Synthetic Aperture GPS Signal Processing

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Synthetic aperture techniquescombine data obtained rommultiple sensors or one sen-sor moving among multiple

locations, or both to construct asingle image. hese techniques havebeen widely researched, developed, andapplied in the area o radar systems.

his article discusses eorts toextend synthetic aperture concepts toGPS signal processing, exploiting thebeam steering capabilities o syntheti-cally generated phased array antennas.In it, we will describe the ast Fouriertransorm (FF)based method used tosimultaneously steer a synthetic arrays

beams in multiple directions. We willalso discuss the results o simulator and

ight tests to demonstrate the ecacy osynthetic beam steering techniques orGPS antennas.

Development o GPS-based SARs

will enable high-resolution imagi ngcapabilities using passive receivers oGPS signals and allow 24-hour globalavailability o imaging technology. Itrepresents a dual-use technology thatcould support military applications suchas imaging o military ground eet hid-den under oliage, as well as humani-tarian applications such as detection ounexploded ordnance.

GPSSAR:ThCocpt

Large synthetic apertures allow or pro-ducing very narrow array beams. Tese

Sthtc apt

GPS Sg PcssgCcpt d Fsbt Dstt

Most people relate to GNSS as a technology for positioning, navigation, and timing.

However, space weather researchers have already demonstrated the use of GPS as

a useful sensor for studies of the Earths atmosphere. This article introduces the

concept of applying synthetically generated, phased-array antennas for processing

GPS signals to create large antenna apertures. In turn, the narrow-beam generationcapabilities of synthetic apertures can be used to mitigate interference and jamming

and for producing high-resolution radar images passively using received GPS signals

which raise the possibility of some interesting civil and military applications.

anDrey Soloviev

University of florida

Frank van GraaS,

Sanjeev GunawarDena

ohio University

mikel miller

air force research laboratory

Aerial view o a transporter-

erector-launcher vehicle covered

with camoufage netting, during

ground launch cruise missile (GLCM)

evaluation.

DoDPhotobyMSGTPaulN.

Hayashi


2/1238 InsideGNSS m a y / j u n e 2 0 0 9 www.insidegnss.com

narrow beams aresteered in desireddirections usingGPS signal process-

ing techniques.As shown in Fig-r 1, an array beamcan be steered in thedirection o a GPSsatellite to mitigatethe eects o radiorequency interer-ence and jammingsignals that are orig-inating rom direc-tions other than the

satellite. Steering the array beam towards reecting objects torecord high-resolution radar images provides the oundationor the development o GPS-based synthetic aperture radars(SARs).

An important consideration in using GPS-based SAR isthat large synthetic arrays are generated with small physi-cal antennas utilizing platorm motion and/or multiplatormintegration. As a result, the physical size o the antenna doesnot act as a limiting actor. Tis, in turn, enables miniatur-ization o the technology or applications on small platormssuch as mini-autonomous aerial vehicles (UAVs) and micro-UAVs.

Phased array antennas have been widely employed orantenna beam steering. In a phased array, phases o individualantennas are adjusted to maximize the array gain in a desireddirection, while increasing the array size narrows the arraybeamwidth. Figr 2 illustrates beam steering in the case o aone-dimensional (1D) array.

In the GPS domain, beam-steering techniques both ana-log beam steering and digital have primarily been exploitedto mitigate intererence.

HardwarvrssSoftwarGPSIn designing our phased array, we needed to decide whether to

implement an architecture with a hardware or soware GPSreceiver.

A hardware-based construction has several limitations. Forinstance, an increase in the physical size o the array is requiredto narrow its beamwidth. Moreover, adjusting the phases oindividual antennas in hardware constrains the systems capa-bility to simultaneously generate multiple beams that can be

used, or example, to track multiple satellites or to simultane-ously track both direct and reected (multipath) signals.o overcome these limitations, we propose a synthetic array

generation scheme that uses a soware GPS receiver architec-ture. Instead o adding new antennas to the array, the beam isnarrowed by exploiting antenna motion that is, the array issynthesized by observing an antenna at dierent locations overtime. Figr 3 and Figr 4 illustrate this principle or 1D andtwo-dimensional (2D) array cases, respectively.

Generation o synthetic GPS antenna arrays is conceptuallysimilar to synthetic aperture radar, where antenna motion is

FIGURE 1 Applications o synthetic aperture GPS signal processing

FIGURE 2 Beam steering with a one-dimen-sional phased array: phase delays are appliedto individual antenna outputs to steer thebeam in the direction o0, the beam width isinversely proportional to the number o arrayelements (N)

FIGURE 3 Synthetic generation o a one-dimensional phased array: anincoming GPS signal is down-sampled by the GPS receiver RF ront-end;signal samples that correspond to dierent spatial antenna locationsare combined to generate a synthetic phased array; phases o individualsamples are adjusted to steer the arrays beam in the direction o theincident angle o the GPS satellite signal 0.

FIGURE 4 Synthetic generation o a two-dimensional phased array:Physical one-dimensional (1D) arrays are used to steer the beam inthe rst dimension (beam direction is collinear to the planar suracethat is perpendicular to the direction o platorm motion); 1D arrays atdierent spatial locations are applied or beam steering in the seconddimension (beam direction is collinear to the planar surace that isparallel to the direction o motion); measurements o individual anten-nas are combined or phased array processing. Note that the 1D physicalantenna arrays can be implemented on a single platorm or can exploit

multi-platorm implementations such as multiple autonomous aerialvehicles (UAVs).

