29
1 INTRODUCTION
GPS position estimation process is a set of signal
processing and estimation methods aimed at
providing the user’s position estimate based on
signals and data broadcast by a GPS satellite and
received by the user’s GPS equipment. During the
process (depicted in Fig 1), the user’s GPS receiver
mea
sures the pseudo‐ranges of all the satellites in
radio‐vicinityofitsaerial,usingthePseudoRandom
Noise (PRN) signal (code) sequences and the wave‐
form structure of Navigation Message binary data.
Then, a dedicated set of estimation methods is
applied on a set of the pseudoranges measured, in
ordertoesti
matethesolutionofnavigationproblem
andyieldthevaluesofthevariablesunknown:three
componentsofthespatial(3D)userpositionestimate
andtheuserclockerror.
TheGPSpositionestimationprocessisspreadover
three spectrum signal processing domains, as
depictedinFig2.InRadioFrequencyProcessingDomain
(RFPD), a GPS receiver processes a received weak
modula
tedsatellitesignal,markedbyininformation
(contextual)sensewithitscarrierwavefrequency(L1
= 1575.42 MHz, for conventional commercial GPS
receiver). The Radio Frequency Processing Domain
signalistransformedintoBase‐bandProcessingDomain
(BPD) signal through double‐conversion process of
demodulation,yielding theBDPsignal ma
rked with
its base‐band spectrum (i. e. the spectrum of PRN
signalsandthenavigationmessageaftertheremoval
ofthecarrier).
Figure1.GPSpositionestimationprocess
Figure2. The essential processing domains of an GPS
positionestimationprocess
An Experimental Identification of Multipath Effect in
GPS Positioning Error
I.Rumora
CroatianNavy,Split,Croatia
N.Sikirica
PolytechnicHrvatskoZagorjeKrapina,Krapina,Croatia
R.Filjar
UniversityofRijeka,Rijeka,Croatia
ABSTRACT:TheanalysisoftheGPSmultipatheffectsinmaritimeenvironmentisconstrainedwiththepractice
oftraditionalGPSreceiverdesign,thatpreventsaccesstoGPSsignalsinBase‐bandProcessingDomain.Here
we propose andvalidate a simple method for experimental identification of multipath effect in Navigation
ProcessingDomain,ba
sedonspectralcharacterisationoftimeseriesofGPSpositioningerrors.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 12
Number 1
March 2018
DOI:10.12716/1001.12.01.02
30
Pseudo‐rangemeasurementprocessisapplied on
theBPDsignalthatstillcomprisesalltheerror effects
inherited from the RFPD signal. The range errors
induced during the satellite signal transmission and
propagation encompasses the results of the
ionospheric and multipath effects. Finally, the
measured pseudo‐ranges and information distilled
fromtheNavigationMessage(includingthesatellite
ephemeris and the parameters of standard error
correction models, such as Klobuchar’s one, for
mitigation of ionospheric effects) enters the purely
numerical (non‐signal) Navigation Processing Domain
(NPD), where the statistical estimation methods are
applied in order to solve the navigation problem
numerically.
The results of the NPD processing
include the estimation of position determination
errors, as inferred from partial statistical processing
results in the Base‐band and Navigation Processing
Domains.
Here we present the results of a recent research,
aimedatidentificationoftheeffectsofoneoftheGPS
positioning error
sources (multipath) in maritime
environment, using the available dat in Navigation
ProcessingDomain.
2 MULTIPATH‐INDUCEDGPSPOSITIONING
ERRORSINMARITIMEENVIRONMENT
TheGPSpositioningerrorbudgetencompassesallthe
effectsthatdeterioratethequalityoftheGPSposition
estimate. Two major single contributors to the GPS
ranging (pseudo‐range measurement)
error are the
ionospheric delay and multipath. Both error causes
extend their stochastic character, that prevents the
successfulremovaloftheireffectsontheGPSposition
estimationquality.
The multipath effects on the GPS position
estimation quality arise from the super‐position
process in the multipath‐prone environments (urban
and
maritimeenvironments,inparticular),asshown
in Fig 3. Multiple reflections of the original satellite
signal, that travels in the straight line, cause the
receptionofanumberofsignalswiththesamecarrier
frequencyanddifferenttravelpathsinthereceiver’s
aerial. As the result, the received signal appears as
travelled the farther distance than it actually did,
causing the pseudo‐range measurement error, and
thus deteriorating the accuracy of the GPS position
estimate.
Theseawavesincreasetheprobabilityofsatellite
signal reflection, thus rendering the maritime
environmentamultipath‐prone.
