663
1 INTRODUCTION
Satellite navigation has become a foundation of
moderncivilisationandanindispensablecomponent
ofthenationalinfrastructure,regardlessoftheactual
ownership of a satellite navigation system (UK
GovernmentOfficeforScience,2018).Astheresultof
a long‐term trend, non‐navigation applications of
GlobalNavigationSatellite
Systems(GNSS)overtook
those navigation‐related, facilitating the new
perspective on GNSS positioning performance
requirements. Smaller administrative regions with
sparse population and the vast impact of the
environment establish increasingly their socio‐
economic services on the utilisation of free‐to‐access
andreadilyavailablesatellitenavigationservices.
A remote oceanic
island community provides an
excellentexampleof the class (Howes, Birchenough,
and Lincoln, 2018), (Yao, and Rhee, 2013). Facing
growing challenges of climate change effects (The
Economist,2018),surroundedbytheraisingsealevels
and extreme weather conditions, the investments in
infrastructure shift to services based on low‐cost
maintenance and
highefficiencyinfrastructure,such
as GNSS. Increasing automation that provides a
framework for sustainable community means
increasing utilisation of GNSS. Considering this
perspective, GNSS positioning performance gains
newresponsibilityandrequirementsforstabilityand
resilience against natural and artificial disturbances
(Porretaetal,2016).
Hereweexamineacaseof
arapidtropicalcyclone
development in close proximity of a Pacific Ocean
A South Pacific Cyclone-caused GPS Positioning Error
and Its Impact on Remote Oceanic Island Communities
M.Filić
Sesvete,Zagreb,Croatia
R.Filjar
UniversityofRijeka,Rijeka,Croatia
ZagrebUniversityofAppliedSciences,Zagreb,Croatia
ABSTRACT:Satellitenavigationgainsimportanceinsustainabledevelopmentofmoderncivilisation.Withthe
increasingnumberofGNSS‐basedtechnologyandsocio‐economicsystemsandservices,satellitenavigationhas
become an essential component of national infrastructure. This calls for novel
requirements on GNSS
positioningperfomance,andincreasingneedforresilientGNSSdevelopment.Hereweexaminedtheimpactof
rapidlydevelopingtropicalcycloneonGPSpositioningperformancedegradation,andtheresultingimpacton
oceanic non‐navigation and navigation GPS applications. We presented the methodology for indirect
simulation‐based GPS positioning performance
evaluation through utilisation of experimental GPS
observations, GNSS Software‐Defined Radio (SDR) receiver, and a statistical analysis and framework we
developed in the R environment for scientific computing. We identified alteration of GPS positioning error
componentstimeseriesstatisticalproperties,anddiscussthepotentialimpactonGPS‐basedservicesessential
for
remote oceanic island communities. Manuscript concludes with the summary of findings, proposal for
recommendationsonimprovedGNSSresilience,andanoutlineforfutureresearch.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 12
Number 4
December 2018
DOI:10.12716/1001.12.04.03
664
island community from the perspective of GPS
positioningperformancedegradationassessment,and
potential impact on technology and socio‐economic
applicationsbasedonsatellitenavigationservices.
2 METHOD
Thissectionpresentsdataandmethodsutilisedinthe
study of troposphere‐driven GPS positioning
performancedegradation.
2.1 Datadescription
International GNSS Service
(IGS, 2018) provides a
systematic access to archived GNSS‐related daily
observationscollectedbytheIGSnetwork(IGS,2018)
of stationary reference station spread across the
Earth’s surface. Provided on the voluntary basis as
the service for scientists, researchers and
practitioners,IGSreferencestationsdifferintherange
of observations
they collect. Several of them deploy
GPS‐only dual frequency receivers, while the others
gather observations from different GNSS systems
simultaneously.
