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GLOBAL SCALE OBSERVATIONS OF IONOSPHERIC INSTABILITIESFROM GPS IN LOW EARTH ORBIT

Leonard Kramer and John L. GoodmanNavigation, United Space Alliance, LLC., 600 Gemini Avenue, Houston, Texas 77058 USA

AIAA 2001-4653

Figure 1. Evidence of scintillation of MAGR/S on STS99 orbits. The range rate residuals are normalized to projection of receiver state error in the range rate space

(ch.2)

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ABSTRACT

The GPS receiver used for navigation on the Space Shut-tle exhibits range rate noise which appears to result fromscintillation of the satellite signals by irregularities inionospheric plasma. The noise events cluster in geo-graphic regions previously identified as susceptible toinstability and disturbed ionospheric conditions. Thesemechanisms are reviewed in the context of the GPSobservations. Range rate data continuously monitoredduring the free orbiting phase of several space shuttlemissions reveals global scale distribution of ionosphericirregularities. Equatorial events cluster +/- 20 degreesabout the magnetic equator and polar events exhibithemispheric asymmetry suggesting influence of off axisgeomagnetic polar oval system The diurnal, seasonaland geographic distribution is compared to previouswork concerning equatorial spread F, Appleton anomalyand polar oval. The observations provide a succinct dem-onstration of the utility of space based ionospheric mon-itoring using GPS.

INTRODUCTION

In evaluating the implementation of the MAGR/S GPSreceiver for eventual replacement of on-board TACANsystems currently in use for the United States shuttle pro-gram we have incidentally observed rather un-ambiguous evidence of ionospheric scintillation in thereceiver velocity measurements9. The MAGR/S is a fivechannel, dual frequency, keyed receiver speciallyadapted by the manufacturer, Rockwell-Collins, forspace flight use. In the early phases of receiver evalua-tion, periods of noisy velocity in the output state from theGPS receiver were observed by ground controllers. Thephenomenon was seen on many consecutive orbits andwould persist for 10 to up to 20 minutes. Subsequentanalysis indicates that this noise is related to delta phase,range rate measurements which usually cluster aroundthe magnetic equator. The noise is a source of concern

to the manned space effort as it exceeds nominal systrequirement thresholds.

Since at least the early 1950’s, ionospheric irregularitihave been known to contribute to interruptions in radcommunication. This disturbance is known as scintillation and the processes creating it are known to exhiglobal scale effects. Many studies have documentobservational and theoretical basis for this scintillatio

of radio frequency radiation. Most important of thesinvolve instability processes connected with neutral themospheric atmosphere circulation and the geomagnefield in equatorial regions and particle precipitatiorelated to aurora in the polar cap latitudes. Aarons1 hasarticulated theories related to the geographic and ssonal occurrence of equatorial scintillation. The book bKelly5 has extensive discussion on the geophysiccauses and consequences of ionospheric irregularit

seconds mission elapsed time

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no-edCopyright © 2001 by United Space Alliance, LLC. Publishe

by the American Institute of Aeronautics and Astronautics, Inwith permission.

Efforts have been undertaken to create GPS based iosphere monitoring systems based on ground bassystems6,11.

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The GPS system, utilizing a dual L band frequency(1.57542 and 1.2276 GHz) signal, is subject to scintilla-tion and can be used to monitor the global nature of ion-ospheric processes contributing to scintillation andperhaps better understand these processes. We assert thatthe noise seen in the velocity are a result of ionosphericscintillation of the range rate measurements. In this workwe develop techniques to diagnose scintillation fromrange rate measurements. We present geographic and tothe extent possible, the seasonal and solar hour angledependence of our events. We also describe a theoreticalbasis for spacecraft velocity augmentation of the effectand observational evidence supporting it.

We would like to advance the idea that satellite borneGPS receivers in low earth orbit can contribute to globalunderstanding of occurrence and geophysical causes ofionospheric irregularities.

