using gps reflections for satellite remote sensing

Available online at www.sciencedirect.com

Acta Astronautica 55 (2004) 39–49www.elsevier.com/locate/actaastro

Using GPS re ections for satellite remote sensing

David Mickler1, Penina Axelrad, George Born∗

Colorado Center for Astrodynamics Research, The University of Colorado, Boulder, CO 80309, USA

Received 19 December 2002; received in revised form 11 September 2003; accepted 19 December 2003

Abstract

Global positioning system (GPS) signals that have re ected o0 of the ocean’s surface have shown potential for use inoceanographic and atmospheric studies. The research described here investigates the possible deployment of a GPS re ectionreceiver onboard a remote sensing satellite in low Earth orbit (LEO). The coverage and resolution characteristics of thisreceiver are calculated and estimated. This mission analysis examines using re ected GPS signals for several remote sensingmissions. These include measurement of the total electron content in the ionosphere, sea surface height, and ocean wind speedand direction. Also discussed is the potential test deployment of such a GPS receiver on the space shuttle. Constellations ofsatellites are proposed to provide adequate spatial and temporal resolution for the aforementioned remote sensing missions.These results provide a starting point for research into the feasibility of augmenting or replacing existing remote sensingsatellites with spaceborne GPS re ection-detecting receivers.c© 2003 Elsevier Ltd. All rights reserved.

Keywords: GPS; GPS re ections; Remote sensing

1. Introduction

Since its inception, the global positioning system(GPS) has produced a wide variety of applications be-yond the original goals of providing position, velocity,and timing information to users worldwide. One of themost recent innovations is the use of GPS satellitesas the transmitters in a bistatic radar for ocean remotesensing. A high altitude GPS receiver, properly ini-tialized and calibrated, intercepts both the direct GPSsignals and those signals re ected by the ocean sur-face. The receiver is equipped with an upward-looking

∗ Corresponding author. Tel.: +1-303-492-6677; fax: +1-303-492-2825.

E-mail address: [email protected] (G. Born).1 Currently with Northrop Grumman Space Technology,

Relondo Beach, CA 90277, USA.

standard right hand circularly polarized (RHCP) an-tenna and a downward-looking antenna of oppositepolarization (LHCP) which favors the re ected sig-nals. This research investigates the design of severallow Earth orbiting (LEO) satellite missions that uti-lize this new technology to provide inexpensive globalocean remote sensing.First we discuss the emerging Celd of GPS re ec-

tion measurements and their scientiCc applications.Then we propose several LEO satellite constellationsto provide the necessary spatial and temporal sam-pling characteristics. We also investigate mounting aprototype re ection receiver on the space shuttle. Thedistribution, azimuth, and elevation angle of the re- ected GPS signals as seen by the space shuttle arecalculated through simulation and evaluated.The background material Crst covers bistatic sig-

nal scattering of GPS signals and their subsequent

0094-5765/$ - see front matter c© 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.actaastro.2003.12.016

mailto:[email protected]

40 D. Mickler et al. / Acta Astronautica 55 (2004) 39–49

measurement. Then we discuss some of the literatureand necessary astrodynamics needed for constellationdesign. The coverage and resolution characteristics ofthe potential GPS re ection-measuring instrument arealso discussed.

1.1. GPS bistatic radar concept

The Crst to propose using re ected GPS signals foroceanography was Martin–Neira [1], who introducedthe passive re ectometry and interferometry (PARIS)concept in 1993. Then, in 1994, French engineers re-ported the accidental acquisition of ocean re ectedGPS signals by an aircraft mounted receiver. Thisstudy was documented by Auber et al. [2]. Katzbergand Garrison [3] quickly recognized the potential ofthese signals as the basis for a new remote sensingtechnique. Results from the application of their theo-ries are found in Garrison et al. [4]. Very signiCcantly,they proceeded to modify an open-architecture GPSreceiver into a re ected signal mapping receiver asdetailed by Garrison et al. [5]. They called their in-strument the delay mapping receiver (DMR).Such an instrument could conceivably be used for

several oceanographic applications. Martin–Neira [1]discussed the potential for re ected GPS signals toperform altimetry. Katzberg and Garrison [3] devel-oped the technique to calculate ionospheric delay fromdual frequency GPS forward-scattered signals. Kom-jathy et al. [6] outlined how the signal scattering couldbe used to perform scatterometry with a properly con-Cgured receiver.The implementation of a GPS re ection instrument

onboard a satellite for remote sensing has been con-sidered by Armatys et al. [7], Emery et al. [8], andCardellach [9]. We describe a mission analysis to con-sider the feasibility and characteristics of using sucha properly equipped receiver on a LEO remote sens-ing satellite mission. The ability of a GPS receiver toperform each of these missions, altimetry, scatterom-etry, and ionospheric measurement, will be examinedin terms of spatial and temporal resolution.