The effects of multipath become visible in Base‐
band Processing Domain, where various advanced
statistical signal processing approaches may be
applied for identification and mitigation purposes.
However, the design of traditional GPS receivers
keepsthebase‐bandprocessingactivitymanufa cture ‐
proprietary and thus depriving third‐parties
(researchers)fromanopportunityforassessmentand
potential improvement (statistical signal processing
methods
arethe common core‐businessassetsinthe
GPSreceivermanufacturingindustry).
Figure3.GPSmultipathonthesea
A so‐called code–phase combination method was
developed to estimate the multipath error in
Navigation Processing Domain providing both the
single‐frequencyGPScodeandphaseobservablesare
available. The method is founded on the assumed
models of the GPS ranging (R) and phase (Φ)
observables,aspresentedin
(1)and(2),respectively.
,
( *
ss
p
rjprppp
RcdtdtTSTECKKM
(1)
,
Φ ( *
ss
L
rjLrLLLLLL
cdt dt T STEC k k N m
(2)
Therange–phasedifferenceyields(3),asfollows:
˘
11 1
Φ2 RIBiasM
(3)
The code‐phase combination methods yields a
mathematical model (3) that can be utilised for
multipath error estimation, after calibration
(removing Bias) and the appropriate compensation
fortheionosphericeffects(I).
3 ANEXPERIMENTALASSESSMENTOF
MULTIPATHEFFECTONGPSPOSITIONINGIN
NAVIGATIOPROCESSINGDOMAIN
Thus paper presents the results of
a research study
that focusedon identification of multipath effects in
GPSpositionestimationerrorstimesseries,basedon
the post‐processinganalysis conductedon theset of
experimental pseudoranges taken at a buoy and
utilising the contextual domain expertise. The
information processing procedure revealed patterns
of maritime activity and
the effects of various GPS
positioning error sources in operation. The
appropriate information filtering through the
assessment of the positioning errors spectrum
signaturesextractedtheeffectsrelatedtomultipath.
The research was conducted using two
characteristic scenarios with the GPS pseudo‐ranges
collected during calm sea, and moderately windy
conditions,respectively.
31
3.1 Datasource
Raw pseudo‐range observations in RINEX format
fromtheGPSreferencestationbuoysituatedinPort
Garibaldi,Italywereused(Sonel,2017).Twouse‐case
scenarios were assessed, base on assumption of sea
wavescreatedbythewindconditions:
Case 1: calm wind condition, with
pseudoranges
taken during quiet conditions (wind’s velocity
mostly under 4 mph) throughout 7th May, 2016,
every30s,and
Case 2: moderate wind condition, with
pseudoranges taken during moderate wind
conditions(wind’svelocityinrangeof10mph‐20
mph,andgustsofupto26mph)throughout13th
May,2016,every30s.
The content of the Navigation Message was
obtainedinRINEXformatforbothdaysinquestion.
Case 1 was used as a reference (benchmark), under
presumptionoftheinsignificantmultipatheffects.
3.2 Methodology
A post‐processing (simulation) approach based on
experimental data was taken in the
research
presented.theRTKLIB,anopen‐sourceGPSpseudo‐
ranges processing tool, was utilised for GPS
positioningerrorestimation,based ontheRINEXfiles
ofactualpseudo‐rangeobservations.Themask‐angle
parameter, commonly used for suppressing the
multipath effects, was set to 10°, thus allowing for
performance assessment of
a commercial‐grade
receiver. RTKLIB returns time series of the GPS
northing‐, easting‐, and height‐errors. Time series
were analysed in time‐ (descriptive time series
analysis) and frequency‐ (spectrum determination)
domains with the dedicated software developed by
our team in R, an open‐source framework for
statistical computing, analysis
and simulation. A
detailed methodology of utilisation of RTKLIB for
GPS post‐processing for research may be found
elsewhere (Takasu,, 2013, Filic, Filjar, Ruotsalainen,
2016).
3.3 Assessmentresults
Time series of GPS northing‐, easting‐, and height‐
errors(depictedinFigs4and5,forCases1and2,
respectively) were produced and analysed. All the
timeseriesforbothscenariosexpressseasonaleffects
due to partially compensated ionospheric effects
(dailypatternoftheGPSionosphericdelaydynamics
is clearly visible), despite the application of the
Klobuchar GPS ionospheric correction model. In
addition,thetimeseriesextendveryregularpatterns
local peaks in GPS positioning error time series,
probablyduetothescheduled maritimeactivitiesin
port.
