Simulation and Measurements ofthe Effects ofDifferentUrban Environments on GPS Location Errors UsingDigital Elevation Models and Building Databases

Em anoel Costa

Centro de Estudos em telecornunicacoes (CETUC)Pontiffcia Universidade Cat61ica do Rio de Janeiro (PUC-Rio)

Rua Marques de Sao Vicente 225, 22451-900 Rio de Janeiro RJ, BRASILepoc@ce tuc.puc-rio.br

Abstract-A simulation model will be described and employed tostudy the propagation channel of the Global Positioning System.Initially, a digital elevation model, building databases, and avegetation model are processed to generate azimuth-elevationmaps of path states (clear, shadowed and blocked) for a largenumber of observers. At each simulation step, satellite positionsare updated using an orbit predictor and azimuths and elevationsof paths from satellites to observers calculated. Signal strengthsand range errors are assigned to paths with the aid of a randomnumber generator for each path state. This information isprocessed to determine the cumulative distribution functions forposition errors. It will be shown that, by proper selection ofparameters, model predictions are able to display a goodagreement with measurement results. The simulation model willthen be applied to a large number of observers deployed alongtwo routes in densely urbanized areas in the City of Rio deJaneiro (22.8°S, 43.3°W) with buildings displaying differentheight distributions to show how the position errors change withthe average building height. In combination with the comparisonbetween measurement and prediction results, this indicates thatthe simulation model may be a useful tool for studying andplanning satellite-based location and navigation applications withgood accuracy and sensitivity.

Keywords-Global Positioning System; propagation; simulation

1. INTRODUCTION

Due to blockage by solid obstacles such as buildings andmountains, as well as to shadowing by vegetation, signals fromthe Global Positioning System (GPS) satellites experimentfading and additional delays. Due to deep fades, loss by one ofthe receiver channels of the ability to track the code or thecarrier of the corresponding GPS signal and relatively longtimes to reacquire them [I], the number of satellites beingtracked by multichannel GPS receivers may decrease. Inaddition, the estimated ranges between satellite and receivers,contaminated by the extra signal delays, may also becomeincorrect. The combination of these and other effects inducesposition errors and may also prevent receivers from operating,degrading the performance and reducing the availability ofGPS-based location and navigation services [2]-[4].

This work was sponsored by FAPERJ, through Research Grant E­26/170.204/05.

978-1-4244-5357-3/09/$26.00©20091 EEE

Simulation models are efficient, flexible and inexpensivetools for studying the impact of different environments on theperformance of systems based on non geostationary satellites.These models may be helpful in the interpretation of resultsfrom measurements and, with proper care, may be extended tosimilar scenarios not covered by sometimes costlyexperimental campaigns. Additionally, they may providerealistic input data to protocols designed to test theperformance of new-generation GPS receivers [5]-[7]. Withinthis class of models , a method based on the processing ofdigital hemispherical photographs collected in representativescenarios was used to generate a set of maps of three pathstates (clear, shadowed and blocked) as functions of theazimuth and the elevation of a given direction from a user. Thisset of maps was then combined with probabilistic faderepresentations for each path state to analyze the propagationchannel corresponding to a particular low-earth-orbit satellitecommunication system [8]. More recently, the parameters ofthe same model have also been estimated from outdoormeasurements of the (ClNo) ratio using GPS receivers in urbanCalgary and Vancouver, Canada [7].

Digital elevation models and building databases for severalcities of the world are available at affordable prices or even forfree. This information is sufficiently detailed and reliable to beused in communication and navigation studies. Digitalelevation models and building databases will be used here inplace of digital hemispherical photographs to generate similarsets of path-state maps, following a previous study on thepropagation channel of different low-earth-orbit satellitesystems and on the effects offade-mitigation techniques [9].

Alone, fade models are not able to describe the effects ofurban areas on the position error of GPS receivers and on theservice availability. Extra signal delays due to several sources(atmospheric, hardware, buildings, vegetation, etc.) add errorsto the actual ranges between satellite and receivers. Theseerrors, particularly under unfavorable user/satellite geometriesleading to dilution of precision (DOP), may be mapped ontolarge position errors, even during unfaded or shallow-fadingconditions [I]. Therefore , a range error model that also takesthe features of each of the three states into account will becombined with the fade model [8],[9] to fully characterize theGPS propagation channel.

