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INTRODUCTION

Previous studies have examined GPS relativenavigation for spacecraft performing rendezvousand docking with the International Space Station(ISS) [1, 2]. However, these studies have notaccounted for degradation in GPS navigation per-formance due to multipath signals being reflectedoff the ISS or blockage of GPS signals by the ISS, asshown in Figure 1. Other studies have examined themultipath environment for GPS receivers on boardthe ISS using the uniform geometric theory ofdiffraction [3–5]. However, this approach is numer-ically intensive and not well suited to modeling arendezvous scenario.

The objective of this study is to analyze theseeffects on GPS navigation in the vicinity of the ISSusing simple models for GPS signal blockage andmultipath. In addition to predicting GPS navigationperformance in the vicinity of the ISS, these modelswere developed to predict the performance obtained

by combining various sensors, such as star trackersor inertial measurement units, with GPS fornavigation or attitude determination.

ISS SIGNAL BLOCKAGE MODEL

It has been hypothesized that the ISS will blockGPS signals needed by other spacecraft (referredto as chaser spacecraft or chasers) to navigateduring rendezvous operations. To analyze thiseffect, the GPS signal blockage due to the ISS ismodeled as a sphere centered at the ISS positionwith diameter d � 100 m.

Figure 2 depicts the various vectors used in themodel. The line-of-sight vector from the chaserspacecraft to the j-th GPS satellite can be found by

(1)

The line-of-sight vector from the chaser to the ISScan be found by

�ISS � rISS � r (2)

The GPS antenna of the chaser spacecraft isassumed to be pointed along the r vector; therefore,

�j � rGPSj� r

Effects of Multipath and Signal Blockageon GPS Navigation in the Vicinity ofthe International Space Station (ISS)

DAVID E. GAYLOREmergent Space Technologies, Inc., Greenbelt, Maryland

E. GLENN LIGHTSEYThe University of Texas at Austin, Austin, Texas

KEVIN W. KEYTitan Corporation, Houston, Texas

Received August 2004; Revised April 2005

ABSTRACT: Previous studies examining GPS relative navigation for spacecraft performing rendezvous withthe International Space Station (ISS) have not accounted for degradation in GPS navigation performance dueto multipath or blockage of GPS signals by the ISS. This study analyzes these effects on GPS navigation in thevicinity of the ISS. A simulation of a spacecraft GPS receiver operating near the ISS has been developed. Thissimulation includes orbit models for the GPS constellation, the ISS, and the spacecraft, as well as models forGPS signal blockage and multipath. The blockage simulation shows that aiding of GPS is required when thespacecraft approaches within 60 m of the ISS. The multipath simulation shows the expected trends in range errorsas a function of GPS satellite elevation angle, distance from the ISS, number of multipath rays, and the radarcross-sectional area of the ISS.

NAVIGATION: Journal of The Institute of NavigationVol. 52, No. 2, Summer 2005Printed in the U.S.A.

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the declination angle (�) between the antenna bore-sight and the line-of-sight vector can be found by

(3)

where r � �r� and � j � �� j�.The region of GPS signal blockage is defined by

a cone about the ISS line-of-sight vector. The centralangle of the cone, �, is determined by the radius of theblockage sphere and the distance from the chaser tothe ISS as follows:

(4)

where �ISS � ��ISS�.

tan(�) �d/2�ISS

cos�j �r��j

r��j

The angle between the GPS line-of-sight vectorand the ISS line-of-sight vector can be found by:

(5)

If the angle �j is less than �, the signal will be withinthe blockage cone and considered to be blocked.Additionally, any GPS signals below a 10 deg mini-mum elevation angle from the horizontal plane,which is perpendicular to the antenna boresightvector, are also considered to be blocked. A sideview of the GPS signal blockage model is shown inFigure 3. The shaded areas represent the regionswhere the GPS signals are blocked.

While the ISS is not actually a sphere, and GPSsignals will be received from within the sphere,it is likely that those signals will be corruptedby multipath. This multipath may be severeenough to warrant programming the GPSreceiver to ignore all GPS signals within the block-age cone.