DATA

As part of GPS receiver evaluation, auxiliary instrumen-tation port data is regularly collected during orbitalphases of shuttle flights. These data comprise internalsoftware parameters, pseudo-range and delta-phaserange rate information in 4 simultaneously tracked GPSsatellites and an additional peripheral channel that mon-itors satellite selection and the dual frequency correctionneeded to compensate for ionospheric delay.

The MAGR/S receiver software computes a state (posi-tion and velocity) using a blended solution “Kalman” fil-ter employing process noise intentionally tuned to sub-optimum levels. The practice makes the receiver generi-cally robust since uncertainty in the filter state growsquickly when measurements are absent and thus currentmeasurements are always heavily weighted in the solu-tion. It is fair to say that, in a sense, the receiver is notusing a Kalman filter, rather that it delivers a blendeddeterministic solution. The downside to the practice isthat the receiver is not optimal for space based applica-tion and has higher state uncertainty than is otherwisepossible based on available gravity and drag models.For these reasons the receiver does not propagate its statewell when measurements are absent.

Range Rate Measurements

The data in this investigation comprise 0.2 secondperiod, phase change observables constituting range-ratemeasurements. Both pseudo-range and range rate areincorporated into the receiver’s state estimate. Inertialinformation is contributed in the form of aiding data fromthe shuttle on-board solution and a barometric reading is

used to augment altitude on entry and landing. As paof the usual state processing in the GPS internal filteresiduals are formed representing a difference betwethe state’s projection of range rate and the actual ranrate measurement. These residuals are then normalito the projection of the Kalman filter covariance in thrange rate space. Figure 1 presents a time series of soof these observations from a shuttle mission in Februaof 2000. These signatures form the principle evidenof scintillation that we have seen.

For independent measurements with normally distriuted instrumental error, the normalized observatioshould theoretically correspond to a standard normal dtribution with the caveat that the filter is converged andtuned appropriately. So the noise seen in figure 1, wlevel exceeding 2 or 3 represent profoundly corrupt mesurements and they are weighted correspondingly lessthe receiver solution.

We do not see pseudo-range noise at the same time asrange rate noise as shown in the figure 1 example. Fsome events, the state is sufficiently perturbed to cauerrors to appear in the pseudo-range residuals. Ctainly, the receiver state’s velocity is corrupted when thnoise appears in multiple channels.

In our evaluation of the MAGR/S we have documenteother anomalies contributing to noisy ranges relatedGPS receiver operation and firmware anomalies. Sourof noisy GPS velocity include:

• Sub-optimal intermediate satellite geometry (GDOchimneys) due to “one at a time” changes in selectsatellites. Changes have been delayed by softwanomalies or poor visibility with respect to antenngain pattern.

• Sub-optimal satellite geometry and less than 4 satlite tracking caused by signal obscuration whildocked to Mir, International Space Station or HubbSpace Telescope.

• Occasional receiver restarts due to internally detectsoftware anomalies.

• Switches of satellites tracked for navigation measurments. This is due to the Kalman filter implementation.

Noisy GPS velocity that results from the above has a dferent signature and often a higher magnitude than thcaused by ionospheric scintillation seen in FigureFurthermore, times of sub-optimal geometry anreceiver resets are known and can be compared aganoisy velocity periods. Space Shuttle flights of thMAGR/S, beginning in September 1996, have led

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numerous receiver firmware changes. As firmware cor-rections were applied, the number of non-scintillationnoisy velocity incidents decreased.