267

That is, it is assumed that the fade amplitudes for the C andthe S states follow the Urban Three-State Fade Model(UTSFM) [7]-[9] with parameters KR, KL, mi, aL, ms, and as(all in decibels), considered being more appropriate for highly

The objective of the present contribution is to propose anddescribe an integrated simulation model of the GPSpropagation channel and receiver. The simulation model isspecified in Section II. Section III will show that, by properselection of parameters, model predictions are able to display agood agreement with measurement results. Section IV willanalyze the effects of urban areas on the position error of GPSreceivers by applying the simulation model to two routes indensely urbanized areas in the City of Rio de Janeiro (22.8°S,43.3°W) with different height distributions. The results will bediscussed to highlight the effects of the selected urbanenvironments on the corresponding parameters and to show thecapabilities of the simulation model. Conclusions from thiswork will be presented in Section V.

II. SIMULATION MODEL

The simulation model processes data from a specifiednumber of users, characterized by their coordinates andheights. For each user, a path-state map is generated usingterrain data provided by the 3-arc-second digital elevationmodel resulting from the Shuttle Radar Topography Mission(SRTM) [10], in combination with building and treeinformation to indicate, with a 0.50 resolution in azimuth andelevation, whether a ray path to a GPS satellite is clear (C),shadowed (S), or blocked (B) [9].

Each simulation run involves all the observers in one routeand a specified number of time steps, with 1 s betweenconsecutive time steps. At each time step, the positions of thesatellites are updated using quadratic interpolation based onInternational GNSS Service (IGS) products [11],[12]. Next, theazimuths and elevations of the ray paths between eachcombination of user and satellite are determined and the statesof those with elevations above 100 are obtained using thecorresponding path-state maps. A fade value is then assigned toeach ray with elevation above this threshold using randomnumber generators with the following Rice, Loo, and Suzukiprobability density functions [7]-[9], [13],[14] for the C, S, andB states, respectively,

urbanized environments such as the ones characterized above.In equations (1) and (2), Io(x) is the modified Bessel functionof the first kind, order zero and argument x. The Loodistribution [13] results from the application of the totalprobability theorem to Rice and lognormal distributions. Onthe other hand, the Suzuki distribution [14] results from theapplication of the same theorem to Rayleigh and lognormaldistributions. A discussion on the probability density functionsfor fades corresponding to the three states and their graphicalrepresentations for special parameter values can be found in[9].

The nominal received power (as a function of the elevation)for the Ll signal (carrier frequency equal to 1575.42 MHz) [1]and the assigned fade level are then combined with receivernoise and loss parameters to calculate the corresponding C/No

ratio for each ray path above the elevation threshold. If theresulting C/No ratio exceeds the threshold of 22 dBHz [6], arange error is added to the geometrical length of the ray pathusing a Gaussian random number generator with mean valuemRk (m) and standard deviation aRk (m), where k = C, S or B, torepresent ever-present effects due to clock stabilityperturbations, atmospheric and other delays, receiver noise,etc., for the proper state [9]. The mean values for the clear andblocked states are fixed: mRC = mRB = 0 m. However,pseudoranges in the blocked state are obtained by adding thedifference between the lengths of the two paths user-skyline­satellite and user-satellite for the appropriate azimuth to theassigned random value [15]. It should be noted that the aboverange model and the simplified model for multichannel GPSreceivers to be described next, which are absent from theprevious work [9] for obvious reasons, are essential to andhave been developed for the present study.

If the C/No ratio for a particular channel, previously abovethe threshold of 22 dBHz, drops below it, the simulation modelrecords this instant of time as the beginning of a loss-of-lockevent (temporary loss by the receiver channel of the ability totrack the code or the carrier of the corresponding GPS signal).It also assumes that the corresponding satellite becomesunavailable and that procedures to reacquire and track thesignal [1] are immediately initiated. Consistently withinformation from GPS receiver manufacturers, it assumes thatthese procedures can only be successfully performed andcompleted when the C/No ratio remains uninterruptedly abovethe threshold for one second. In other words, the end of theloss-of-lock event is only reached after a period of onecontinuous second without any drop of the C/No ratio belowthe threshold has been observed. To avoid missing levelcrossings of the C/No threshold between consecutivesimulation steps, C/No values are actually produced at every 20ms for all receiver channels. From the above receiverspecification, note that the number of GPS satellites availableto a user (that is, with elevations above 100 and C/N0 ratioabove the threshold for more than one continuous second) andthe duration of loss-of-lock events are random variables,observed during each simulation run.