IGS network reference stations collect
simultaneously several sets of observations (NASA,
2018), as follows: (i) dual frequency‐GNSS
pseudorange measurements (depending of the
equipment used, GPS, GLONASS, Gailelo, and
Beidou)
at30ssamplingrate,(ii)navigationmessages
broadcast by related GNSS, (iii) (optional) addition
observations of positioning environment, such as
meteorologicaldataat15minsamplingrate,and(iv)
(optional)observationsofGNSSaugmentationsystem
information (WAAS, EGNOS etc.). Observations are
structured in daily sets stored using a dedicated
UNIX‐based RINEX format, specified by (IGS et al,
2015), in related RINEX daily files (RINEX o and d
files for GPS pseudorange measurements, RINEX n
fileforbroadcastorreceivedGPSnavigationmessage
etc.).
Figure1. Noumea, New Caledonia (© OpenStreetMap
contributors,(OpenStreetMap,2018))
Datasetsarefreelyavailbaleforindividual(non‐
automated) access to scientists, researchers,
practitionersandtheotherinterestedparties.Onthe
common ground, the IGS network follow the same
principle of data collection and storage that assures
the quality of data. Primarily, the The IGS network
has been set up to
expose the impact of the GNSS
ionospheric delay by not correcting the ionospheric
effects in any way, while suppressing the other
sources of GNSS pseudorange measurement errors.
Still, a number of IGS reference station allow for
contamination of the observed GNSS pseudoranges
caused by the other sources of disturbance, such
as
troposphericdelayorsatelliteclockerrors,toremain
inrecords,thusallowingforresearchonthesubject.
We identified one source of GNSS pseudorange
observations contaminated by uncorrected
tropospheric delay in data collected at the IGS
referencestationinNoumea,NewCaledonia(Figure
1),andusedRINEXdualfrequencyGPS
pseudorange
measurementsandRINEXnavigationmessagefiles
inthisstudy.
Figure2.Dataprocessingandanalysis
2.2 Dataprocessingandanalysis
A procedure for data processing and analysis was
used in the study, based on utilisation of a GNSS
Software‐Defined Radio (SDR) as a post‐processing
tool for position and positioning error estimation
fromRINEXdata,andadedicatedstatisticalanalysis
softwaredevelopedbyourteam
intheopen‐sourceR
frameworkforstatisticalcomputing(Rproject,2018).
Depicted in Figure 2, the procedure was established
byourteamanddetailedelsewhere(Filic,Filjar,and
Routsalainen, 2016). Essentially, it is a three‐phase
procedural that: (i) post‐process experimental GNSS
observations, corrupted with an error source
under
consideration (tropospheric effects, in this case), to
yield time series of position vector and positioning
error vector estimates; (ii) analyse GPS positioning
error time series, and (iii) develop a model of GPS
positioningerrortimeseriesastheerror residualsof
thepositionestimationprocess.Ourprocedureallows
forassessment
oftheGNSSpositioningperformance
in various scenarios of applications and in different
position environments through: (i) suitable
configuration (switching off or on different
pseudorange error correction models) of GNSS SDR
665
receiver utilised for processing, and (ii) selection of
related GNSS observations sets at the IGS reference
station position and the positioning environment
conditions that corrupt the GNSS observations in a
mannerrequiredfortargetedstudy(Filić,Filjar,and
Weng,2018).
Thefirstphaseoftheproceduralutilisedisbased
on Weighted Least‐Square GPS position estimation
process, as described elsewhere (Filić, and Filjar,
2018),(Oxley,2017),(Filić,Grubišić,andFiljar,2018).
A comprehensive overview of mathematical
foundations of the procedural’s second and third
phaseisgivenintheremainingpartofthissection.
A linear additive
GPS positioning error model is
assumed,inaformpresentedwithEq(1).