Synthetic beam steering(interference and jamming mitigation)

GPS-based synthetic apertureradar (passive imaging)

Synthetic apertureGPS signal processing

Jammer Antenna

beam

Antennabeam

GPS satellite

GPS satellite

Synthetic apertureGPS signal processing

Antennaoutput

Antenna beam

d d

phase delayd cos(

0)

phase delay2d cos(

0)

phase delayNd cos(

0)

0

~1

N

Incoming GPS signal S(t)

S(T0)

Antennaoutput

S(T1) S(T2) S(TN)

d d

phase delayd cos(

0)

phase delay2d cos(

0)

phase delayNd cos(

0)

RFfront-end

RFfront-end

RFfront-end

RFfront-end

Phased arraysignal processing

d d

RFfront-end

RFfront-end

RFfront-end

RFfront-end

SynTHeTiCAPeRTuRe



used to increase the antenna aperturein order to increase the azimuth resolu-tion.

Te synthetic array generation needsto operate with signal samples. In par-

ticular, samples that are taken a certaindistance apart (generally, a hal-wave-length apart: d=/2) must be combined.Hence, we use a soware-defned GPSreceiver to generate a synthetic phasedarray antenna.

Te soware receiver approach alsoallows the generation o multiple beamsthat are steered in dierent directions.Instead o hardware phase adjustments,a phase o a signal sample is adjusted tomaximize the gain in a given direction

(as seen in Figure 3).As a result, multiple beams can begenerated simultaneously by applyingdierent sequences o phase shis to thesame set o signal samples. Tis simulta-neous steering in dierent directions canbe used, or example, or simultaneoustracking o direct and reected signalssuch as urban and ground multipathreections.

In the remainder o this article, wewill irst summarize previous eorts

in the area o synthetic aperture GPSsignal processing. Ten we will discussthe principles o FF-based multi-direc-tional beam steering and how we appliedthem to develop signal processing tech-niques or synthetic phased array GPSantennas.

Finally, we describe the simulationand live data test results used to veriythe beam steering methods that we havedeveloped. In particular, we apply actualight data and ground data to demon-

strate the operation o 1D and 2D syn-thetic phased GPS antenna arrays.

Simulated data are exploited to dem-onstrate the use o 2D synthetic phasedarrays or simultaneous tracking odirect and multipath signals. We alsouse simulated data to demonstrate GPS-based SAR imaging.

earlrWorkTe concept o synthetic aperture signalprocessing or GNSS signals has been

previously considered in both the navi-gation domain, and in the area o radar

systems. (For a discussion o the ormerprinciple, see in particular the papersby A. Broumandan et alia, S. Draganovet alia, and . Pany et alia cited in theAdditional Resources section near the

end o this article. For a discussion othe latter, see the paper by M. Chernia-kov et alia.)

In the navigation domain, theseearlier papers describe synthetic aper-ture GPS signal processing or a singleantenna case as well as the exploitationo circular antenna motion to synthesizea circular phased array.

In the work described by A. Brou-mandan et alia, a synthetic phasedarray is applied or intererence mitiga-

tion while the paper by . Pany et aliadiscusses the application o the circularsynthetic array to suppress multipath.S. Draganov et alia discuss the use othe synthetic aperture technique by the

ultra-tightly coupled GNSS/INS archi-tecture to mitigate multipath.In their paper, Cherniakov et alia dis-

cuss the use o GLONASS signals romthe Russian GNSS system as signals oopportunity or bi-static synthetic aper-ture imaging. here, antenna motionis utilized to achieve high-resolutionimaging capabilities in the direction omotion. he cross-track resolution isachieved through use o the GLONASSprecision (P)-code, based on publicly

available technical specifcations, whichprovides a ranging resolution o about30 meters.

Tis art icle extends synthetic aper-ture GPS signal processing or thosecases in which multiple GPS antennas areused. Antenna motion is used to synthe-size one-dimensional phased arrays. Asindicated in Figure 4, the second dimen-sion is added (synthesized) through thecombining o signals received by mul-tiple antennas mounted perpendicular

to the direction o motion.We will introduce a computationally

ecient 2D FF-based signal processingalgorithm to simultaneously steer thearray beam in multiple directions. Assuggested previously, the array beam canbe steered towards reecting objects to

record high-resolution SAR images withGPS signals.For GPS-based SAR, the range-based

resolution o the cross-track image com-ponent is limited by the duration o thechip o the pseudorandom rangingsequence: 300 meters or the C/A-codeand 30 meters or the GPS P-code.

Focusing the array beam using mul-tiple antennas that are mounted per-pendicular to the direction o motionto resolve the cross-track component

improves the cross-track image reso-lution beyond the C/A or P-code chipduration. Te approach especially bene-fts cases where the multiplatorm signalintegration can be applied to construct

large array apertures in the cross-trackdirection.