Finally, the model collects information from all the GPSsatellite available to each user at the current simulation stepand determines the horizontal and the vertical position errors

(2)

(3)?

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2cr~

00]x f-e

OZ

8.686 v 00 ]«.:(v) =.ji; J-3e2n (Js 0 Z

2009 SBMOIIEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2009) 268

by solving the system of linear equations through the least-squares method [I]

lU,,, u l- 1 v.. III e"IIs,1U // 2 U l-2 UlI 2 .;.. :2= : :

(4)

u // N u l- N u lIN

In (4), N is the number of satellites available to the user atthe current simulation step; Ullk, UJ.k, UlIk are the components ofthe unit vector from the user to the kh available GPS satellite (k= 1,..., N) along or across the route, and upward, respectively;CII, C1., C,l> are the components of the position error for the user,in the same reference frame; eM is the offset of the user timebias, and Sk is the value of the range error along the path fromthe user to the kh available GPS satellite. The horizontal error

is defined by e; = (£/~ +£1r.It is seen that a user needs atleast four available GPS satellites to fix its position. Finally,parameters of interest from all the users update histograms.Note that the results in Section IV describe the average effectsof each of the routes to be specified on the propagationchannel, and not those observed by an individual user.

III. COMPARISON WITH M EASUREMENTS

To validate the model, its results have been compared withthose from measurements performed at the four fixed siteslocated on the campus of Pontificia Universidade Cat6lica doRio de Janeiro (PUC-Rio), centered at 22° 58' 44.25" S, 43°55' 13.00" Wand displayed in the Google Earth map of Fig. I.Site 1, on top of the Cardeal Leme Hall (CLH), is the highestwithin campus (58 m above ground), with visibility for allelevations above 10°. Site 2,36.9 m away from CLH, is locatedwithin a lightly-wooded area, with a conical clearing aroundzenith with an internal half-angle equal to 20°. Site 3 is located9.8 m away from CLH, across a narrow street and just outsidethe same wooded area. The GPS receiver was located 2 mabove ground at sites 2 and 3, below the tree canopies. Site 4 is1 m outside an office window on the seventh floor of KennedyHall (KH), 32 m above ground. The KH structure preventsvisibility for all elevations between azimuths 57° and 237°.

For each site, a path-state map has been generated using thedigital elevation model for the PUC-Rio 's campus, which alsoincludes information on all relevant buildings, as well asapproximate data on the wooded area. In combination with thefact that GPS satellites occupy the oS azimuth/elevation cellswith non-uniform probabilities, the path-state maps provide thefollowing probabilities for the occurrence of the states (C, S,B): (0.991, 0.000, 0.009), (0.040, 0.714, 0.246), (0.033, 0.436,0.531), and (0.430, 0.000, 0.570) for the four sites,respectively. Therefore, sites 1 and 2 are clearly dominated bythe C and S states, respectively, while the other two sites areunder mixed effects of different combinations of states.

The measurements used the Globalsat BU-353 GPSreceiver, connected to a laptop for data acquisition through a

USB interface connection port. This is a low-cost, 20-channelall-in-view tracking receiver, with two-dimensional root-mean­square position accuracy of 10m, based on the SiRFTechnology Star III GPS chipset and an active patch antenna,well suited for diversified consumer applications [16]. Itsupports the National Marine Electronics Association (NMEA)0183 protocol, outputting GGA, GSA, and RMC messagesevery second and GSV messages every five seconds [17].Initially, data were acquired at the four sites during 05 h 28min, 05 h 48 min, 4 h 49 min, and 07 h 28 min, respectively.The average latitude and longitude were determined for each ofthe four data sets and the differences from individual samplesused to estimate horizontal position errors. The maximumvalue of the SIN ratio was determined and fade values weredetermined, also by difference.