1.2. Possible GPS re4ection missions

Detailed knowledge of ionospheric delays is vitalto the performance of spaceborne altimeters and toground-based systems such as the GPS Wide AreaAugmentation System (WAAS) (see Komjathy [10]).

To establish real-time ionospheric corrections for sci-entiCc satellites one must have knowledge of totalelectron content (TEC) with quite stringent require-ments on both the temporal and spatial resolution.The TEC, a measure of ionospheric activity, is ob-tained by di0erencing range measurements on the twocarrier frequencies (1575.42 and 1227:60 MHz) thatGPS is currently transmitted on. Currently, no globalionospheric measurements have been taken in realtime. The International GPS Service (IGS) providesdual frequency data that can be used to form globalTEC maps after processing (see Komjathy [10]). Forreal-time applications, the resolution needs to be onthe same scale as the spatial decorrelation length anddecorrelation time of the TEC. To provide a usefulglobal map of the ionosphere one needs to achieve aresolution of roughly 500 km spatially and 2 h tem-porally. Obviously, the only way to achieve such hightemporal resolution is by deploying a constellation ofremote sensing satellites. One may suggest adding in-struments to a geostationary satellite but the re ectedGPS signals are too weak to be practically measuredfrom beyond LEO.Several scatterometry missions have own or are

manifested. NSCAT, which ew on a short-lived mis-sion, and QuikScat, were designed to measure globalocean wind speed and direction. The scatterometersachieve global coverage in 2 days with 25 km spatialresolution. The QuikScat instrument has a 1800 kmswath width and covers 90% of the ocean’s surfacein a day from its 803 km sun-synchronous orbit. TheRMS accuracy in determining wind speed and direc-tion is 2 m=s (in a range from 3 to 20 m=s) and 20◦,respectively. This work attempts to make a compari-son with the wind vector resolution.Altimetry has a longer heritage. The most accurate

altimeters currently in use are TOPEX/Poseidon andJason-1 that achieve 2–3 cm RMS accuracy in theirmeasurements, repeated every 10 days. The ERS-2and Geosat Follow-On altimeters also currently pro-duce ocean topographic data with a reduced accuracyof 5–7 cm. The high level of accuracy achievedby TOPEX and Jason-1 are gained mainly throughadvances in orbit determination. If a GPS re ectionreceiver were mounted on a future generation of alti-meter, real-time observed ionospheric correctionscould be obtained; thereby eliminating the need for adual frequency altimeter.

D. Mickler et al. / Acta Astronautica 55 (2004) 39–49 41

h = altitudeλ

λ

=footprint length η

η=field of view

ρ=angular radius ofEarth

sin ρ

ρ

= cos λ= Re/(Re+h) for our case,η = ρ

Re

h

Fig. 1. Nadir pointing instrument viewing angle geometry.

1.3. LEO constellations

Using constellations of satellites decreases obser-vation repeat times. The more satellites in a uniformconstellation the more often a point on the Earth’s sur-face is under observation, and the shorter the time gapswhen that point is not under observation. Global cov-erage cannot be achieved from LEO (1000 km or less)by a single satellite in much less than a day becausethe instruments onboard cannot view a wide enougharea of the Earth’s surface. The coverage angle geom-etry of a satellite in orbit is related to the altitude ofthe spacecraft above the Earth’s surface and the instru-ment’s Celd of view. The geometry is diagrammed inFig. 1. The instrument Celd of view is the angle �. Theangular radius of the Earth, which is the cone-angleof the Earth’s surface visible from a certain altitude h,is labeled �. See Wertz [11] for a full exposition oncoverage angles. For a GPS re ection receiver we canconsider view angles up to � = �. However, a morelimited Celd of view may be required for some appli-cations. This is described below.Two orbital elements a0ect the cost of placing