ˆ
iono tropo sat clock sat ephem
xx x x x x
(1)
where:
ˆ
x
…GPS‐basedpositionestimate,contaminatedwith
effectsoferrorsources
x
…real(true)position
iono
x
… position estimation error vector, due to
ionosphericeffects
tropo
x
… position estimation error vector, due to
troposphericeffects
s
at clock
x
… position estimation errorvector, due to
satelliteclockserroreffects
s
at ephem
x
…positionestimationerrorvector,dueto
satellitepositionestimationerroreffects
… residual position estimation vector, due to
causes un‐accounted for in previous position
estimationerrorvectors
Suppose the means exist for removal entirely of
the position estimation error, due to tropospheric
effects.In thatcase,theGPS‐based position estimate
wouldcomprisealltheothereffects,butwithoutthe
tropospheric
one,andbeexpressedasinEq(2).
ˆ
t
iono sat clock sat ephem
xxx x x
(2)
Assumingthepositionestimatesderivedfrom(1)
and(2),respectively,areknown,theGPSpositioning
error,duetotroposphericeffects,maybedetermined
usingthemodel(3).
ˆ
tropo t
x
xx
(3)
Wecreated atime series of tropo‐free GPS‐based
position estimates time series (2) by introduction of
Saastamoinen tropospheric delay correction
(Parkinson, and Spilker Jr, 1996) during post‐
processing RINEX observation with RTKLIB GNSS
SDR receiver. Saastamoinen developed an empirical
modelvalidforsatellitesignalsapproachingtheGPS
receiveraerialatelevationangleshigherthan10°,as
givenwithEqs(4),(5)and(6).
2
00 0 0
0
1255
0.002277 1 0.005
tropo R
dm DsecP eBtan
T
(4)
where:
0.0026 2 0.00028Dcos h
(5)
…denoteslatitudeofaGPSreceiver
h…denotes height above the mean sea level of the
GPSreceiver’sposition,in[m]
P
0…denotesatmosphericpressurein[hPa]
e
0…denotespartialwatervapourpressurein[hPa]
T
0…denotesairtemperaturein[K]
0
90 E
(6)
E … denotes elevation angle of satellite signal
approachin[°]
B,
R
… two height‐dependant correction terms
(Parkinson,andSpilker,Jr,1996)
AllthevectorslistedinEqs(1),(2),and(3)maybe
expressed with the related three independent
components from the end user’s perspective, as
definedbyEq(7).
i northing i easting i vertical i
x
xixjxk
(7)
where:
i
x
…avectorfrom(1)
northing i
x
…northingcomponentof
i
x
easting i
x
…eastingcomponentof
i
x
vertical i
x
…verticalcomponentof
i
x
,,ijk
…a setof unitvectorsfordefinitionof the
northing,eastingandverticaldirections,respectively,
according to World Geodetic System 1984
(Eurocontrol,1998)
Components of the GPS positioning error vector,
due to tropospheric effects, (3) may be presented in
themannerof(7)withEq(8).
tropo northing tropo easting tropo vertical tropo
x
xixjxk
(8)
ThehorizontalcomponentoftheGPSpositioning
error vector, due to tropospheric effects, may be
determined as the combination of the GPS northing
and easting positioning error components, as in Eq
(9).
22
horizonatl tropo northing tropo easting tropo
xxx
(9)
Eqs (8) and (9) define time‐series of the GPS
northing,easting,verticalandhorizontaltimeseries,
respectively. Characterisation of time‐series may be
performedusingaprocedureinvolving:(i)thetime‐
series mean and standard deviation values
determination,(ii) residual statistical distribution, or
(Gaussian)kerneldensityanalysis,(iii)
theQuantile‐
Quantile (Q‐Q) diagram analysis, (iv) Partial Auto‐
Correlation Function (PACF) analysis, and (v)
residual error Auto‐Regressive (AR) model
development.
The Kernel density estimation method is defined
asfollows.Let(10)beatimeseriesofthepopulation
samples with the unknown distribution f. The f
distribution
may be estimated using kernel density
estimator(11).
666
12,
, ...,
n
x
xx (10)
11
11
nn
i
hhi
ik
x
x
fx Kxx K
nnhh
(11)
with:
K … Gaussian kernel (non‐negative integrable
function)
2
1
2
1
2
u
Ku e
h…bandwidth(smoothingparameter)
Bandwidthhisdefinedintheoptimalmannerthat
minimisesthemeanintegratedsquareerror,withthe
resultingoptimisedmodelgivenwith(12).