Scanner Code

Our approach to the data in the present work is to identifynoisy periods based on the normalized delta ranges. Wehave identified scintillation on numerous flights. In thiswork we have selected 4 flights to study in detail. Refer-ring to the normalized units in Figure 1 as “sigma level”we have written a scanner program that selects eventsbased on that sigma level. The characteristics of theselection algorithm are:

1. Sigma level exceeds 2 for 2 seconds (2 measurementcycles) or more.

2. Must be 3 seconds after a set of satellites are switchedto a new channel.

3. Receiver has good lock on the satellite (FOM = 1.)

We selected a sigma level threshold of 2 based on accu-mulated histograms of normalized range rate observa-tions. These indicate that greater than 2 sigmameasurements are profound outliers when compared tothe background distribution. Criteria number 2, reflectsawareness of a known deficiency of the system in that thereceiver state does not solve for range biases. When, a setof 4 satellites are assigned to hardware channels, theexisting state covariance is not adjusted to reflectincreased uncertainty in a new state. As a result, anoma-lous sigma levels appear in the measurements. Exclud-ing events for three seconds permits influence of thesatellite set switch to be absorbed into the state. Thethird criteria which simply masked against the internalfigure of merit (FOM) evaluation of the receiver. Select-ing events with good FOM, reduces effects of poor track-ing due to blockage and firmware deficiency.

The event selection list does not exhaust all alternatesources for false positive detection of scintillation. Forexample there is statistical clustering of noisy events inrange-rate immediately before a set of satellites areswitched. This may be the result of some sensitivity toweak signal associated with factors contributing satelliteswitching logic. The issue is still under study.

Events meeting the scanner criteria are further processedto evaluate latitude and longitude, solar hour angle, andgeomagnetic field at the event position. The lines of sightto all 4 satellites are computed and satellite attitudeangles between the spacecraft velocity vector, the geo-magnetic field and local horizontal are also computed.

GEOGRAPHIC DISTRIB UTION

The shuttle orbits the earth approximately every 90 miutes so the low earth orbit platform samples all gegraphic longitudes in a few days. Compared to grounbased observations, little variation in solar hour angleafforded. This is because the local time at a particular laitude does not vary much during the orbit and only asresult of the orbit motion of the earth around the sun duing the mission and the precession of the spacecraft oras a result of the earth’s oblateness. Evidently satellbased observations permit a wide geographic samplwith comparatively little ability to observe local timevariation (at a given latitude) in the geophysical proces

Figure 2 presents the geographic clustering for four msions. Geomagnetic dip angles at +/- 15, and 45 degrare superimposed on the plots as well as the geomagnequator. In the Figure 2 a inset, we see the latitude-logitude distributions for STS 88 which was flown onDecember 4 through December 15 1998. The north asouth limits are dictated by the limited inclination of theorbit. There are a large number of false positive scintlation signatures in Figure 2 a which manifest as isolatedevents occurring through-out the plot. The significafirmware changes mentioned previously, related to erroidentified during evaluation of the receiver, we believare responsible for these false positive events. Manythe firmware issues were corrected subsequent to tflight. Nevertheless, here, in Figure 2a we see clusteriof linear trains of events along the inclined orbital tracoccurring over equatorial regions of South AmericaThese are seen on consecutive orbits, stretching eastwacross the equatorial Atlantic ocean. Events taperover the western to central sub-Saharan Africa. Othlinear strings of events occur over the Indian ocean, souwest of India and over Sumatra and eastward over cenregions of Indonesia.

In addition, there is a hint of clustering of events near thmost poleward extent of the spacecraft’s orbit suggestithat we are intercepting scintillated signals througauroral zones. As a result of the large number of falpositive events on STS 88 (Figure 2 a) the conclusiothat we are seeing auroral scintillation is tentative. Wwould also caution that latitude sampling of any purerandom process is biased toward higher latitudes by tapproximately sinusoidal variation of latitude withrespect to longitude as the spacecraft orbits. We canthat the appearance of individual time series for STSthat we examine for events occurring south of Australin particular is, consistent with the morphology of scintillation signatures seen in the equatorial regions.