FFT-BasdMlt-DrctoalBamStrgAs reported by M. I. Skolnik (see Addi-tional Resources), FF-based multi-directional beam steering techniqueshave been previously employed or radarapplications. In our work described here,we adopted these techniques to developcomputationally ecient methods or

multi-directional beam steering o syn-thetic GPS antenna arrays.

Te FF-based beam steering tech-nique processes synthetic phased arraydata to construct a GPS signal image inwhich each image pixel contains signalparameter inormation correspondingto a signal that is received rom a par-ticular steering angle. Figr 5 illustratesthe FF-based signal image constructionor the 2D antenna array.

Each cell o the 2D FF requency

grid corresponds to a particular 2Dsteering angle, where the correspon-

Focsgtharrabamsgmltplatasthatarmotdprpdclartothdrctoofmototorsolvthcross-trackcompotmprovsthcross-trackmagrsoltobodthC/AorP-codchpdrato.



dence between requency and angles is defned by the antennasize and FF parameters. (We will present detailed equationslater in this section.)

Essentially, the FF-based approach provides a signal imagethat is similar to the one constructed by a digital photographiccamera: each pixel in the image is defned by the intensityo the signal that is received rom the angular direction asso-ciated with this pixel. In the case o multi-directional beamsteering, the pixel intensity is represented by a post-correla-tion complex amplitude that contains the in-phase (I) value(real part o the complex amplitude) and quadrature (Q) value

(imaginary part o the complex amplitude).Tis signal image can be used to identiy and process mul-

tiple signal sources that may include direct signals, intererencesignals, and multipath reections. Hence, this image can beapplied to simultaneously track multiple signal sources suchas direct signal and multipath reections.

Te ollowing section describes the principles o FF-basedmulti-directional beam steering or synthetic GPS antennaarrays.

FFTforMlt-DrctoalBamStrgo steer a phased array in the angular direction o

0(see Figure

2), phases o individual antennas are adjusted by , which isdefned as ollows:

where R is the absolute value o the distance between the cur-rent antenna and the frst antenna o the array.

For the physical array case, R is the distance between anten-

nas:

In (2), m is the antenna index number within the array(starting with index zero or the frst antenna) and d is thedistance between two adjacent antennas (see Figure 2).

For the synthetic array case, R is the antenna displacement,as ollows:

where R is the displacement vector and || is the absolutevalue.

Beam steering is perormed by multiplying samples S o theincoming signal by a complex exponential:

he array output is then ormed by adding individualantenna outputs:

In (5), Sm is the output o the mth

antenna, M is the num-ber o antennas in the array, and d=/2 is normally chosen toavoid beam ambiguities (i.e., a creation o multiple beams inthe angular range rom 0 to 180 degrees).

For d=/2, equation (5) is modifed as ollows:

Te antenna beam can be steered simultaneously in multi-ple directions i we use the FF mechanism to implement equa-tion (6). FF harmonic requencies can be chosen to satisy thedesired steering angular range and angular resolution.

For the case o a physical antenna array, the use o the FFinstead o summation transorms single-direction steering intomulti-directional steering as ollows:

where {k} are steering angles and k is the FF requency

index.Note that k is changing rom 0 to M/2 and not rom 0 to

M-1. Tis is due to the act that the FF spectrum amplitudeswith the index numbers M/2+1 to M are complex conjugates othe spectrum amplitudes with the index numbers 1 to M/2-1.

Consequently, the ormer do not provide any new inormationand are not considered.

Signal imageNormalized signal power

Angular grid

FFT frequency grid

mapping(defined by FFT

parameters)

Elevation, deg Azimuth, deg

pixel

angular cell

2

1.5

1

0.5

0180

150120

9060

300 0

3060

90120 150

180

FIGURE 5 FFT-based multi-directional beam steering: In this simulation, a2D GPS signal image contains the received direct signal and a multipathrefection; each image pixel corresponds to a particular 2D steeringangle derived rom the FFT requency grid; multiple signal sources (suchas direct and multipath signals) can be identied and processed basedon the signal image.

SynTHeTiCAPeRTuRe



From equations (6) and (7), the FF spectrum amplitudeor the kth requency harmonic is defned as ollows:

On the other hand, this spectrum amplitude can be relatedto the amplitude o the phased array that is steered in the direc-tion o

k:

From equations (8) and (9):

or:

Equation (11) defnes mapping o the FF requencies intosteering angles or multi-directional beam steering. Tus, theFF that is applied to outputs o individual antennas generatesmultiple beams that are steered in dierent directions. Tesesteering directions are defned by the initial steering angle

0

and FF harmonic requencies as specifed by equation (11).o steer multiple beams within the angular range rom 0 to180 degrees, the FF is frst applied or

0= 0

Tis provides beam steering in the angular range rom 0 to90 degrees. o extend the steering angles to the range rom 90to 180 degrees, the second FF is applied or

0= /2

Hence, a complete FF-based multi-direction beam steer-ing procedure combines FF outputs or initial steering angleso 0 and 90 degrees:

FFT-BasdSthtcBamStrgforGPSAtasFigr 6 illustrates an FF-based multi-direction beam steeringmethod or the synthetic array case.

First, batches o signal samples are ormed in such a waythat the spatial distance between frst samples in the adjacent

batches is d.Second, FFs are applied to samples that have the sameindex number within dierent batches: or example, to frstsamples o each batch, second samples o each batch, and soon. Te total number o FFs required equals P; where P is thenumber o samples in the batch.