1
5
1
5
5
6
ˆ
4
1.0
3
hn
n
(12)
The Quantile‐Quantile (Q‐Q) diagram is a
graphical method for comparison between two
statistical distribution by plotting their quantiles
againsteachother(Shumway,andStoffer,2017).
The Partial Auto‐Correlation Function (PACF) is
defined (Box, Jenkins,and Reinsel, 2008) as follows.
Let z
t denotes a given time series of samples. The
PACF is defined as a set of partial auto‐correlation
coefficients of lag k, defined as the auto‐correlation
betweenz
tandzt+kwithlagslargerthan1andlessor
equaltok‐1notincluded(13),(14).
1
1,
tt
Corr z z
(13)
,,
,
tk tk tk t tk t
kCorz Pz zPz
(14)
where
,tk
P
referstoprojectionofxtospacedetermined
byxt+1,…,xt+k‐1.
The GPS positioning errors, due to tropospheric
effects,timeseriesunderobservationwereconsidered
timeseriesofresiduals,andcharacterisedusingAuto‐
Regressive(AR)modelsofrandomprocesses.AnAR
model of order p is of the form
expressed with Eq
(15).
1
p
iti t
i
xt c x
(15)
where:
12
, ,...,
p
…denoteasetofthemodelparameters
c…denotesaconstant(bias)
t
…denoteswhitenoisemodelerror
ARmodelandthemethodologyforitsparameters
determination are discussed elsewhere, for instance
(Shumway,andStoffer,2017).
The methods and algorithms presented in this
Section were deployed in the R programming
frameworkfor statistical computing (R project team,
2018), and assembled into the dedicated
time series
analysisframeworkbyourteam.
3 CASESTUDYDESCRIPTION
A case study of a rapid development of a tropical
cyclone in a close vicinity to the observation (IGS
reference station Noumea, New Caledonia in South
Pacific)sitewasselected,asacaseofbothanextreme
(tropospheric) positioning
environment condition,
and of real situation encountered by remote oceanic
island community. The severe tropical cyclone Ola
developedon 29
th
January, 2015(DOY029)farin the
north to north‐west direction from the Noumea
reference station. Ola progressed in southern
direction,reachingtheclosestpointtoNewCaledonia
on 30
th
January, 2015, finally disintegrating on 3
rd
February,2015.Initspeakintensity,Ola reachedthe
Category 3 severe tropical cyclone strength
(Australian scale) on DOY030, with winds at 150
km/handbarometricpressureof955hPaatitspeak
intensity(StormScienceAustralia,2018).
Theextreme (tropospheric) weather conditions in
rapid developments cause considerable impact on
GPS pseudorange measurement by introduction of
random tropospheric delay (Parkinson, and Spilker,
Jr,1996).ThecaseofOla’speakintensitytakingplace
close to the IGS reference station in New Caledonia
was examined in this study for potential effects on
GPS positioning performance with repercussions on
GPS‐basedapplications.
4 STUDY
RESULTS
Obtained during the implementation of data
processing and analysis procedure, outlined in
Section2.2,arepresentedinthisSection,asfollows.
Tables 1 and 2 show the mean and standard
deviation values of the GPS positioning error
components,duetotroposphericeffects,onthedays
028and030in
2015,respectively.
Table1.MeanvaluesofGPSpositioningerrorcomponents,
duetotroposphericeffects
_______________________________________________
Residualmeanvalues DOY028 DOY030
_______________________________________________
Northingerror[m]‐0.309‐0.307
Eastingerror[m]‐0.017‐0.009
Horizontalerror[m] 0.436 0.855
Verticalerror[m]9.351 9.188
_______________________________________________
Table2.StandarddeviationvaluesofGPSpositioningerror
components,duetotroposphericeffects
_______________________________________________
Residualstandarddeviation DOY028 DOY030
_______________________________________________
Northingerror[m]0.857 0.851
Eastingerror[m]0.525 0.502
Horizontalerror[m]0.750 0.582
Verticalerror[m]1.836 1.824
_______________________________________________
667
Figure3.TimeseriesofGPSnorthing(red),easting(blue),horizontal(green),andvertical(magenta)positioningerrors,on
DOY028(left)andDOY030(right),respectively.