Figure I. Google Earthmap of PUC-Rio's campusand locationsofmeasurementsites

For every UTC, the position of each satellite listed incorresponding GSA message were determined, using quadraticinterpolation based on information provided in theInternational GNSS Service (lGS) file [11],[12] for the sameGPS day of the measurements. Next, the azimuth and elevationof the ray path from the site to the satellite were calculated.Whenever possible (that is, every five seconds), the calculatedresults were compared with the ones in the corresponding GSVmessage for quality control purposes only, with excellentagreement. For each site, a file containing multiple records wascreated and stored for further processing. Each record contains:(I) an UTC; (2) the corresponding number of satellites used inposition fixing; and (3) the corresponding list of PRN codenumbers, elevations, and azimuths. These files were used as theonly specification of the receiver under test in the simulationmodel of the GPS propagation channel described in Section II.This approach is similar to that by Aloi and Korniyenko [18],who utilized ranging information from a GPS receiver atmultiple epochs to generate independent position estimates intheir comparative analysis of navigation filters. Here, fade andranging information were supplied not by measurements , butonly by the simulation model, which was run for the timeperiod of the measurement at each site using the correspondingfile and map of path states previously described, as well asfixed parameters KR = - 4.2 dB; KL = - 13. 0 dB, mi, = - 10 dB,aL = 3 dB; ms = - 15.5 dB, as = 7.3 dB; aRC = 2 m; mRS = 0.14m, aRS = 6.5 m; and aRB = 6 m.

2009 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2009) 269

Figure 4. PartialGoogle Earthmaps of Irajaand Copacabanain Rio de Janeiro,as well as the selectedroutes

A total of 443 and 523 1.75 m-tall users are deployed with2-m spacing along the Iraja and Copacabana routes, withlengths equal to 884 m and 1044 m, respectively. For eachuser, a path-state map is generated as previously described. Thepath-state maps, in combination with the fact that GPSsatellites occupy the 0.5° azimuth/elevation cells with non­uniform probabilities, provide the following probabilities forthe occurrence of the states (C, S, B): (0.680, 0.070, 0.250) forIraja and (0.296, 0.008, 0.696) for Copacabana. Theseprobabilities indicate an inversion of the relative importance ofthe C and the B states, as well as a minor role for the S state,for the selected routes. It should be remarked that the role ofterrain is also secondary in the two selected areas. Eachsimulation run involved all the observers in one route and atotal of 604,800 steps, corresponding to the duration of 7 days,with I s between consecutive time steps, and used the samemodel parameters selected in Section III.

The dotted curves in Fig. 5 represent the conditional CDFsof the horizontal position errors eh for the same routes. It isinteresting to note that the CDF of the measured horizontalerror in downtown Detroit (MI) [18] indicates larger errors thanthese ones for the same probability values in the interval (0.0,0.9). For higher probability values, corresponding to eh > 60 m,the CDFs for Copacabana and downtown Detroit (M!) becomeincreasingly coincident. The continuous curves in the lowerpanel of Fig. 5 represent the probability that the horizontalposition can be fixed with an error less than the abscissa for theIraja and Copacabana routes. These curves have been obtainedfrom the corresponding dotted ones, in association with theprobabilities that positions can be fixed along the routes,respectively equal to 0.913 and 0.153. It should be observedthat, under the applicable U. S. Federal CommunicationsCommission regulations, wireless carriers are required to

Janeiro [19] have been selected for the study of the effects ofurbanized areas on the propagation channel of GPS. The mainfeatures of the two regions can be observed on the GoogleEarth maps displayed in Fig. 4. While Iraja is mainlycharacterized by one- to two-floor houses separated by yards,Copacabana is dominated by tall buildings that share acommon wall with their immediate neighbors to definecompact blocks and deep street canyons. The correspondingdata bases include three-dimensional vector information on12,946 and 8,831 buildings, respectively [19]. The heightdistributions of the buildings in Iraja and Copacabana [9] arehighly different: they show peaks at approximately 5 m and 45m, with average heights equal to 11.4 m and 39.7 m, andstandard deviations of 10.1 m and 13.3 m, respectively.

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In these Figures, measurement and simulation results arerespectively represented by full and hollow symbols(connected by continuous curves in the latter case). A goodagreement is observed between results from the same site,represented by the same symbol. It should be noted that thesimulation model is capable of reproducing the differencebetween the distribution of fades resulting from measurementsat sites 1 (essentially clear) and those from the other three sites,as well as the differences between the distributions ofhorizontal errors resulting from measurements at sites I(essentially clear), site 2 (essentially shadowed) and the othertwo sites (mixed).

