange measurements
and information obtained from the
navigation
messages into the user’s coordinates. It concerns
theidenticalmodelsalsobecauseineachunitthe
local oscillator, fundamental element in all radio
receivers,isdifferent.
the accuracy of the position obtained from
professional GPS receiver with augmentation
DGPS, SBAS or from GPS/GLONASS receiver,
errorσ
2D(95%)lessthan1m,isgreaterthanfrom
GPSstand‐aloneconsiderably.
in the case of maritime GPS receiver the biggest
influence on the accuracy of its position has the
masking elevation angle and sudden changes in
satellite constellation, in integrated GPS/GLO‐
NASSreceiver,inparticular.
19
OnaccountofveryrobustGPSconstellationof30
or 31 satellites fully operational currently
produced GPS receivers usually determine and
indicate the user’s position in mode 3D, i.e.
latitude, longitude and antenna height above sea
level(geoide).
REFERENCES
Admiralty Manual of Navigation. 2008. The Principle of
Navigation,vol.1,TheNauticalInstitute,London.
Gruber B. 2012. Status and Modernization of the US Global
PositioningSystem,MunichSatelliteNavigationSummit,
Munich.
Hofmann‐WellenhofB.etal.2008.GNSS–GlobalNavigation
Satellite Systems GPS, GLONASS, Galileo & more. Wien:
SpringerWienNewYork,.
Januszewski
J. 2005. GPS Vertical Accuracy for Different
Constellations,ScientificJournalsMaritime Universityof
Szczecinnr6(78),pp.181–190
JanuszewskiJ.2010.Systemysatelitarne GSP, Galileoi inne.
Warszawa:PWN,(inpolish).
JanuszewskiJ. 2010.VerticalComponentofSatelliteNavigation
Systems. Artificial Satellites, Journal of Planetary
Geodesy,vol.45,No
3,pp.129–141
Kaplan, E.D. & Hegarty, C.J. 2006. Understanding GPS
Principles and Applications. Boston/London: Artech
House,.
Martin H. 2013. U.S. Space‐Based Positioning, Navigation
andTiming policyandProgramUpdate. 8
th
InternationalCommitteeonGNSS,Dubai
www.gpsworld.com
www.imo.org
www.km.kongsberg.com
www.marinetraffic.com
www.navcen.uscg.gov
www.saabgroup.com