Tird, FF results are added together to improve the sig-nal-to-noise ratio (SNR) or the received GPS signal. Te FFaddition operation in the synthetic array case is equivalent tothe incoming/replica signal correlation in the conventionalGPS receiver architecture. Addition o FF outputs orms theoutput o the synthetic phased array.

o reduce the computational load, the number o signalsamples in the batch can be reduced using averaging. In caseswhere P4 and d=/2, distortions associated with this averag-ing have negligible inuence on the FF-based multi-direc-tional beam steering.

We should note that GPS carrier phase tracking must bemaintained or phased array antenna ormation. Coherent sig-nal accumulation over the entire synthetic aperture is requiredto maintain carrier phase tracking capabilities.

o support coherent signal accumulation, down-sampledGPS signals must be compensated or changes in the carrierphase due to intermediate requency (IF) variations and sat-

ellite motion as well as or changes in the code phase o thepseudorandom code sequence (PRN). Equation (15) providesthe corresponding compensation expression or satellite j:

where:t

nis the discrete time within the current aperture

accumulation interval: , tn = t0 + n t, t is the timediscrete o GPS signal down-sampling;

Signalsamples

FFT1

FFT2

FFTP

Synthetic

array output

d d

FIGURE 6 FFT-based beam steering or the synthetic array case



IF

is the intermediate requency, which is the requency odown-conversion o the incoming GPS signal to baseband;R

SVj(t

n) is the increment in the satellite/receiver range (or

the line-o-sight LOS increment) that is due to satellitemotion;

L1 is the wavelength o the GPS Link 1 (L1) carrier;PRNj

is the PRN or satellite j; and,is the estimate o the code phase at the start o the aperture

accumulation, where early, prompt or late code phase estimatescan be used.

Equation (16) is applied to compute the RSVj

term:

In (16), (. , .) is the vector dot product, ej

is the satellite/

receiver LOS unit vector, RSVj is the satellite position vector;and Rrcvr

is the receiver position vector.Note that equation (16) does not compensate the PRN code

phase or antenna motion. Synthetic apertures stay in the rangerom 1.2 to 6.2 meters or experimental scenarios reportedin this article (see next section), which ocuses on GPS C/Acode applications. In this case, because the antenna apertureis signifcantly shorter that the code chip length (equivalentto approximately 300 meters), the signal-to-noise ratio (SNR)processing loss caused by uncompensated antenna motion isnegligible (less than 0.2 dB).

For apertures that are comparable to the length o the C/A-

code chip or or precision (Pcode) applications where the chipduration is equivalent to approximately 30 meters, changes inthe code phase resulting rom antenna motion must be takeninto account.

Future research will address modiications o syntheticaperture algorithms that account or code phase changes dueto antenna motion. Note that antenna motion must be compen-sated or the construction o the synthetic antennas as detailedin the next section.

Navigation message data bits in the GPS signal must bewiped-o to avoid energy losses due to bit transitions or thosecases where the time duration o synthetic aperture exceeds the

duration o navigation data bits (20 milliseconds). Te bit wipe-o can utilize bit estimates rom GPS receiver tracking loops.

Alternatively, an energy-based bit estimation algorithmdescribed in a orthcoming article by A. Soloviev et alia (seeAdditional Resources) or Kalman flter bit estimation routines(see the articles by N. I. Zeidan et alia and M. L. Psiaki et aliain Additional Resources) can be used or those cases where lowcarrier-to-noise ratio (C/N

0) signals are processed.

o determine the spatial distance between signal sampleswe used the motion trajectory computed by an inertial navi-gation system (INS). We applied a quarter-wavelength spatialseparation between synthetic antennas to the methods reported

in this article (see Equation [21] below). Tis separation cor-responds to approximately fve centimeters or the GPS L1 car-

rier. Tus, the INS must provide centimeter-accurate trajectoryestimates. Tis requirement is satisfed i INS error states are

periodically estimated by a Kalman flter that uses GPS carrierphase measurements as flter observables.A pattern o the synthetic phased array that is constructed

by adding outputs o individual FFs (see Figure 6) can beapproximated by a sinc unction:

where is the steering direction, * is the direction o the

incoming signal, and A is the total length o the array.he sync unction corresponds closely to the pattern othe physical phased array or the case in which the distancebetween individual antennas is equal to a hal-wavelength:

Figr 7 illustrates close agreement between patterns o thehal-wavelength physical array and a synthetic array using asimulated case where the satellite signal is received rom a 45-degree angle.

In applying equation (17) we can see that the pattern othe synthetic array does not depend on the spatial distancebetween synthetically generated antenna locations. As a result,this spatial distance can be chosen to provide a desired angularrange or the multi-directional beam steering.