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STS 106 10/2/00 to 10/13/00.STS 96 5/27/99 to 6/6/99,

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Figure 2. Geographic distribution of noise events seen in GPS receiver range rate for space shuttle. Geomagnetic equa-tor and dip-angle contours shown at +/- 15 and 45 degrees. Wide range of activity is noted and clustering of eventsnear the geomagnetic equator and in polar regions. The satellite technique permits wide geographic coverage. Solarhour angles are confined by the evolution of the orbit to about 3 or 4 hours of local time. The record for STS 88 seenin inset (a) may be have many false positive events resulting from now corrected firmware issues.

STS 88 12/4/98 to 12/15/98. STS 99 2/11/00 to 2/22/00.

(a) (c)

other words, we have confidence that we are seeing someauroral zone scintillation on STS 88 in figure 2 a.

In Figure 2 b we see thegeographic distribution of scin-tillation events from STS 96 flown from May 27, 1999 toJune 6, 1999. The results from this mission contrast tothat in STS 88 seen in Figure 2 a. The number of falsepositive signatures is greatly reduced as a result of, webelieve, significant firmware changes mentioned previ-ously. But in addition, the number, degree and extent ofwhat we identify as scintillation is reduced as well. Theprimary contributions are from linear tracks of eventsalong ascending portions of orbits occurring over theeast-central Pacific and a group of events again occurringover central and north Africa. Indonesia appears also tobe favored with a significant event during this period. Itis interesting that the event over the east central Pacificocean is isolated yet extends from the dip-angle contourat 45 degrees in the southern hemisphere all the way tothe conjugate dip-latitude in the northern hemisphere.

That event is accompanied by one other orbital track wgreatly reduced extent.

The geographical extent of scintillation observed on ST99 which flew from February 11 to February 22 is showin Figure 2 c. These results are in striking contrastthose seen on STS 96 and STS 88. Here, we asserbroad extent scintillation in the equatorial regionroughly bracketed by the dip angle contours at 4degrees in both north and south hemispheres. The eveare seen on very many consecutive orbits stretching frothe east central Pacific, across South America continuuninterrupted across the equatorial Atlantic, with somlessening of incidence across Africa but continuing ovthe Indian Ocean, India, South East Asia and the WestPacific. Events are absent from the central paciregion. There is also clear evidence of polar events dtributed geographically somewhat consistent with knowlocations of the auroral zones-polar oval systems for tgeographic coverage afforded by the spacecraft orbThese are, over east central Canada and the north cen

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United States3. There is an absence of events with similarcharacter over other northern hemisphere polar regions.In the southern hemisphere, the polar events are distrib-uted with greatest density south of Australia and theIndian ocean. Significant activity is also present over theextreme south central Pacific. It is significant, that theequatorial zone very nearly merges with the polar eventssouth of continental South America.

Finally, Figure 2 d presents latitude/longitude distribu-tion of scintillation events on STS 106 which flew fromOctober 2, 2000 to October 13, 2000. Here, scintillationis very much reduced from STS 99. Equatorial eventson STS 106 are seen in the eastern Pacific and once againover Africa. Southern polar events are very much in evi-dence but with no apparent significant activity in thenorthern hemisphere for this time.

The observations are consistent with previously identi-fied regions where scintillation is believed to occur andthe seasonal variation is consistent with those publishedpreviously1 although the STS 99 case in figure 2 c exhib-its considerably broader longitudinal extent of the distur-bances than the literature leads us to understand.

Instabilities

As we mentioned in our introduction, two geographicregions are of interest in contributing to disturbances inionospheric plasma. The more important of these is theequatorial regions within about 20 to 30 degrees latitudeof the geomagnetic dip equator roughly corresponding todip angles of +/- 45 degrees. According to Anderson2,the dynamics of the equatorial zone is controlled by aframe effect electric field which appears in response tothe ionosphere being dragged across the geomagneticfield lines as a result of neutral atmosphere winds.