Figure4.Case1,maskanglesetat10°
Figure5.Case2,maskanglesetat10°
ThespectralcharacteristicsoftheGPSpositioning
errortimeseriesforCase2arepresentedinFig6.
Figure6. Spectral characterisation of the GPS northing‐ ,
easting‐, and height‐ error time series, respectively, for
Case2
4 DISCUSSION
The comparison with the spectral characteristics of
the Case 1 time series reveals two remarkable
findings,asfollows.
First,thecommon spectral componentsare either
of the same intensity, or even more pronounced in
32
Case 1. We find this a consequence of the other
positioningerrorsources(suchasanuncompensated
local ionospheric disturbance) in operation, that
overcomethemultipatheffectswhenthetime‐domain
isconsidered.
Second,theCase2spectralcharacterisationreveals
morespectral componentsthan inCase1, rendering
thema
signatureofthemultipatheffect.Theintensity
ofthenewCase2spectralcomponentsaregenerally
lowerthan the intensityofthe components common
tobothcases, thus suppressingtheir visibilityin the
inspectionoftimeseriesinthetimedomain.
Despitethepresence oftheintensive influence of
the
otherGPS positioningerrorsources, thespectral
characterisation reveals the effect of multipath
throughcorrespondencebetweentheencounterofthe
expanded GPS positioning error spectral and sea
wavesactivity.
5 CONCLUSION
A study is presented here, that addresses the
identificationofmultipatheffectintimeseriesofGPS
positioningerrordata
takeninmaritimeenvironment.
An information‐ (contextual‐based) approach was
takenbasedondomainexpertiseininterpretationof
theanalysisoftheGPSpositioningerrorstimeseries
in time‐ and frequency‐ domains. In that way, the
GPS positioning performance was assessed in the
Navigation processing, rather than in the GPS
receiver design‐constrained Base‐band Processing
Domain. The spectral characterisation of the GPS
positioning errors time series reveals multipath
spectralsignatureintimeseriesofpossiblemultipath‐
prone (moderately windy) maritime conditions,
despite the masking fromthe otherGPS positioning
errorsourcesinoperation.
We intend to continue related research in
cataloguing the spectral signatures of characteristics
maritime GPS positioning conditions, following the
path of development of a general maritime GPS
multipathmodel.
REFERENCE
Brown, A. (2000). Multipath Rejection Through Spatial
Processing. Proc of ION GSP 2000 (8 pages). Salt Lake
City,UT.
Filic, M, Filjar, R, Ruotsalainen, L. (2016). An SDR‐Based
Study of Multi‐GNSS Positioning Performance During
Fast‐Developing Space Weather Storm. TRANSNAV,
10(3),395‐400.doi:10.12716/1001.10.03.03
Goldhirsh, J, and
Vogel, W J. (1998). Handbook of
Propagation Effects for Vehicular and Personal Mobile
Satellite Systems: Overview of Experimental and
Modeling Results. Johns Hopkins University, Laurel,
MA,andUniversityofTexasatAustin,Austin,TX.
Joodaki,G,Nahavandochi,H,andCheng,K.(2013).Ocean
Wave Measurement Using GPS Buoys. J of
Geodetic
sciences,3(3),163‐172.doi:10.2478/jogs‐2013‐0023
Lachapelle, G et al. (2003). Ship GPS Multipath Detection
Experiments.ProcoftheION AnnualMeeting(13pages).
Albuquerque,NM.
Petrovski,I andTsujii,T.(2012).DigitalSatelliteNavigation
and Geophysics: A Practical Guide with GNSS Signal
Simulator and Receiver
Laboratory. Cambridge
UniversityPress.Cambridge,UK.
Sanz Subirana, J et al. (2013). GNSS Data Processing –
Volume I: Fundamentals and Algorithms.European
Space Agency (ESA). Nordwijk, The Netherlands.
Available at: http://bit.ly/1QV4KAL, accessed on 10
February,2016.
Sonel. (2017). The global network GNSS assembly data
centre for the Global Sea Level Observing
System
(GLOSS). Available at: http://www.sonel.org/?lang=en,
accessedon10February,2017.
Soubielle, J, Fijalkow, I, Duvaut, P, and Bibaut, A. (2002).
GPS Positioning in a Multipath Environment. IEEE
TransonSignalProc,50,141‐150.
Takasu, T. (2013). RTKLIB: An Open Source Program
Package for GNSS Positioning. Software and
documentation
available at: http://www.rtklib.com/,
accessedon10February,2016.