ISS MULTIPATH MODEL

For spacecraft operating in the vicinity of theISS, GPS signals may be degraded by multipathsignals being reflected off the ISS. It is difficult tomodel the effects of these multipath signalsbecause the ISS is composed of several reflectivesurfaces, some of which are moving relative to theISS main body. Furthermore, the chaser spacecraftis moving relative to the ISS, and both are movingrelative to the GPS constellation. A geometricalmultipath model would have to account for eachreflecting surface and the relative motion amongthe ISS, the chaser spacecraft, and the GPS satel-lites. This would be computationally intensiveand not practical for use in some applications,

cos� j ��ISS �� j

�ISS �� j

62 Navigation Summer 2005

Fig. 1–ISS Blockage and Multipath Scenario

Fig. 3–GPS Signal Blockage Model

Fig. 2–Vector Definitions

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such as an integrated GPS/inertial navigationsystem (INS) navigation simulation of a ren-dezvous scenario. Therefore, a statistical multipathmodel was selected instead of a geometrical multi-path model.

The following assumptions are made in formulatingthis model:

● If a GPS signal is not blocked by the ISS, it issubject to multipath.

● For each GPS signal that is not blocked by theISS, many reflections are caused, and there isno dominant reflector.

● The phases of the reflections are uniformly dis-tributed over the interval [0, 2�). The rationalefor this assumption is explained later in thepaper.

● The relative velocity between the chaser space-craft and the ISS is small, so that there is nosignificant Doppler effect between the directand reflected signals.

According to [6], an electromagnetic signal mayreach an antenna by a single direct path or indi-rectly through one or more reflected paths. Thepresence of signals arriving at the antenna frommultiple reflected paths is called multipath.Because of the extra path length they travel, mul-tipath signals arrive at the antenna with a delayrelative to the direct signal. For GPS carrier-phasemeasurements, multipath signals combine withthe direct signal to distort the received phase.Assuming there are multiple reflections, eachreflected path has an associated propagation delayand attenuation factor. Both the propagationdelays and attenuation factors are time varying asa result of the relative motion and geometry of thevehicles.

Consider the transmission of an unmodulated car-rier at frequency fc. The transmitted signal can beexpressed as

(6)

The multipath channel consists of multiple paths orrays that have real positive gains k, propa-gation delays k, and phase shifts �k, where k is thepath index and in principle ranges from 0 to �. Thecomplex, low-pass channel impulse response isgiven as [7]

(7)

where �(�) is the Dirac delta function. The compositereceived signal is the time convolution of x(t) andh(t) and can be represented as [7]

(8)rc (t) � � k

A0 k e j2�fc(t� k) �k

h(t) � �k

k e j�k�(t � k)

x(t) � A0ej(2�fct)

If the direct path term is separated out and therange of k is limited to a finite number N of multi-path rays, the composite received signal becomes

(9)

If the direct signal phase is defined as �d � 2�fctand the multipath relative phase shift of the k-thray is defined as �k � 2�fck �k, then the receivedsignal can be expressed as

(10)

GPS Carrier-Phase Measurement Errors

The error in the carrier-phase measurement, ��,due to multipath, assuming the error is small, canbe approximated by [8]

(11)

where A0 represents the amplitude of the signaltransmitted by the GPS satellite. Factoring out A0

leaves

(12)

GPS C/A-Code Measurement Errors

The error due to multipath in GPS coarse/acquisi-tion (C/A)-code measurements for a noncoherentGPS receiver is described in [9]. An approximationof the code correlation function is

(13)

where T is the pseudorandom noise (PRN) code bitperiod. The normalized form of the discriminatorfunction with a single multipath ray is given by [9]

(14)

where is the delay lock loop (DLL) tracking error,� is the multipath relative amplitude, d is the timeadvance of the early code or time delay of the latecode (relative to the on-time code), m is the multi-path relative time delay, and �m is the multipath rel-ative phase angle. The corresponding to the zerocrossing of the discriminator function is the DLLtracking error caused by multipath, which is equal

� R( � d)R( � d m)] 2� cos(�m)[R( d)R( d m) �2[R2( d m) � R2( � d m)]