For our particular purposes, we chose a spatial distanceequal to /4 so as to cover the angular range between 0 to 180degrees. In this case, the FF amplitude that corresponds to

the kth

requency harmonic is expressed as ollows:

Array pattern for 12 antennas

SV LOS anglePhysical array patternSynthetic array pattern (sync function)

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Normalizedenergy

Steering angle, deg

0 20 40 60 80 100 120 140 160 180

FIGURE 7 Simulated synthetic array pattern versus physical array pattern

SynTHeTiCAPeRTuRe



Tis spectrum amplitude also serves as a synthetic arrayoutput or steering direction

k. As a result, it satisfes the ol-

lowing equation:

Comparison o equations (19) and (20) maps FF requen-cies into beam steering angles:

Equation (22) provides the fnal expression or the FF-based multi-directional beam steering or synthetic phasedarrays:

Two-DmsoalBamStrg

For multi-directional steering in two dimensions, one-dimen-sional FFs or the synthetic and physical phased arrays inaccordance with equations (22) and (14) are combined intoa two-dimensional FF:

In (23), m and n are index numbers o the antenna in thephysical and synthetic arrays, respectively, with correspondingsteering angles and , as shown in Figr 8.

FFT-BasdMlt-DrctoalSgalTrackgTe outputs o the 2D FF-based steering procedure that wehave described correspond to post-correlation complex ampli-tudes o incoming signals received or dierent antenna steer-ing angles. More specifcally, the real part o the FF spec-

trum represents the in-phase (I) post-correlation values and theimaginary part represents the quadrature (Q) post-correlation

values or the anten-na steering anglesdefned by FF re-quencies as specifedby equation (23).

Hence, the 2DFF mechanism or-mulated by equation(23) simultaneouslyprovides Is and Qs or multiple beam steering angles, whichcan be applied or multi-directional carrier phase tracking. Iand Q values or each FF requency grid and its correspond-ing steering direction are treated independently rom otherrequency grids.

Multi-directional carrier phase tracking is perormed byprocessing I and Q values o each steering direction. Signalparameters or dierent steering directions can be estimated

rom I and Q values using an open-loop receiver architecturedescribed in the orthcoming article by F. van Graas et alia(Additional Reources). FF-based multi-directional trackingwill be i llustrated later in the section describing simultaneoustracking o direct and multipath signals.

So, with the oregoing theoretical background in mind, letsturn to the easibility demonstration and experimental verifca-tion phases o our discussion.

1DSthtcArra:FlghtTstRsltsSynthetic generation o 1D antenna arrays was verifed usingexperimental data collected in actual light environments.

Figr 9 shows the confguration o equipment on the OhioUniversity Avionics Engineering Center (OU AEC) McDonaldDouglas DC-3 aircra used or the ight test.

We selected a straight segment o the ight to demonstratethe generation o synthetic arrays, with the aircra travelingat approximately 63 meters per second.

Te synthetic array approach was verifed using sampledGPS data recorded during the ight test by the AECs so-ware instrumentation receiver described in the article by S.Gunawardena et alia (Additional Resources). o implementmulti-directional beam steering in the range rom 0 to 180degrees using a single FF per Equation (18), antennas

in synthetically generated arrays are spatially separated by aquarter-wavelength o the GPS L1 carrier wavelength (approxi-mately fve centimeters).

As described earlier in this ar ticle, quarter-wavelengthbatches o GPS signal samples are irst ormed and thenprocessed. Te motion trajectory reconstructed by the INSis applied to determine the spatial separation o GPS signalsamples in order to combine samples that are quarter-wave-lengths apart.

Te INS motion trajectory is computed rom measurementso a low-cost inertial measurement unit (IMU). Tis units sen-sor errors are specifed as 0.1 degree/second (one sigma) gyro

dri and one milligal (one sigma) accelerometer bias. IMUmeasurements are periodically calibrated in-ight using GPS

Physical array

Synthetic array Beam direction

FIGURE 8 Two-dimensional steering angles



carrier phase in order to maintain the centimeter-accuratereconstruction o motion trajectory needed to generate thesynthetic phased arrays.

For each satellite, the down-conversion requency IF

, PRNcode, and satellite motion are wiped o rom the incoming sig-

nal prior to applying the FF-based beam steering procedure.Figrs 10 and 11show synthetic array patterns (with 13 and

26 elements, respectively) computed by the FF-based steeringmethod or the case where the motion o the GPS satellite iden-tifed by its pseudorandom noise code PRN 7 is wiped o

rom the incoming signal. An estimated carrier-to-noise ratio(C/N0) or PRN 7 is 47 dB-Hz.In the fgures, the synthetic array patterns are represented

as normalized signal energy (y-axis) versus steering angle,where the signal energy is normalized such that the maximumenergy over the entire steering angular range is equal to one.Tese fgures reveal patterns or cases in which the syntheticaperture corresponds to a 13-element array (Figure 10) and a26-element array (Figure 11) that use hal-wavelength separa-tion between their antennas.

In the fgures, the maximum energy is observed when theantenna beam is steered towards the satellite. An energy loss

is introduced as the beam is steered away rom the satellite.Essentially, an energy loss or the angle is equivalent to asuppression that would be applied to an intererence signal (orany other unwanted signal) rom a given angle while the beamis steered towards the satellite.

Te beamwidth is approximated as the distance betweenthe points or which the energy is degraded by three decibelsrom its maximum (boresight) value. Hence, the beamwidthsare approximately 10 degrees and 5 degrees or the 13-elementand 26-element synthetic antenna arrays, respectively.

2DSthtcArra:GrodTstRslts

We use ground vehicle test data to demonstrate the generationo 2D synthetic phased arrays. Figr 12 shows the experimentalsetup in the AEC test van that was used or data collection.