Figure4. Estimated statistical kernel densities of GPS northing, easting, vertical and horizontal positioning errors,
respectively,onDOY028(left)andDOY030(right).
Time series of northing, easting, horizontal, and
vertical positioning error components, due to
troposphericeffects,ondays028(quietweather)and
030(thefullextentof atropical cyclone) in2015are
depictedwithcombineddiagramsinFigure3.
Kernel density estimates of the northing, easting,
horizontal, and vertical GPS positioning
error
components on the days 028 and 030 in 2015 are
depictedinFigure4.
Q‐Qdiagramsofthenorthing,easting,horizontal,
andverticalGPSpositioningerrorcomponentsforthe
days028and030in2015aredepictedinFigure5.
668
Figure5.Q‐QplotsofGPSnorthing,easting,vertical,andhorizontalpositioningerrorstimeseries,respectively
PartialAuto‐CorrelationFunctiondiagramsofthe
northing, easting, horizontal, and vertical GPS
positioning error components for the days 028 and
030in2015aredepictedinFigure6.
Finally, summary of Auto-Regressive (AR)
models (mean and variance values) for the
northing, easting, horizontal, and vertical GPS
positioning error components are outlined in
Tables 3 and 4, respectively.
Table3. Auto‐Regressive (AR) model means for the
northing, easting, horizontal and vertical GPS positioning
errorcomponentsonthedays028and030in2015
_______________________________________________
ARmodelmeanDOY028 DOY030
_______________________________________________
Northingerror[m]‐0.3091199 ‐0.3068283
Eastingerror[m]‐0.01667184‐0.009313357
Horizontalerror[m] 0.4359185 0.854925
Verticalerror[m]9.351068 9.187918
_______________________________________________
Table4. Auto‐Regressive (AR) model variations for the
northing, easting, horizontal and vertical GPS positioning
errorcomponentsonthedays028and030in2015
_______________________________________________
ARmodelσ
2
DOY028 DOY030
_______________________________________________
Northingerror[m]0.0315 0.02935
Eastingerror[m]0.02155 0.01846
Horizontalerror[m] 0.05241 0.02472
Verticalerror[m]0.2326 0.2605
_______________________________________________
669
Figure6.
5 DISCUSSIONANDCONCLUSION
The GPS position estimation accuracy is the GPS
positioning performance index largely affected by
introduction of tropospheric delay. The statistical
propertiesoftroposphericdelayguidesthe selection
of approach in error correction model development.
The over‐all position estimation error due to
troposphericeffectsdeterminestheGPS
suitabilityfor
robust and resilient GPS‐based applications
developmentandoperation.
Meanandstandarddeviationvalues(Table1and
2,respectively)ofGPSpositioningerrorcomponents
time series (Figure 3) do not reveal a substantial
differencebetweenquiettroposphericconditionsand
atropicalcyclone.Thismaybeunderstoodtheresult
of dominance of dry‐air component of tropospheric
delay. However, it is the wet‐air component of
tropospheric delay that delivers va riation in time
series,withitsincreasingimpactduringthetimeofa
tropicalcyclone.Estimatesofkerneldensity(Figure4)
for the cases of quiet atmosphere and a tropical
cyclone shows evident differences, with the only
exception of easting GPS positioning error
component, that remained in following the normal‐
like statistical distribution. The findings were
confirmed with Q‐Q diagrams for related GPS
positioning error components (Figure 5), were again
the eastern GPS positioning error component
produced the normal‐
like distribution plots for both
quietanddisturbedatmosphere.Furtherexamination
of Partial Auto‐Correlation Function (PACF)
diagrams revealed low variations of all GPS
positioning error components in quiet atmospheric
conditions, without auto‐correlation coefficients
exceeding the confidence bounds. Tropical cyclone
conditions altered dynamics of all, but the easting
GPS positioning
error components, adding several
auto‐correlation coefficients that exceeded the
confidencebounds,makingthecaseofintroductionof
AR(2)model as a suitable one capable of taking the
newlyintroducedvariabilityintoaccount.