D() � R2( d) � R2( � d)

R () � �1 �� �T � � � T

0 � � � T

tan �� ��N

k�1k sin �k

0 �N

k�1k cos �k

tan �� ��N

k�1A0 k sin �k

A0 0 �N

k�1A0 k cos �k

rc (t) � A0 0 e j�d �N

k�1A0 k e j(�d �k)

rc (t) � A0 0 e j2�fct �N

k�1A0 k e j2�fc(t�k) �k

Vol. 52, No. 2 Gaylor et al.: Effects of Multipath and Signal Blockage on GPS 63

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in magnitude but opposite in sign to the rangingerror due to multipath.

This equation is extended in [10] to include theeffects of multiple multipath rays. In this case, thediscriminator function is given by

(15)

where

(16)

Conjectures

Some conjectures about the nature of multipathsignals have been made because limited spaceflightexperiment data are available. These conjecturesare based on existing terrestrial multipath modelsand measurements. Conjectures about the relativephase shifts, relative amplitudes, multipath powerdelay profile, and relative time delays are describedin this section.

Phase Shifts

The multipath relative phase angle �k changesby 2� when the path length changes by one wave-length. For the GPS L1 signal, fc � 1575.42 MHz,the wavelength is about 19 cm. This implies thatsmall motions of the reflector or receiver cancause �k to change by 2�. The delays associatedwith different paths are expected to change at dif-ferent rates and in an unpredictable or randommanner. If one considers a fixed transmitter and amobile receiver and imagines an ensemble ofreceiver positions spread over hundreds or thou-sands of wavelengths, then the geometry of asingle path with delay k will lead to a uniformdistribution of phase for that path, while the geo-metrical relationship between separate pathswith different delays will lead to a uniform jointdistribution of pairs of phases, so that the phaseswould be independent. Therefore, the phaseangles are assumed to be statistically independ-ent random variables with a uniform distributionover [0, 2�) [7].

Amplitudes

The received multipath signals can be modeled asrandom processes. When there is a large number of

�k �k

0

� R( � d k)R( � d l)][R( d k)R( d l)

Nk � 1�Nl � 1��k �l cos(�k � �l)

� R( � d)R( � d k)] 2Nk � 1��k cos(�k)[R( d)R( d k)

D() � R2( d) � R2( � d)

paths (in practice, greater than 6), the central limittheorem may be applied so that the received signal,rc(t), can be modeled as a complex-valued Gaussianrandom process [7]

The received signal can be broken down intoin-phase and quadrature components, I(t) and Q(t),which are independent Gaussian processes. Thismeans they are completely characterized by theirmean value and autocorrelation function. I(t) andQ(t) have equal variance �2 equal to the meansquare power. The total amplitude of the signal isthe square root of the sum of the squares of I(t) andQ(t), which are Gaussian. This leads to the conjec-ture that the amplitudes are Rayleigh distributed.Therefore, the k’s are Rayleigh distributed suchthat

(17)

where � the average power gain at k [11].

Power-Delay Profile

The multipath power-delay profile for a givenenvironment is the expected power received as afunction of delay. Numerous measurements of themultipath power-delay profile for various environ-ments have been made, such as those in [12] and[13]. Based on these studies, a general model ofthe multipath average power-delay profile can begiven as [14]

(18)

where is the mean excess delay of the multipathreflections, and P0 is the total multipath power. Thetotal multipath power is estimated by using thebistatic radar equation

(19)

where �ISS is the distance from the spacecraft to theISS, rGPS/ISS is the distance from the ISS to the GPSsatellite, ARCS is the radar cross-sectional area of theISS, � is the wavelength, is the antenna gainof the receiver in the direction of the multipath, andPtGt is the effective isotropic radiated power fromthe GPS satellite.