a satellite in orbit, and hence the feasibility of anew remote sensing technology in an era of limitedbudgets. The altitude of the orbit desired is the mainfactor a0ecting how much a launch costs. A launchvehicle can place a satellite of a speciCed mass withina certain orbit. With a larger launch vehicle the space-craft mass or altitude can be increased, or a mixtureof both. The smallest, and therefore least expensive,launchers are intended for spacecraft of less than onemetric ton and for altitudes of 800 km or less. For auseful spaceborne remote sensing mission, the alti-

tude needs to be high enough to mitigate the e0ects ofatmospheric drag and allow a large instrument view-ing footprint. The altitude (of a circular orbit) needsto be above 300 km to ensure a mission lifetime of 1year. However, in most cases, the lower the altitudethe better the resolution of the instrument. Cardellach[9], for example, only considered satellite altitudes inthe range of 350–400 km.The other orbital element increasing the launch cost

is inclination. A satellite’s minimum inclination islimited by the latitude of the launchpad. This can beseen from the equation for orbit inclination i, cos(i)=cos(�gc) sin(), where �gc is the geocentric latitudeof the launch site, and is the launch azimuth of therocket [12]. The more that deviates from the di-rection of Earth’s velocity the higher the velocity thelauncher needs to impart to get the satellite to its de-sired orbit. Thus, to achieve higher inclinations thanthe launch latitude, it is necessary to burn more fuelfor the same orbital altitude. The higher the inclinationthe larger the zone of coverage a satellite can achieve.Thus a constellation of satellites can be used to

achieve multiple coverage planes. A constellation planattempts to optimize by selecting the fewest numberof satellites, the lowest inclination, and the lowest alti-tude. The objective function to be optimized Cnds theorbital elements needed to achieve the desired cover-age subject to the minimizing constraints.Much work has been done on satellite constella-

tion patterns. The Crst paper on constellations was byVargo [13]. Most of the work since that time has beenon continuous global coverage from altitudes aboveLEO. The seminal works are by Walker [14], Draim[15,16], Lang [17,18], and Ballard [19]. One of theCrst works on zonal coverage was by Rider [20]. Forour case global coverage is not needed. Ocean scat-terometry and altimetry are not as useful over the po-lar regions, unless to detect the edge of the pack ice.Research is underway regarding GPS re ections fromice, and initial results have been presented by Kom-jathy et al. [21]. Lang and Hanson [22] discuss mini-mizing revisit times. That is to say, how soon does acertain constellation provide repeat coverage of a cer-tain location? After the location has been observed,how much time passes until the location comes un-der observation again? A short revisit time is neededto meet our temporal resolution requirements, espe-cially for an ionospheric mapping mission. Another


good treatise on low altitude constellation design is byHanson and Linden [23]. The Hanson et al. [24] pa-per on partial coverage satellite constellations was themost applicable to this work and is used extensively inthese results. They deCne ‘best’ to mean a minimumnumber of satellites at a minimum possible inclinationwith the smallest maximum, or shortest, revisit time.These criteria are the same needed by a small satellitemission such as the one proposed here.

2. Methods

First we needed to estimate the spatial resolution ofa GPS re ection tracking receiver. The area observedby a satellite is called the footprint. The smallestdetail that can be discerned within the footprint istypically called the spatial resolution. The re ectionmeasuring instrument is nominally nadir pointing tomaximize the gain from all areas of its footprint alongthe groundtrack. Within the instrument’s Celd ofview, re ections from several GPS satellites will ap-pear, each centered on the respective specular point.The location of the specular points can be solved forusing an algorithm from Wu et al. [25]. The size ofarea surrounding the specular point that contributesto the re ection determines what area of the ocean’ssurface is sampled. The size of this region, termed theglistening zone, is determined by the ocean surfaceroughness, which is related to surface wind speeds.Also, the higher the altitude of the observing instru-ment, the larger the glistening zone. These re ectionareas are well illustrated in Fig. 2 of Komjathy et al.[6].A simulation was set up for this research that cal-

culates the re ection points between the GPS constel-lation and a proposed re ection receiver in LEO at350 km altitude. A receiver mask was used to elimi-nate any GPS satellites whose re ection had traveledthrough too much of the ionosphere. This precludedthe receiver from using any re ections with an inci-dence angle greater than 70◦. We found an averageof 9 GPS satellite re ection points available for track-ing at any one time. This number was as low as 6and as high as 12. The average glistening zone diam-eter, labeled d in Fig. 2, is 65 km. This correspondsto an average wind speed of 5–8 m=sec, as seen froma 350 km altitude. This yields an average re ection