Since the ionospheric plasma is magnetized as a result ofthe earth’s field, the charged electrons and ions are con-strained to move in quasi circular orbits around field lineswhen collisions are infrequent and are relatively uncon-strained in the direction parallel to the magnetic field.The field is not dipolar but can be accurately modeled aswe have shown in figure 2. In equatorial regions, thefield is horizontal; and assumes crescent shaped arcs thatare more or less meridionally oriented. As we approacha pole along a field line, the field assumes a verticalaspect or dip angle. In figure 2, we illustrate dip anglecontours from a standard model corresponding to themagnetic equator, +/- 15 and +/- 45 degrees dip angle.The 45 degree dip angle provides a logical divisionbetween equatorial and high latitudes.

As a result of the electron and ion motion beinrestrained across magnetic field lines, but unconstrainparallel to them, the lines tend to be equipotential asupport electric fields. At low altitudes in the ionospherion-neutral collision frequency is higher and currents cflow perpendicular to the field lines. The currents themselves further contribute to magnetic fields and thedivergence leads to charge separation giving risepolarization electric fields. The condition of the equatorial ionosphere is thus a complex system with competidynamic processes involving variable and anisotropconductivity. This, in turn, is a function of neutral atmosphere abundance and dynamics. Ultraviolet flux on tdayside and convection on the nightside contribute to iand electron source terms while neutral atmospheabundance and constitution provide the loss terms.

For many years, an important instability known as equtorial spread F has been known to exist. Formally spreF refers to ionogram signatures which are dispersed ofrequency. These kind of observations, which have beundertaken for more than 50 years, have lead to extensstudy of the ionosphere in equatorial regions. The studidentify enhanced ionospheric density know as thAppleton anomaly located a 15 to 25 latitude degresymmetrically distributed about the magnetic equator.

It is generally believed that equatorial spread F is a resof an magnetic field-gravitational Rayleigh-Taylor modinstability in analogy to that which occurs when a layeof buoyant fluid rises though a heavier fluid. It appeathat on the night side, just after dusk, production of ionfrom ultraviolet sunlight are shut off and chemicarecombination at low altitudes rapidly erodes the ionsphere creating sharp vertical ion density gradienThis condition is maintained by the overlying horizontamagnetic field since ion motion is restrained across fielines. It is nevertheless energetically unstable to collaps

The instability grows because the “falling” plasma creates horizontal currents that exhibit divergences alothe gradient boundary leading to charge distributions thfurther feed perturbing electric fields parallel to thboundary. These then contribute to drift of plasmon the boundary that further increases the amplitudethe boundary perturbation. The evolution of this instabity proceeds into a non-linear magneto hydrodynamregime which, in the theoretical models, resultsupwelling of voids in the plasma that extend to altitudeof order 500 kilometers. Kelly5 and Aarons1 highlightthe essential physics and observations that we revihere including the description of plumes of ionospherdensity depletions seen in backscatter radar that risehigh as 1000 kilometers.

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We would also like to point out that, although we havebroadly categorized equatorial events as occurring within+/- 45 degrees dip angle of the geomagnetic equator.The equatorial events extend beyond this limit in thesouth central atlantic ocean. These events are seen in fig-ure 2 insets a, c and d. We think this is related to signif-icantly weaker magnetic field at this location and iscoincident with the well known South Atlantic Anomaly.We postulate that the crescent shaped meridionally ori-ented structures thought to comprise the events rise tohigher altitudes and extend to wider latitudinal extent asa result of the weaker geomagnetic field which wouldpermit greater cross field motion of ions at these points.

Furthermore, radiation hazard cited for astronaut safetyin the South Atlantic Anomaly is entirely independentfrom processes associated with scintillation and we haveno theoretical basis to assume that the high energy parti-cles entering the earth’s ionosphere in the region duringgeomagnetic storms are directly effective in causingscintillation of the GPS L band signals. However, coinci-dental thermospheric heating and changes in neutralatmosphere circulation might, we speculate, introducevariability to the process that contributes to spread F.