The average power in each multipath signal is

(20)

Equating this with equation (18) and solving for leads to

(21)�k2 �

2P0

A20

e��

�2k

P�k �12

A20

�2k

Gmpr

P0 �ARCS �

2Gmpf PtGt

(4�)3�ISS2r2

GPS/ ISS

�

P�() � P0 e��

�2k

p(2k) �

1

2k

e��2k�

�2k�

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Substituting equation (19) into equation (21) andrecognizing that A0

2 � 2PtGt results in the followingexpression:

(22)

Since the multipath rays are being reflected off theISS, the mean excess delay is approximated by

(23)

where c is the speed of light. The power of the directsignal is estimated by using the Friis equation:

(24)

Since A02 � 2PtGt,

(25)

If a cardioid pattern antenna is used, then

(26)

where �direct is the angle between the direct line-of-sight vector and the antenna boresight vector.Substituting equation (26) into equation (25) leads to

(27)

Delay Times

The mean excess delay and root mean square(RMS) delay spread are commonly used to charac-terize multipath time delays. The parameters aredetermined from a multipath power delay profile.The mean excess delay is the first moment of thepower delay profile and is defined as [15]

(28)

In [16], it is proposed that the delay times form aPoisson sequence. The probability distribution oftime delays is given by [17]

(29)

Multipath Model Algorithm

The algorithm for calculating the multipath errorfor each GPS measurement is as follows:

1. For each simulation time and each GPS satel-lite, compute r, rGPS/ISS, and �direct.

2. Compute �0 using equation (27) and usingequation (23).

��

p(�k) �1��

e�

�k

�–

����k

�2k �k

��2k

k

�0 � √ �2(1 � cos �direct)(4�j)2

Gdirectr � 1 � cos �direct

�20 �

�2Gdirectr

(4�rGPS/STS)2

Pdirect �12

A20 �

20 �

�2Gdirectr PtGt

(4�j)2

�� �ISS

c

�2k(�) �

ARCS �2Gmp

r

(4�)3ρISS2r2

GPS/ ISSe����

3. Given N, obtain the �k’s from the Poisson dis-tribution given in equation (29).

4. For each �k:a. Given ARCS, compute using equation (22).b. Obtain the �k’s from the Rayleigh distribu-

tion given in equation (17).c. Obtain the k’s from a uniform distribution

over [0, 2�).d. Construct �k sin k and �k cos k

5. Determine the carrier-phase range error fromequation (12).

6. Determine the code range error from equa-tion (15).

SIMULATION ORBIT MODELS

The orbit models used for the simulation of theGPS constellation, ISS, and chaser spacecraft arepresented in this section.

GPS Constellation Model

A model of the GPS constellation was constructedfrom a daily global broadcast ephemeris file in theReceiver Independent Exchange (RINEX) formatdownloaded from the National Geodetic Survey(NGS) Continuously Operating Reference Stations(CORS) website. This file contains the GPS broad-cast ephemeris parameters for each satellite in theconstellation for March 1, 2001. There were a totalof 28 satellites in the active constellation. Theephemeris parameters and the equations used todetermine the positions of the GPS satellites ata given time are described in the [18]. This GPS con-stellation model was used for all simulations in thisstudy.

ISS and Chaser Spacecraft Orbit Models

The ISS orbit model was an unperturbed two-bodyorbit with orbit elements presented in Table 1. Todetermine the GPS signal blockage, the chaserspacecraft was positioned so that it remained at aconstant distance �r directly below the ISS along theradius vector from the center of the earth to the ISS.�r was varied for each simulation run to determinethe GPS signal blockage and multipath effects at dif-ferent distances below the ISS. While this does notrepresent a rendezvous scenario, it allows a largenumber of samples to be collected over the course ofthe simulation while maintaining the same geome-try relative to the ISS. Another reason for placing thechaser at various distances below the ISS is to eval-uate the blockage at different points during an R-barapproach in which the chaser approaches the ISSalong the earth to the ISS radius vector.

��2k

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Table 1—ISS Orbit Elements

Element Value

a 6678.0 kme 0.005i 56.0 deg

ISS BLOCKAGE STUDY RESULTS

The results of the computer simulation developedto study the GPS signal blockage due to the ISS arepresented in this section.