In summary, we accentuated the impact of
tropospheric delay on GPS positioning performance
throughassessmentofthe
caseofrapidandextreme
tropospheric weather deterioration. The evidence
670
shows different nature of troposphere‐driven GPS
positioningerrorduringatropicalcyclone,compared
with the case of quiet tropospheric weather. While
essential statistical parameters of GPS positioning
error components remain balanced and stable
regardless of tropospheric conditions, statistical
propertiesofGPSpositioningerrorcomponentsvary
largely in relation to
the nature and intensity of
tropospheric disturbance. Different nature of
troposphericdelay(i. e. tropospheric contribution to
GPSpseudorangemeasurementerror)reflectsonthe
over‐allGPSpositioningaccuracy(Filić,Filjar,2018).
Deterioration may not affect oceanic cruise
navigation, due to its low requirements on position
estimation accuracy, but
impacts significantly
performance of numerous technology and socio‐
economic GPS‐relying services for remote oceanic
island communities. With restricted budget for
expensive infrastructure, those communities utilise
satellitenavigation extensively. Thus, anyimpact on
stability and reliability of GPS‐based services may
underminecommunitiesalreadyfacingchallengesof
climatechange, and potential
devastating impact on
community’s survival. Considering results of this
study, recommendations may be proposed on: (i)
continuousobservationsofmeteorologicalparameters
related to GPS positioning performance, (ii) timely
deliveryofmeteorologicalobservationparametersto
GPS receivers for more effective tropospheric error
mitigation; and (iii) continuous research on user
equipment adaptation
to positioning environment
dynamics in a sense of intelligent mitigation of the
effectsofpotentialdisruptions.
Weintendtocontinueourresearchonthesubject
through examination of cases with transitional
periodsbetweenextremeconditions,andtheirimpact
onGPStroposphericdelayandGPSpositioningerror
dynamics in continuous aim to
develop an adaptive
positioning estimation model capable of detecting
anomalies in positioning environment and
responding to their mitigation without affecting the
GNSSpositioningperformanceandqualityofGNSS‐
basedapplications.
REFERENCE
Box,GEP,Jenkins,G,andReinsel,GC.(2008).TimeSeries
Analysis,ForecastingandControl(4
th
ed).JohnWiley&
Sons.Hoboken,NJ.
Filić,M.(2018).Ondevelopmentoftheforecastingmodelof
GNSS positioning performance degradation due to
spaceweatherandionosphericconditions.Proc2
nd
URSI
AT‐RASC (4 pages, electronic format). Gran Canaria,
Spain. Available at:
http://www.atrasc.com/content/stick/papers/URSISumm
aryPaperMFilic.pdf
Filić, M, and Filjar, R. (2018). Forecasting model of space
weather‐drivenGNSSpositioningperformance.Lambert
AcademicPublishing.Riga,Latvia.
Filić,M, Grubišić, L, andFiljar, R. (2018).Improvement of
standard GPS position estimation
algorithm through
utilizationof Weighted Least‐Sqaureapproach. Proc of
11thAnnual Baška GNSS Conference, 7‐19. Baška, Krk
Island, Croatia. Available at:
https://www.pfri.uniri.hr/web/hr/dokumenti/zbornici‐
gnss/2018‐GNSS‐11.pdf
Filić,M,Filjar,R,Weng,J.(2018).AnIGS‐basedsimulatorof
ionospheric conditions for GNSS positioning quality
assessment. Coordinates, 14(1), 31
‐34. Available at:
http://mycoordinates.org/an‐igs‐based‐simulator‐of‐
ionospheric‐conditions‐for‐gnss‐positioning‐quality‐
assessment/
Filić, M, Filjar, R, and Ruotsalainen, L. (2016). An SDR‐
based Study of Multi‐GNSS Positioning Performance
During Fast‐developing Space Weather Storm.