Scintillation is also observed in the polar regions. Muchof the same complexity attached to equatorial regionsalso apply to the polar ionosphere. In addition, geomag-netic field lines in the high latitude regions map to themagnetosphere and the interplanetary medium connect-ing with the solar wind and embedded magnetic field. Asa result of the non-axially symmetric contributions to theearths field and partly as a result of the attendant diurnaland space weather forcing, polar scintillation should notdistribute symmetrically around the poles.

Apparently, there are two agents contributing to iono-spheric disturbances at the poles. First, solar wind drivenelectric fields are created in the magnetosphere that mapalong the field lines to the polar ionosphere where suffi-cient collisions occur to permit limited electric fielddirected currents to flow. Second, during periods of geo-magnetic disturbance, energetic particles enter the earthsionosphere along magnetic field lines essentially con-necting to interplanetary space and interacting with theneutral atmosphere. These cause ion production andheating contributing to convection and ion density vari-ability. Presumably, these density enhancements ordepletions produce the similar effects on GPS satellitesignals as the better known scintillation near the equator.

Variability from mission to mission is striking and mightbe explained by known seasonal and solar weatherdependence of the factors that contribute to scintillation.

We submit, though, that the noise we are observingmuch more globally extensive and includes significafeatures at polar latitudes which have not been presenin the literature. As Aarons1points out, the known selec-tive factors that contribute to the global scale occurrenof scintillation are modulated by neutral wind and electric field changes which are not well understood anwhich can theoretically either enhance or inhibit thdevelopment of the irregularities.

SOLAR ANGLE

The satellite based technique does not permit exhaussampling of local time as was mentioned previouslNevertheless, we can investigate local time occurrenfor the few hours local time represented by each of tflights studied. Figure 3 shows the local time occurrendivided between equatorial and polar events. Poevents are separated from equatorial events by sortaccording to magnetic dip angle and forming histogramby of number of events that occurred in solar hour angbins. From figure 2, for example, it is evident that polaevents may be separated from equatorial events bydip angle equal to 45 degrees. The only exception athose events occurring in the south Atlantic which wmentioned previously and the false positive events thare most prominent on STS 88 in figure 2 b. Figureshowing our solar hour distributions should not be intepreted as describing any significant composite diurnvariability. The differences in event occurrence seebetween missions is certainly dominated by seasonal aspace weather effects rather than a manifestation of dinal variability.

The geophysical processes controlling equatorial spreF phenomena are associated with plasma instabilitoccurring after dusk. In Figure 3a, we show solar hoangle distributions of equatorial scintillation event. Thsolar hour angle trace for STS 99 shows the largest nuber of events occurring primarily between 01:00 an06:00 but we emphasize that this was the only oppornity to observe during night side passes. A comparabperiod of time was available on the dayside betweabout 12:00 and 18:00 hours for STS 99 but, as we seesignificant activity evident during the period. Thisshows that the equatorial process contributing to the sctillation may be prominent during the time between midnight and dawn and not just during the post sunset perioa point which has also been made in the literature13.

Similarly, the results for STS 88 show prominent equatrial activity between the hours of 22:00 and 04:00 whicwas the interval of time on the nightside available foobservation while the opposite side of these orbits on t

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dayside show small elevation in activity which we canattribute to the false positive phenomenon described ear-lier. The events for STS 96 and STS 106 also cluster inthe nightside period.

The overall impression from figure 3 a is that the equato-rial scintillation we are observing is a nightside phenom-enon. This is particularly established by the results fromSTS 99 and STS 88 where the majority of equatorialevents are registered on the nightside despite equalopportunity to observe on the conjugate dayside hourangles. We would add that sampling of orbits on thenightside also explains the prominence of either ascend-ing or descending orbit tracks seen in figure 2. For exam-ple, on STS 99 seen in figure 2 c, the predominance ofdescending tracks from north-west to south-east in theequatorial zone is a result of scintillation selecting those

portions of the orbit on the nightside. Few ascendintracks were available on the night side.