Two kinds of GPS receivers were modeled. The firstwas an all-in-view receiver that is able to track all vis-ible GPS satellites with no delay in acquisition andtracking of a satellite as soon as it becomes visible. Thesecond was a 12-channel receiver programmed to trackthe twelve highest-elevation space vehicles (SVs). Forthis receiver, it was also assumed to have no delay intracking a satellite as soon as it becomes visible.

The simulation was run over a time span of 1 day,with samples taken once/s for the following values of�r: 10, 20, 30, 40, 50, 60, and 100 m. At each point intime, the number of visible GPS satellites wasrecorded and analyzed. Whenever fewer than fourGPS satellites were visible, this was considered tobe an outage. The data collected on outages for theall-in-view receiver are summarized in Table 2.

The data show that at least four GPS satellites werein view at all times when the chaser was 100 m ormore below the ISS. At 60 m below the ISS, there werefewer than four satellites in view for a small percent-age of the time, but the average outage was over 102 slong. The amount of blockage increased as the chaserwas brought closer to the ISS.When it was 10 m belowthe ISS, no GPS position fixing was possible. Theseresults suggest that aiding of GPS is needed when achaser spacecraft is within 60 m of the ISS.

The 12-channel receiver results were almostidentical to the all-in-view receiver results. Theonly difference was that the number of satellitesbelow the horizon mask was higher for the all-in-view receiver. Therefore, the number of visibleGPS SVs for a 12-channel receiver programmed toselect the 12 highest-elevation SVs was the same asfor an all-in-view receiver.

MULTIPATH STUDY RESULTS

The multipath model described in this paper wasadded to the ISS signal blockage simulation. Thecarrier-phase and code-range errors for each channelof an all-in-view GPS receiver were computed and con-verted to meters. Time histories for the carrier-phaseand code-range errors for channel 1 of this receiverwere computed for various values of �r to determinethe behavior as the chaser approaches the ISS. Thevalues of N and ARCS were also varied to determine thesensitivity to these two model tuning parameters. d

was one-half of the C/A-code chip period. The errorswere computed and recorded once/s for 3600 s.

Geometry Dependence

The errors due to multipath are dependent on theGPS satellite geometry because a stronger direct sig-nal is less susceptible to multipath. Higher-elevationsignals are stronger because the receiving antennagain is higher, and the GPS satellite is closer to thereceiver. Both of these effects are accounted for inequation (27).

The time history of carrier-phase and C/A-coderange errors and the corresponding direct signal ele-vation angles are shown in Figure 4. As expected,the magnitude of the range errors increases as thedirect signal elevation decreases.

66 Navigation Summer 2005

Table 2—GPS Signal Outage Statistics (all-in-view receiver)

Meters % Outage Max. Outage Avg. Outage Below ISS Duration (s) Duration (s) Duration (s)

10 99.99 58059.0 43197.020 85.85 2111.0 501.230 42.04 1119.0 167.440 12.79 602.0 107.350 4.92 389.0 103.660 2.38 249.0 102.8

100 0.0 0.0 0.0Fig. 4–Range Errors and Direct Signal Elevation Angles

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Distance from ISS

It is expected that the range errors due to multi-path will increase as the spacecraft approaches theISS. This effect is evident in the time histories ofcarrier-phase and C/A-code range errors at 50, 100,and 200 m below the ISS, as shown in Figures 5and 6, respectively.

Number of Multipath Rays

One of the model parameters is the number ofmultipath rays per GPS signal. The number ofreflected rays would be expected to increase as moremodules, solar arrays, and thermal radiators areadded to the ISS. It is expected that the range errorsdue to multipath will increase as the number ofmultipath rays (N) increases. This trend is seen inthe time histories of carrier-phase and C/A-coderange errors at 100 m below the ISS shown inFigures 7 and 8, respectively.

ISS Radar Cross-sectional Area

The ISS radar cross-sectional area is another modelparameter. It acts as a scaling factor on the totalreceived multipath power and can be used to accountfor the reflective properties and size of the various ISS

structures. The radar cross-sectional area would beexpected to increase as more modules, solar arrays,and thermal radiators are added to the ISS. The rangeerrors due to multipath are expected to increase as theISS radar cross-sectional area (ARCS) increases. Thiseffect is seen in the time histories of carrier-phase andC/A-code range errors at 100 m below the ISS inFigures 9 and 10, respectively.