Lf, footprint length Lf = 111.319 km/deg Fa = footprint area Fa = (π/4)Lf 2 Glistening zone area

of diameter, d

Fig. 2. Resolution estimate.

area of just over 3000 km2. The Celd of view �, cal-culated from the equations in Fig. 1, is estimated to be70◦. This corresponds to a swath width of 4102 kmand a footprint area of 3; 345; 000 km2 of the Earth’ssurface. To Cnd an estimate of the Earth’s surfacesampled by a re ection receiver we estimate the per-centage of the area sampled by the glistening zone ascompared to the footprint area. This resolution con-cept is illustrated in Fig. 2. We use this estimate ofarea of the footprint sampled along the groundtrackto estimate the spatial resolution of a GPS re ectionreceiver.For the viewing angle study the space shuttle’s orbit

parameters are used in the simulation. We look hereat two classes of shuttle missions, split by inclination.The basic shuttle science mission has an inclinationof 28◦, whereas an International Space Station (ISS)service mission currently has an inclination of 52◦.From the simulation calculations we can observe

several parameters that potentially a0ect the re ec-tion receiver design and mounting. These include theazimuth and elevation angles to the re ection. The az-imuth angle measures the orientation of the GPS con-stellation with respect to the shuttle’s inertial velocitydirection. The elevation angle measures how low theGPS satellite is on the shuttle’s horizon. The largerthe elevation angle, the lower the signal to noise ra-tio for similar surface conditions. The elevation angle, which is measured here from the nadir direction, isillustrated in Fig. 3.Coverage calculations were computed using the grid

method. A grid of coverage was deCned between thelatitude bounds of the study region. For altimetry andscatterometry, we adopt the same bounds as TOPEXand QuikScat, roughly 70◦. That is, we measure thecoverage ability of our constellation designs between−70 and 70◦ N latitude. For ionospheric mappingwe use a grid with 500 km spatial resolution. For


GPS

shuttle

β nadir α

π−α

reflection P U point

Earth’ssurface

from Law of Sines:

( ) ( )βαπ sinsin

PU=

− ( ) ( − α)

U

P πβ =

sinsin

Center of ECEF frame

Fig. 3. Geometry of the re ected signal.

scatterometry we use a grid with 50 km spatial reso-lution. Our simulation divides the globe into squareswith area equivalent to the desired spatial resolution,either 500 or 50 km. Then the satellite groundtracksand coverage swaths are projected over these grids.We consider full coverage to be when a satellite viewsall the grids within the desired temporal resolution.Percent coverage is calculated based on what percentof the grid is observed by the satellite in a speciCedtime. Repeat time analysis is done by calculating howlong a certain grid area goes unobserved.Altimetry missions are a little di0erent because the

altimeter samples in a narrow band directly beneath itsgroundtrack. Thus the main di0erence between a radaraltimeter and a re ection receiver is that an altimeterhas one instrument groundtrack that repeats and a GPSre ection receiver has an average of 9 non-repeatinggroundtracks. Since spatial resolution is not an issue,we did not compute grid coverage simulations foraltimetry missions.

3. Results

3.1. Viewing angle study

The Crst results presented here are from the viewingangle study involving the space shuttle. Fig. 4 showsthe location of the specular re ection points seen fromthe space shuttle on a typical day, using the loca-tions of the GPS constellation on March 30, 1998. A

1/4-degree land mask was used to calculate these re-sults. One can see that the GPS re ection points formmultiple instrument groundtracks beneath the shut-tle’s groundtrack. This data set is used to examine theazimuth and elevation angles seen by the re ectionreceiver.Next we look at a histogram of azimuth angles for

both shuttle missions, the low and the high inclination.For both missions the results in Fig. 5 are basicallythe same. One can see that the azimuth angles arenearly uniformly distributed about the nadir pointingantenna of the re ection receiver. The azimuth angleswere sampled at a period of once every 30 s. Thus,each sample constitutes a point in the histogram.The next Cgure examines the elevation angles of the