Similar to the ight test, we implemented a straight motiontrajectory with the vans velocity at approximately our meters

Array pattern for 13-antenna array

SV LOS angle0

-10

-20

-30

-40

Normalizedsignal

energy,

dB

Steering angle, deg

0 20 40 60 80 100 120 140 160 180

Array pattern for 26-antenna array

SV LOS angle0

-10

-20

-30

-40

Normalizedsignal

energy,

dB

Steering angle, deg

0 20 40 60 80 100 120 140 160 180

FIGURE 10 Pattern o a one-dimensional synthetic antenna array w ith 13elements generated using fight data and FFT-based multi-directional

beam steering. PRN 7 satellite motion is wiped o rom the incomingsignal;

FIGURE 11 Pattern o a one-dimensional synthetic antenna array w ith 26elements generated using fight data and FFT-based multi-directional

beam steering. PRN 7 satellite motion is wiped-o rom the incomingsignal

SynTHeTiCAPeRTuRe

FIGURE 9 Flight test setup

GPS antenna

OU AECfront-end

Data collection computer(Low-cost IMU mounted inside)



per second. An AEC two-channel so-ware instrumentation receiver was used

to record raw GPS signal samples. IMUdata were applied to reconstruct themotion trajectory or the synthetic arrayormation.

wo antennas mounted on the vanrooop ormed the array beam in thedirection perpendicular to motion.Array aperture in the direction omotion was synthesized by observingthese antennas at dierent spatial loca-tions.

We calibrated the systems inter-

channel and inter-antenna biases inadvance o the ground test and removedtheir associated phase delays rom rawsignal samples prior to implementing thesynthetic signal processing routines.

Note that thebeam steering capa-bilities in the cross-t r a c k d i r e c t i o nwere limited by the

number o ront-endchannels (two) cur-rently available inthe soware receiv-er. his limitationcan be mitigatedby increasing thenumber o ront-end channels and/or by implementing

multi-platorm signal integration tech-niques.

Figrs 13 and 14 show 2D syntheticarray patterns generated or the groundexperiment. In these igures, is thesteering angle in the direction o motionand is the steering angle in the cross-track direction. Figure 13 shows testresults or a phased array constructedusing two physical and six syntheticantennas.

Similar to the 1D array case, themaximum signal energy is receivedwhen the array beam is steered in the

direction o the satellite. As the beamis being steered away rom the satel-lite, signal attenuation occurs. At a spe-cifc angular direction, this attenuationis equivalent to that which would be

applied to a multipath or an intereringsignal coming rom this direction.

As mentioned previously, beam-steering capabilities in the cross-trackdirection are currently limited by the

number o ront-end channels in thereceiver. With only two channels avail-able, thereore, the array beam in thecross-track direction is rather wide:approximately 30 degrees. Nevertheless,the experimental results demonstratethe easibility o generating 2D arraysby using synthetic aperture GPS signalprocessing and combining signals rommultiple antennas.

Figure 14 shows the 2D syntheticarray pattern or the case where the

synthetic aperture is extended to 31 ele-ments. Tis extension narrows the arraybeam signiicantly in the direction omotion. he beamwidth in the cross-track direction remains unchanged.

FFT-basdMlt-DrctoalBamStrg:SmlatoRsltshe ollowing section uses simulatedresults to demonstrate the easibility othe FF-based multi-directional signal

tracking with simulated results.For the simulation, a multipath signalwas added to the direct satellite signal.Multipath was simulated as a specularreection rom a horizontal planar sur-

SynTHeTiCAPeRTuRe

Pattern of 2x6 element array180

150

120

90

60

30

0

0

-10

-20

-30

-40

-50

-60

-70

,

d

eg

, deg0 30 60 90 120 160 180

SV location

Pattern of 2x31 element array180

150

120

90

60

30

0

0

-20

-40

-60

,d

eg

, deg0 30 60 90 120 160 180

SV location

FIGURE 13 Pattern o a two-dimensional antenna array that is comprisedo two physical and six synthetic antennas. Satellite motion has been

wiped o rom the incoming signal rom PRN4, which had a carrier-to-noise ratio o 49 dB-Hz.

FIGURE 14 Pattern o a two-dimensional antenna array that is comprisedo two physical and thirty one synthetic antennas; PRN 4 satellite mo-

tion is wiped-o rom the incoming signal; PRN 4 C/N0 is 49 dB-Hz

RF front-end

Data collection computer(AGNC IMU mounted inside)

GPS antennas

FIGURE 12 Ground vehicle test setup



ace collinear to the Y-Z plane. Figr 15illustrates this multipath scenario.

For the FF-based synthetic arrayprocessing, the synthetic aperturecorresponds to 20 physical antennas

separated by a hal-wavelength. A our-element physical array with hal-wave-length antenna separation was simu-lated to steer the beam in the directionperpendicular to motion. Array beamswere steered in multiple directions using2D FFs (see Equation [23]).

For the direct signal, a C/N0

o 40dB-Hz was implemented. Te multipathpower was simulated to be three decibels

below the direct sig-nal power.