Model Tuning

The following parameters can be used to tune themultipath model: the ISS radar cross-sectional area,the number of multipath reflections per direct signal,and the direct signal antenna gain. As more modules,solar arrays, and thermal radiators are added to theISS, its radar cross-sectional area and the number ofmultipath reflections are expected to increase.Therefore, the multipath model can readily adjust tothe changing configuration of the ISS over time.

CONCLUSIONS

Models of the GPS blockage and multipath effectsnear the ISS have been developed. These modelshave been incorporated into a simulation to show

Vol. 52, No. 2 Gaylor et al.: Effects of Multipath and Signal Blockage on GPS 67

Fig. 5–Carrier-Phase Range Errors at 50, 100, and 200 m belowthe ISS

Fig. 6 – C/A-Code Range Errors at 50, 100, and 200 m belowthe ISS

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how GPS signal blockage and multipath impactGPS navigation in the vicinity of the ISS. The block-age simulation shows that aiding of GPS is neededwhen the spacecraft approaches within 60 m of theISS. The multipath simulation results show theexpected trends in the range errors as a function ofthe GPS satellite elevation angle, the distance fromthe ISS, the number of multipath rays modeled, andthe radar cross-sectional area of the ISS. Botheffects may significantly degrade GPS navigationnear the ISS. These models can be used to predictthe performance obtained by combining various sen-sors with GPS for navigation or attitude determina-tion for spacecraft operating near the ISS or someother large reflecting body.

After consulting with engineers at the NationalAeronautics and Space Administration’s (NASA)Johnson Space Center, it was determined that thedata needed to validate the ISS blockage and multi-path models do not currently exist. Therefore, thevalues of the tuning parameters used in the multi-path study were chosen based on anecdotal experi-ence, not empirical data.

Since engineers are currently designingautonomous rendezvous and docking systems for theISS using GPS, it is recommended that a flightexperiment to determine the levels of GPS signal

blockage and multipath for pseudorange and carrier-phase measurements near the ISS be flown as soonas possible.

FUTURE WORK

The next logical step is to validate these modelswith actual flight data. If appropriate flight datacannot be found, the results of this paper could beused to justify a future flight experiment. It mayalso be possible to compare these results with datafrom other existing simulations. The conjecturesthat lead to the multipath model presented herehave been used in developing statistical multipathmodels for wireless communication systems in thepast [15]. However, the multipath environment nearthe ISS has not yet been characterized by experi-mental data.

If the multipath average power-delay profile,excess time delays, and delay spread were measuredduring a flight experiment as described in [12], theapproximations from the Friis and bistatic radarequations could be replaced by curve fits. The aver-age time-delay approximation could also be replacedby a measured value.

68 Navigation Summer 2005

Fig. 7–Carrier-Phase Range Errors with Various Numbers ofMultipath Rays Fig. 8 – C/A-Code Range Errors with Various Numbers of

Multipath Rays

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Alternatively, if GPS measurements and a veryaccurate reference trajectory (with errors smallerthan the predicted multipath errors) were availablefrom a flight experiment, it should be possible toadjust the number of multipath rays and ISS radarcross-sectional area to match the measured multi-path-induced range errors.

A very simple GPS receiver model was used inthis study. Most if not all commercially availableGPS receivers smooth the pseudorange measure-ments using carrier-phase aiding, carrier smooth-ing, or both. This study yielded pseudorange andcarrier-phase errors due to multipath with nosmoothing applied. The analysis of multipath miti-gation by the use of smoothing and other tech-niques is another suggested topic for future research.

ACKNOWLEDGMENTS

This research was partially funded by the NSTLRelative Navigation Support Grant (NAG9–1189)from the Navigation Systems and TechnologyLaboratory at NASA Johnson Space Center.

The results presented in this paper were producedusing software from the Java AstrodynamicsToolkit, an open source software library available onthe Internet at http://jat.sourceforge.net.