GPS re ection points, as deCned in Fig. 3. A histogramof the elevation angles seen on March 30, 1998, is pre-sented in Fig. 6. One can see that elevations greaterthan 70◦ are masked out. This previously mentionedreceiver mask is a standard procedure for a spaceborneGPS receiver. These elevation angles were also cal-culated at 30 s intervals. We see that the observingplatform, here the space shuttle on a high inclinationmission, is not often directly underneath a GPS satel-lite. This is mainly due to the fact that the shuttle, inthis simulation, is not in the same orbital plane as theGPS spacecraft. When a GPS satellite is nearly over-head of the observing platform the elevation angle isless than 10◦. This occurs less than 3% of the timefor a typical day, according to Fig. 6. The elevationangle is greater than 50◦ over half the time. Resultsfrom other days were similar to those shown here.Fig. 7 shows a scatter plot of elevation angle versus

latitude of the observing platform’s groundtrack. Onenotices a bias toward higher elevation angles. One canalso see a higher number of re ections over the south-ern ocean. This makes sense because similar latitudesin the northern ocean are dominated by the Asian andNorth American landmasses.Several things can be said to conclude the viewing

angle study. The antenna should be mounted pointingdown, in the nadir direction, to avoid biasing re ec-tions from one side or the other. This conclusion canbe drawn from Fig. 5 and the uniformity of azimuthangle distribution. The predominance of low elevationangles leads to the suggestion that the antenna gainpattern be designed such as to maximize the signalgain from lower elevations.


Fig. 4. Simulation of GPS re ection points as seen in high inclination orbit.

3.2. Constellation design

A constellation was selected to perform the missionof ionospheric mapping in real time. The selection wasmade by minimizing the number of satellites neededand the inclination of their orbital planes. The orbitalgroundtracks during the 2-h temporal resolution timeperiod are shown in Fig. 8. The constellation consistsof four spacecraft in four separate orbital planes. Theplanes are at two di0erent orbital inclinations. Sta-tion keeping is minimal because the orbits selected arerepeat groundtrack orbits (from [24]). The Keplerianorbital elements for each plane are presented belowin Table 1.The orbital elements in Table 1 are as follows; a is

the semimajor axis, e is the eccentricity, i is the in-clination, ! is the argument of perigee, � is the rightascension of the ascending node, and f is the trueanomaly. The two high inclination satellites, labeledHigh 1 and High 2 in Table 1, are at an altitude of523:569 km. The two low inclination spacecraft, la-beled Low 1 and Low 2 in Table 1, are at an altitude

of 484:499 km. These orbits are repeating groundtrackorbits selected from Hanson et al. [24]. They were se-lected to meet the desired temporal resolution of 2 h.Coverage tests were run which concluded that the de-sired spatial resolution of 500 km was met 95% of thetime. This corresponds to 95% coverage of the desiredarea. Total (100%) coverage of the latitude boundswas satisCed with temporal resolution of about 11:8 h.The repeat time is slightly higher than 11:8 h for thehigh inclination planes and slightly lower for the lowinclination planes.For the scatterometry mission it was found that a

single spacecraft could meet the required resolution.This indicates that a re ection receiver could even bemounted on a future scatterometry mission, providinga redundant independent measurement source. Suchan uncorrelated independent measurement, capableof correcting the ionospheric delay, would certainlyincrease the accuracy of a scatterometer. The scat-terometry orbit is also selected to have a repeatinggroundtrack. The groundtrack is shown in Fig. 9. Therepeat time for this orbit is 10:73 h. The Keplerian


Fig. 5. Histograms of Azimuth angles.

Table 1Keplerian orbital elements for ionospheric measurement constellation

Element a (km) e i (deg) ! (deg) � (deg) f (deg)

High 1 6901.706 0 68 0 266.8662 0High 2 6901.706 0 68 0 86.8662 180Low 1 6862.636 0 29 0 86.8662 0Low 2 6862.636 0 29 0 266.8662 180


Fig. 6. Histogram of angle from Nadir.

Table 2Keplerian orbital elements for scatterometry mission

Element a (km) e i (deg) ! (deg) � (deg) f (deg)

Scatter 1 6910.284 0 74 0 199.3549 0

orbital elements for the selected scatterometry mis-sion are listed in Table 2. The elements are the sameas the ones described for Table 1 above.The altitude of this orbit is 532:147 km. The incli-

nation allows coverage of the global oceans. The cov-erage calculations indicate that for this particular orbit100% coverage at a 50 km resolution is obtained in12 h 4 min.The coverage calculations quoted here were com-

puted assuming the 70◦ Celd of view. However, asseen in Fig. 2, the re ection points do not Cll thisfootprint. Assuming that the re ection points to theGPS satellites are not repeated from day to day, adi0erent part of the footprint is sampled after each

pass. Thus over the requisite 2 day temporal reso-lution the 500 km spatial resolution should be met.This would require further research into appropriateinterpolation techniques. One suggestion would be touse a weighted least-squares routine for the regionabout each grid point and use that to get a Ct for eachgrid point as well. However, our main concern hereis feasibility.