Figr 16 showsa 2D signal imageconstructed using

the 2D FF-basedb e a m s t e e r i n gmethod. he plotdemonstrates simul-taneous recovery othe direct and mul-tipath signals.

F F - b a s e dmulti-directionalsignal tracking wasimplemented andsimulated or the

case o simultaneoustracking o directand multipath signals or the scenarioillustrated in Figure 15. FF-based Isand Qs are applied to track the carrierphase o direct and multipath signals.Real and imaginary parts o FF com-plex amplitudes or beams steered in thedirection o direct and multipath signalsare exploited as I and Q values, respec-tively.

Figr 17 illustrates the results o

the simulated tracking. Carrier phasetracking errors are shown as dierencesbetween true carrier phase (known inthe simulation) and measured carrierphase based on I and Q values providedby 2D FF computations.

Standard deviations o carrier phaseerrors are evaluated as 3.2 and 4.3 mil-limeters or the direct and multipathsignals, respectively. Hence, the simula-tion results presented demonstrate theeasibility o simultaneous tracking o

multiple signals using the FF-basedmulti-directional beam steering.

GPS-BasdSARimaggFigr 18 illustrates a simulation scenarioimplemented to demonstrate GPS-basedSAR imaging.

A simulated receiver platormincludes our GPS antennas mounted onan unmanned aerial vehicle (UAV) thatis ying at 20 meters above the groundwith a 2 meters per second ground veloc-

ity. he simulated scenario assumes asingle point reector located at ground

level. he C/N0

o the relected signalwas simulated to represent an army tankhidden under a dense canopy.

Analysis o RF GPS data collectedin orestry areas shows that or high-elevation satellites the signal is generallyattenuated by 7 decibels as it propagatesthrough the canopy. Tereore, the sig-nal attenuation o 14 decibels was intro-duced or the two-way propagation paththrough the canopy, that is, rom the sat-

ellite to the target and rom the target tothe receiver.

he radar cross section (RCS) othe target is assumed to be fve squaremeters. For the 14-decibel signal atten-uation due to the propagation throughthe canopy and a ive square meterRCS value, the C/N0 o the signal thatis received at the UAV platorm is esti-mated at 17 dB-Hz.

We simulated and processed the C/A-code component o the GPS signal.

o process the GPS signal at a 17 dB-Hzlevel, a one-second coherent integration

4x20 antenna array

Normalizedsignalenergy

x axis steeringangle, deg

y axis steering

angle, deg

1

0.8

0.6

0.4

0.2

0

30 0 0 3060 90

120150180

6090

120150

Direct phase minus estimated direct phase, m

Time, s

0.04

0.02

0

-0.02

-0.040 0.2 0.4 0.6 0.8 1

Multipath phase minus estimated multipath phase, m

Time, s

0.04

0.02

0

-0.02

-0.040 0.2 0.4 0.6 0.8 1

FIGURE 16 Simulated FFT-based signal imageor a two-dimensional antenna array: Directand multipath signals are simulated; directsignal carrier-to-noise ratio is 40 dB-Hz;multipath signal power is three decibelslower than the direct signal power; anglesbetween X and Y axes o the antenna arrayand direct signal are simulated as 90 and 46degrees, respectively; angles between X andY axes o the antenna array and multipathsignal are simulated as 90 and 134 degrees,respectively; energy peaks are clearlyobserved or cases where the antenna beam

is steered towards the direct signal andmultipath

FIGURE 17 Simultaneous tracking o direct and multipath signal using FFT-based multi-directional beam steering

FIGURE 18 Simulation scenario implemented todemonstrate GPS-based SAR imaging

V = 2 m/s

h = 20 mY

X

SynTHeTiCAPeRTuRe

FIGURE 15 Multipath refection scenariosimulated to veriy multi-directional beamsteering in two dimensions

Receivery

z

x

SV

direct path

multipath

vrcvr


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interval was implemented. Construction o SAR images wasbased on the 2D FF-based processing approach discussed inthe previous section, augmented by beam ocusing techniquesdiscussed in the book by J. C. Curlander and R. N. McDonough(Additional Resources) to avoid image distortions that are dueto the motion o the platorm.

Figr 19 shows an example o a simulated SAR image. oconstruct this image, steering angles were converted into Xand Y Cartesian coordinates using the known height above

the ground (20meters).he GPS-based SAR image shown in Figure 19 clearlyidentifes the presence o a target. Note that the image resolu-tion in the direction o motion is achieved using the syntheticaperture. For the cross-track direction, the image is resolvedby ocusing the array beam with multiple physical antennasmounted perpendicular to motion.

his implementation diers rom the classical SARapproach that uses a single antenna and the cross-track imagecomponent is resolved using the carrier modulation by a rang-ing signal. For the GPS case, the chip duration o the C/A-coderanging modulation is 300 meters. Clearly, this resolution is

insucient or most imaging applications. Hence, multiple-antenna beam ocusing is applied to resolve the cross-trackimage component.

As shown in Figure 19, the multi-antenna ocusing approachallows or resolving the cross-track image component withinapproximately three meters. In other words, the ranging resolu-tion o the C/A code is improved by two orders o magnitudein the simulation scenario.