REFERENCES

1. Ebinuma, T., R. Bishop, and E. G. Lightsey, SpacecraftRendezvous Using GPS Relative Navigation, PaperNo. AAS 01–152, AAS/AIAA Spaceflight MechanicsMeeting, Santa Barbara, CA, February 2001.

2. Um, J., Relative Navigation and Attitude Deter-mination Using a GPS/INS Integrated SystemNear the International Space Station, Ph.D.thesis, The University of Texas at Austin, December2001.

3. Gomez, S. and S. Hwu, Comparison of Space ShuttleGPS Flight Data to Geometric Theory of DiffractionPredictions, Proceedings of The Institute ofNavigation’s ION GPS-97, September 1997.

4. Hwu, S., B. Lu, J. Hernandez, R. Panneton, S. Gomez,and P. Saunders, A New Modeling Approach forSpace Station GPS Multipath Analysis IncludingDynamic Solar Panel Movements, Proceedings of TheInstitute of Navigation’s National TechnicalMeeting, 1997.

5. Byun, S., G. Hajj, and L. Young, Assessment of GPSSignal Multipath Interference, Proceedings of TheInstitute of Navigation’s National Technical Meeting,2002.

6. Comp, C., GPS Carrier Phase MultipathCharacterization and a Mitigation Technique Usingthe Signal-to-Noise Ratio, Ph.D. thesis, University ofColorado, July 1996.

Vol. 52, No. 2 Gaylor et al.: Effects of Multipath and Signal Blockage on GPS 69

Fig. 9–Carrier-Phase Range Errors with Different ISS RadarCross-sectional Areas

Fig. 10–C/A-Code Range Errors with Different ISS Radar Cross-sectional Areas

46010_02_p61-70 10/4/05 5:06 PM Page 69

7. Proakis, J., Digital Communications, J. Wiley & Sons,New York, NY, 1989.

8. Axelrad, P., C. Comp, and P. MacDoran, SNR-BasedMultipath Error Correction for GPS Differential Phase,IEEE Transactions on Aerospace and ElectronicSystems, Vol. 32, No. 2, April 1996.

9. Braasch, M., Multipath Effects, Global PositioningSystem: Theory and Applications, Vol. 1, Chapter 14,AIAA, 1996, pp. 547–68.

10. Mora-Castro, E., C. Carrascosa-Sanz, and G. Ortega,Characterisation of the Multipath Effects on the GPSPseudorange and Carrier Phase Measurements,Proceedings of The Institute of Navigation’s IONGPS-98, September 1998.

11. Saleh, A. and R. Valenzuela, A Statistical Model forIndoor Multipath Propagation, IEEE Journal onSelected Areas in Communications, SAC-5, No. 2,February 1987.

12. Van Rees, J., Measurements of the Wide-Band RadioChannel Characteristics for Rural, Residential andSuburban Areas, IEEE Transactions on VehicularTechnology, VT-36, February 1987.

13. Belloul, B., S. Saunders, M. Parks, and B. Evans,Measurement and Modelling of Wideband Propagationat L- and S-bands Applicable to the LMS Channel,IEEE Proceedings: Microwave Antenna Propagation,Vol. 147, No. 2, April 2000.

14. Van Nee, R., Multipath Effects on GPS Code PhaseMeasurements, NAVIGATION, Journal of TheInstitute of Navigation, Vol. 39, No. 2, 1992.

15. Rappaport, T., Wireless Communications: Principlesand Practice, 2nd Edition, Prentice-Hall, Inc., UpperSaddle River, NJ, 2002.

16. Turin, G., F. Clapp, T. Johnston, S. Fine, and D. Lavry,A Statistical Model of Urban Multipath Propagation,IEEE Transactions on Vehicular Technology, VT-21,No. 1, February 1972.

17. Lee, W., Mobile Communications Design Funda-mentals, Howard W. Sams & Co., Indianapolis, IN,1986.

18. GPS Program Office, NAVSTAR GPS SpaceSegment/Navigation User Interfaces, Technical ReportICD-GPS-200, ARINC Research Corporation,Fountain Valley, CA, 1997.

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