4. Summary

GPS bistatic radar or re ection receiver technologypromises many new opportunities for geophysical


Fig. 7. Scatterplot of angle from Nadir.

observations. This paper considered several applica-tions of such an instrument. First, an estimate of theresolution was derived in order to allow comparisonwith other remote sensing technologies. Then, a view-ing angle study was completed in order to validate atest ight on the space shuttle. Finally, a constellationdesign analysis was completed to begin missionplanning for a future remote sensing mission usingGPS re ections.Resolution was estimated using the size of the glis-

tening zone as a percentage of the satellite’s Celd ofview, looking down at Nadir. The average number ofre ected GPS signals seen at any one time during thesimulation was nine. This indicates a little under 10%of the Celd of view area was sampled. The distributionof specular points was assumed random.The viewing angle study saw a uniform distribution

of azimuth angles about the down-looking antenna.The elevation study showed higher elevation anglesto be more likely. Elevation angles were measuredfrom Nadir for this analysis. These results indicate aspaceborne re ection receiver’s antenna gain pattern

should be designed to maximize high elevation anglesignal gain.A four-satellite constellation has been proposed

to enable the real-time mapping of the ionospherefor use in realtime remote sensing corrections and inGPS WAAS. This four-satellite implementation neednot be prohibitively expensive. A Pegasus rocketis currently the smallest available launch vehicle.Such a rocket could loft the suggested constellationin two launches. One launch would be for the highinclination satellites, the second for the low satel-lites. Based on the orbital inclination, the speciCedaltitude, and the known launch vehicle capability, alimit for the spacecraft mass can be obtained. Thislimit is about 350 kg per spacecraft (from [26]).This is certainly feasible in terms of today’s tech-nology. The scatterometry (or altimetry) missioncould either be launched with a single rocket or be own onboard a future scatterometer (or altimeter)mission. This may be the most useful means of de-ployment for a GPS re ection receiver. In this way itcould provide both backup measurements for the


Fig. 8. Ionospheric measurement constellation groundtracks.

scatterometry mission and provide instantaneousionospheric corrections for the altimetry mission.Using a GPS re ection receiver could mean that futurealtimetry missions do not need to be dual frequency,which may allow cost (and weight) savings onthe altimeter itself.In conclusion, evidence has been presented that

GPS re ection receivers could perform several remote

Fig. 9. Scatterometry mission groundtracks.

sensing missions from low Earth orbit. Work wasbegun on determining the spatial resolution of are ection receiver. Coverage studies indicate thisinstrument is a feasible means of providing scat-terometry and ionospheric mapping. It is also recom-mended that more study be done on carrying a re ec-tion receiver on future altimetry and scatterometrymissions.


References

[1] M. Martin–Neira, A passive re ectrometry and interferometrysystem (PARIS): application to ocean altimetry. ESA Journal17 (4) (1993) 331–355.

[2] J.C. Auber, A. Bibaut, J.M. Rigal, Characterizationof multipath on land and sea at GPS frequencies,Proceedings of ION GPS-94, Salt Lake City, UT, 1994, pp.1155–1171.

[3] S.J. Katzberg, J.L. Garrison, Utilizing GPS to determineionospheric delay over the ocean. Technical Memorandum,TM-4750, NASA Langley Research Center, Hampton, VA,1996, 13pp.

[4] J.L.Garrison, S.J. Katzberg, M.I. Hill, E0ect of sea roughnesson bistatically scattered range coded signals from the globalpositioning system, Geophysical Research Letters 25 (13)(1998) 2257–2260.

[5] J.L. Garrison, S.J. Katzberg, M.I. Hill, C.T. Howell, Sea StateSensing, GPS World Application Contest VI, GPS WorldShowcase Issue, August 1998.

[6] A. Komjathy, J.L. Garrison, V. Zavarotny, GPS: a new toolfor ocean science. GPS World 10 (4) (1999) 50–56.