CoclsosTis article has described the generation o synthetic phasedGPS antenna arrays using moving antennas. Signals received

rom a GPS antenna at dierent spatial locations are combinedinto a synthetic phased array to sharpen the array beam with-

out increasing its physical size. We introduced an FF-basedapproach to simultaneously steer the array beam in multipledirections and to perorm multi-source signal tracking.

Tis approach can be applied or improving GPS robust-ness to radio-requency intererence, simultaneous tracking

o multiple signal sources such as direct signal and multipathreections, and or recording high-resolution images utilizingGPS signal reections.

Future research in the area o synthetic aperture GPS signalprocessing will ocus on the demonstration o the GPS SARconcept with experimental data and multi-platorm signal pro-cessing or generating large array apertures in the directionperpendicular to motion.

AckowldgmtTis article is based on a presentation made at the 2009 Insti-tute o Navigation International echnical Meeting in Ana-

heim, Caliornia.

MafactrrsTe low-cost IMU used in the AEC ight test is a Coremicromanuactured byAmerican GNC Corporation, Simi Valley,Caliornia, USA.

AthorsAndrey Solovievisaresearchassistantproessorat

theUniversityoFlorida,ResearchandEngineering

EducationFacility.Previouslyheservedasasenior

researchengineerattheOhioUniversityAvionics

EngineeringCenter,Athens,Ohio.HeholdsB.S.andM.S.inAppliedMathematicsandPhysicsromMos-

cowUniversityoPhysicsandTechnologyandaPh.D.

inElectricalEngineeringromOhioUniversity.Solovievsresearchinterests

ocusonallaspectsomulti-sensorintegrationornavigationapplications.

HeisarecipientotheInstituteoNavigation(ION)EarlyAchievementAward

andtheRTCAsWilliamJacksonAward.

Sanjeev Gunawardenaisaseniorresearchengineer

andco-principalinvestigatorwiththeOhioUniver-

sityAvionicsEngineeringCenter.HeearnedaPh.D.

inelectricalengineeringromOhioUniversityand

wasthe2007recipientotheRTCAWilliamE.Jackson

award.HisresearchinterestsincludeRFsystems

design,digitalsystemsdesign,reconfgurablecom-puting,andallaspectsoGNSSreceiversandsignalprocessing.

Frank van GraasistheFritzJ.andDoloresH.RussPro-

essoroElectricalEngineeringandaprincipalinves-

tigatorwiththeAvionicsEngineeringCenteratOhio

University.APastPresidentoTheInstituteoNavi-

gation,vanGraasreceivedthe1996JohannesKepler

AwardromtheIONsSatelliteDivisionotheION.His

researchinterestscenteronallacetsoGPS,includ-

ingaircratprecisionapproachandlanding,attitudedetermination,andsys-

temintegration.

Mikel MilleristhetechnicaldirectorortheAdvancedGuidanceDivision,

MunitionsDirectorate,AirForceResearchLaboratory,EglinAirForceBase,

Florida.HereceivedhisPh.D.inelectricalengineeringromtheAirForce

Focused SAR image180

150

120

90

60

30

0

Y,m

X, m

-10 -5 0 5 10

Target location

FIGURE 19 Simulated SAR image or the GPS-based SAR implementation

www.insidegnss.com m a y / j u n e 2 0 0 9 InsideGNSS 46a


12/12

InstituteoTechnology

(AFIT),WPAFB,Ohio.

Since 1986, he has

ocusedonnavigation

systemR&Drelatedto

GPS,GPS/INSintegra-

tion,alterativenaviga-tiontechniquesincludingbio-inspirednaviga-

tionandsignalsoopportunitybasednavigation,

autonomousvehiclenavigationandcontrol,and

multi-sensorusion.Heiscurrentlyresponsible

ordirectingbothin-houseandcontractedR&D

projectsadvancingguidance,navigation,and

controltechnologyorweaponsystems.

AddtoalRsorcs[1]Akos,D.M.,ASotwareRadioApproachto

GlobalNavigationSatelliteSystemReceiver

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WidebandTransorm-DomainGPSInstrumen-

tationReceiverorSignalQualityandAnomalous

EventMonitoring,NAVIGATION, Journal of the

Institute of Navigation,Vol.53,No.4,2007

[9]Kaplan,E.,andC.Hegarty(Editors),Under-

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mentErrorCharacterizationandCompensation,in

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Y.Tsui,andQ.Zhou,BroadBandIntererence

CancellationusingDigitalBeamForminganda

SotwareGPSReceiver,inProceedings of the ION

GNSS-2005,September2005

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J.Marchese,T.Upadhyay,andW.E.VanderVelde

ComputerSimulationoDigitalBeamForming

AdaptiveAntennaeorGPSIntererenceMitiga-

tion,inProc.otheIONNationalTechnicalMeet-

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aSyntheticPhasedArrayAntennaorCarrier/Code

MultipathMitigation,inProc. of the ION GNSS-

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FilterMethodsorTrackingWeakGPSSignals,inProceedings of the ION GPS-2002,September

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Davis,ElevenElementBeamSteeringGPSAnten-

naArrayinaGAS-1CRPAFootprint,presentedat

theFOUOsessionotheIONGNSS-2008,Septem-

ber2008

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3rded.NewYork:McGraw-Hill,2001

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SynTHeTiCAPeRTuRe

Documents

Synthetic Aperture GPS Signal Processing