IV. PREDICTIONS OF THE EFFECTS OF DIFFERENT

URBAN ENVIRONMENTS ON GPS POSITIONING

The regions of Iraja (22°50' 19"S 43°19' 18"W) andCopacabana (22°58' IO"S 43°11'09"W) in the City of Rio de

Figure2. Complementary cumulative distribution functions of measured(fullsymbols)and simulated(continuous curveswith hollowsymbols)fades for the

four sites

Figure 3. Complementarycumulative distribution functions of measured(fullsymbols)and simulated(continuous curveswith hollowsymbols)horizontal

errors for the four sites

1.000 __~..,...,., -;:."""""= ;:-0- - -,--- - -,--- - --.- - --,

The results from the measurements and the simulation runswere processed to estimate complementary cumulativedistribution functions of fades and horizontal position errors,displayed for all sites in Figs. 2 and 3, respectively.

1.000 I!:TII-ITII-IT-;:r:===~1

2009 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2009) 270

I. SUMMARY AND CONCLUSION

Figure 5. Conditional cumulative distribution functions of the horizontalposition errors (dotted curves) for the selected routes and probability that the

horizontal position can be fixed with an error less than the abscissa (continuouscurves)

,.-.-1-"

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! ---Copacabana Horizontal Nsat > 3 l-I

I--- Iraja Horizontal Nsat> 3 I-

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provide enhanced 911 (E911) Phase II Automatic LocationIdentification services according to specific standards. Forhandset-based technologies, 67 % and 95% of the callersshould be located with accuracies of 50 m and 150 m,respectively. The continuous curves indicate that a solutionentirely based on standalone GPS: (1) easily meets the firstcriterion and falls slightly short of meeting the second for theIraja route; and (2) significantly fails to meet both criteria forthe Copacabana route.

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Horizontal position error (m)

The results discussed in the previous sections haveindicated that the present simulation model is capable ofdetecting the effects of the degree of urbanization of differentregions on several channel parameters. In combination with thecomparison between measurement and prediction results, thisindicates that, by proper representation of the environmentthrough path-state maps and selection of parameters, thesimulation model may be a useful tool for studying andplanning GPS-based location and navigation applications withgood accuracy and sensitivity.

The simulation model has also estimated the probabilitiesthat the horizontal position can be fixed with errors less thanspecified values. The results have indicated that a GPSstandalone solution would easily meet the E911 accuracy of 50m for 67 % of the cases and would fall slightly short ofmeeting the accuracy of 150 m for 95 % of the cases for theIraja route. However, it would significantly fail to meet bothrequirements for the Copacabana route, making assisted-GPSor equivalent solutions [2]-[4] mandatory.

Finally, it should be remembered that several of theUTSFM parameters estimated by Klukas et al. [7] for urbanCalgary and Vancouver differ from the corresponding onesobtained here or by Akturan and Vogel [8] for Tokyo. Thiscould be taken as an indication that the set of UTSFMparameters may depend on the environment to some extent. Ithas been shown that the selection of parameters has a clearinfluence on the model results, also deserving further study.

ACKNOWLEDGMENT

The author thanks engineers Paulo Lerner and Pedro C. dosSantos (Pvlnova Ltda.) for providing the equipment used in themeasurements, as well as their expertise and time, Prof. LuizFernando Martha (Department of Civil Engineering, PUC-Rio)and technician Pedro Ramur (TEC Consultoria e ServicesLtda.) for providing PUC-Rio's digital elevation model, andtechnicians Rogerio S. Pereira and Marcelo N. Alves(CETUC/PUC-Rio) for their support during the measurements.

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[15) S. S. Wang and M. Green, "Mobile location method for non-line-of­sight situation," Proceedings of the 52nd IEEE Vehicular TechnologyConference 2000 , vol. 2, pp. 608-612, Boston, MA U.S.A. , Sep. 2000.

[16] http://www.globalsat.com.tw/eng/product detaiI 00000044.htm

[17] http://www.nmea.org/content/nmea standards/nmea 083 v 400 .asp

[18] D. N. Aloi and O. V. Korniyenko, "Comparative performance analysisof a Kalman filter and a modified double expon ential filter for GPS-onlyposition estimation of automotive platforms in an urban-canyonenvironment," IEEE Transactions on Vehicular Technology, vol. 56, no.5, pp. 2880-2892, Sep. 2007.

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2009 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2009) 271