[7] M. Armatys, P. Axelrad, D. Masters, GPS-based remotesensing of ocean-surface wind speed from space, IEEEGeoscience and Remote Sensing Systems (IGARSS) 2001,Sydney, Australia, 2001, pp. 2522–2524.

[8] W.J. Emery, P. Axelrad, R.S. Nerem, D. Masters, M.Armatys, A. Komjathy, Student re ected GPS experiment(SuRGE), IEEE Geoscience and Remote Sensing Systems(IGARSS) 2001, Sydney, Australia, 2001, pp. 1518–1520.

[9] E. Cardellach Gali, Sea surface determination using GNSSre ected signals, Ph.D. dissertation, Universitat Politecnicade Catalunya, Barcelona, Spain, December 2001.

[10] A. Komjathy, Global ionospheric total electron contentmapping using the global positioning system, Ph.D.Dissertation, Department of Geodesy and GeomaticsEngineering Technical Report No. 188, University of NewBrunswick, Fredericton, New Brunswick, Canada, 1997,248pp.

[11] J.R. Wertz, Orbit and constellation design, in: Larson andWertz (Eds.), Space Mission Analysis and Design, 2ndEdition. Microcosm Inc., Torrance CA, 1992, pp. 160–174.

[12] D.A. Vallado, Fundamentals of Astrodynamics andApplications, McGraw-Hill, New York, 1997, pp. 294–298.

[13] L.G. Vargo, Orbital patterns for satellite systems, Advancesin the Astronautical Sciences 6 (1960) 709–725.

[14] J.G. Walker, Coverage predictions and selection criteriafor satellite constellations, Royal Aircraft EstablishmentTechnical Report 82116, December 1982.

[15] J.E. Draim, A six satellite continuous global double coverageconstellation, AAS Paper 87–497, AAS/AIAA AstrodynamicsSpace Conference, Kalispell, MN, August 10–13, 1987.

[16] J.E. Draim, Three- and four-satellite continuous coverageconstellations, Journal of Guidance Control, and Dynamics6 (1985) 725–730.

[17] T.J. Lang, Optimal low Earth orbit constellations forcontinuous global coverage, AAS Paper 93-597, AAS/AIAAAstrodynamics Space Conference, Victoria, BC, Canada,August 16–19, 1993.

[18] T.J. Lang, Symmetric circular orbit satellite constellationsfor continuous global coverage, AAS Paper 87-499,AAS/AIAA Astrodynamics Space Conference, in Progressin Astronautical Sciences, Vol. 65, Kalispell, MN, August10–13, 1987.

[19] A.H. Ballard, Rosette constellations of earth satellites, IEEETransaction on Aerospace and Electronics Systems AES-16(5) (1980) 656–673.

[20] L. Rider, Analytic design of satellite constellations for zonalEarth coverage using inclined circular orbits, Journal ofAstronautical Sciences 34 (1) (1986) 31–64.

[21] A. Komjathy, J. Maslanik, V.U. Zavorotny, P. Axelrad, S.J.Katzberg, Sea ice remote sensing using surface re ected GPSsignals, IGARSS 2000. IEEE 2000 International Geoscienceand Remote Sensing Symposium, Honolulu, HI, 24–28 July2000.

[22] T.J. Lang, J.M. Hanson, Orbital constellations whichminimize revisit time, AAS Paper 83-402, Progress inAstronautical Sciences 54 (1983) 1071–1086.

[23] J.M. Hanson, A.N. Linden, Improved low-altitudeconstellation design methods, Journal of Guidance Controland Dynamics, 12 (1989) 228–236.

[24] J.M. Hanson, M.J. Evans, R.E. Turner, Designing good partialcoverage satellite constellations, AIAA Paper 90-2901-CP,AIAA/AAS Astrodynamics Conference, Portland, OR,August 1990, pp. 20–22.

[25] S.-C. Wu, T. Meehan, L. Young, The potential use of GPSsignals as ocean altimetry observables, Proceedings of IONNational Technical Meeting, Santa Monica, CA, January1997, pp. 543–550.

[26] J.P. Loftus, Jr., C. Texeria, Launch Systems, in: Larson& Wertz, (Eds.), Space Mission Analysis and Design, 2ndEdition, Microcosm Inc., Torrance CA, 1992, pp. 669–681.

using gps reflections for satellite remote sensing

Documents