TransNav, 10, 395‐400. doi: 10.12716/1001.10.03.03.
Availableat:http://bit.ly/2fxAvph.
HowesE
L,Birchenough,S,andLincoln,S.(2018).Effectsof
Climate Change Relevant to the Pacific Islands (in
Pacific Marine Climate Change Report Card).
CommonwelathMarineEconomiesProgramme(Funded
by HM Government of the United Kingdom). London,
UK. Available at: https://bit.ly/2qdI2gZ (HM
GovernmentoftheUKinternetresource).
IGS. (2018). International GNSS
Service (IGS) Network.
Availableat:http://www.igs.org/network
IGS, RINEX Working Group, and RTCM‐SC104. (2015).
RINEX: The Receiver Independent Exchange Format
(version 3.03). Available at:
ftp://igs.org/pub/data/format/rinex303.pdf
NASA. (2018). IGS Archive of daily GNSS observations,
hosted by NASA. Available at:
ftp://cddis.gsfc.nasa.gov/gnss/data/daily
OpenStreetMap. (2018). Data base of world spatial data
under Open Database
Licence. Cartography provided
undertheCreativeCommonsAttribution‐ShareAlike2.0
license.Availableat:https://www.openstreetmap.org
Oxley, A. (2017). Uncertainties in GPS Positioning: A
mathematical discourse. Academic Press/Elsevier.
London,UK.
Parkinson, B W, and Spilker, Jr, J J (eds). (1996). Global
Positioning System: Theory and Applications (Vol. I.).
AIAA.Washington,DC.
Porretta,M
etal.(2016):GNSSEvolutionsforMaritime:An
Incremental Approach. Inside GNSS, May/June, 2016,
54‐62. Available at:
http://insidegnss.com/auto/mayjune16‐WP.pdf
R‐project team. (2017). The R project for Statistical
Computing (software, documentation, and books).
Availableat:https://www.r‐project.org.
Shumway, R H, and Stoffer, D S. (2017). Time Series
Analysisand
ItsApplicationsWithRExamples(Fourth
Edition).SpringerVerlag.Cham,Switzerland.Available
at:https://www.stat.pitt.edu/stoffer/tsa4/tsa4.pdf
StormScienceAustralia.(2018).TropicalCycloneOlainthe
EasternCoralSea.StormScienceAustralia.Availableat:
http://bit.ly/2BJkunK
Stull, R. (2017). Practical Meteorology: An Algebra‐based
SurveyofAtmosphericScience(version1.02b). Univ. of
British Columbia.
Vancouver, BC.Available at:
https://bit.ly/2QXfG66
Takasu, T. (2013). RTKLIB: An Open Source Program
Package for GNSS Positioning. Software and
documentationavailableat:http://www.rtklib.com
TheEconomist.(2018).StormyWeather:StormsinAmerica
and the Pacific are evidence of climate change. The
Economist UK ed), Sep 22, 2018, 52‐54.Available at:
https://econ.st/2MPZwZJ
Thomas, M et al. (2011). Global Navigation Space Systems:
reliance and vulnerabilities. Royal Academy of Engineering.
London, UK. Available at: http://bit.ly/1vrIenu
UK Government Office for Science. (2018). Satellite-Derived
Time and Position: A Study of Critical Dependencies. HM
Government of the UK and NI. Available at:
https://bit.ly/2E2STnd
Eurocontrol, and IfEN. (1998). WGS 84 Implementation
Manual.Availableat:http://bit. ly/2wM4xPn
Yao, X, and Rhee, C. (2013). The economics of climate
change in the Pacific. Asian Development Bank.
Mandaluyong City, Philippines. Available at:
https://bit.ly/2pcpCi9