The polar events do not have any particular diurnal clutering. The plot in figure 3 b is dominated again, bevents sampled during STS 99 which is seen in the gegraphic latitude-longitude distribution of figure 2 c to bextensive and un-ambiguously clustered at the polewaextremes of the orbit.

INTERFERENCE PATTERN

Scintillation is thought to result from variability in boththe permittivity of the ionosphere and variations in thickness of ionospheric layers between transmitter areceiver. Electrodynamic theory holds that transmittephotons exhibit interference from multiple availablpaths. The received signal is contributed by the paths texhibit least first order variation in phase from onanother8. Conventional analytical and experimentaresults of optics are explained using this theory. Thleast time principle attributed to Fermat and straight linpropagation of light are derivative from it.

In the ionosphere, as a result of the stochastic distributiof dispersive layers and in-homogeneities, the multippaths over which the first order variation in phase is miimum are contributed by paths that are geometrically fapart and changing rapidly either as a result of their seular motion or as a result of the motion of the receiveThis interpretation may be at variance to a conventionview that scintillation is somehow a mixture of “phaseor “amplitude” variability and that the signal is attenuated while following a single ray to the receiver.

We view the physics of electromagnetic ionospherpropagation as the same for both of these “types” of sctillation. The distinction between phase and amplitudfading, must be related to individual variability in howreceivers process range data. It has certainly been notithat the degree of susceptibility to interference is highreceiver dependent3. It appears that the Shuttle’s MAGR/S, employing an automatic gain control circuit, is senstive to weak signals and thus we do not observe any coventional fading. Our receiver is quite sensitive to phanoise, explaining the observations we see in Figure 1

Electrodynamics of Plasma

The primary contribution to index of refraction in theionosphere may be derived from plasma theory. At thGPS L band frequencies a high frequency, cold plasmlimit applies and the only contribution to permittivity is

Equatorial scintillation events selected forgeomagnetic dip angle magnitude less than45 degrees for several shuttle missions.

Polar scintillation events for dip anglesmagnitude greater than 45 degrees.

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where is the free space permittivity, a fundamentalproperty of space and , the plasma frequency,which represents a normal mode frequency associatedwith displacement of the electrons relative to the heavypositive charge carriers in the plasma (primarily O+.) Toderive this expression, the Maxwell equations and theequation of motion for the charged species are expressedin a fourier spacial wave number, time frequencydomain. Algebraic manipulation then permits a disper-sion relation to be expressed which provides the analyti-cal tool needed to understand how wavelength is relatedto the frequency and index of refraction in the media.

Equation 1 is a high frequency limit to that general dis-persion relationship which is appropriate because all thephysical cutoffs and resonance such as electron, ion gyrofrequencies, plasma and hybrid frequencies are orders ofmagnitude smaller than the GPS signal frequency. Therelative simplicity of equation 1 reflects an advantage ofhigh frequency for use in GPS. Readers are referred to abook by Swanson12 which we think is a good treatmenton the details of this analysis. An alternate approach isthe Hartree-Foch equation exposed by Klobuchar6 whichis a a formulation that explicitly and appropriatelyneglects motion of ions but otherwise is identical. Wewould like to note especially that equation 1 contains noconductivity term and is positive real valued. The fre-quency is high enough that the mode exhibits no loss.Without a collision term there is no theoretical basis toexpect a decaying amplitude as there would be in a highloss medium like sea water for example.

As the GPS signal transits the medium, the net effect isan accumulated phase shift over all possible pathsbetween the transmitter and the receiver. For any geo-metric path between transmitter and receiver, the phasecontribution to the total signal is computed according to:

(2)

where is an arbitrary path (which could even be tortu-ous or convoluted.) Equation 2 expresses the combinedphase change along the path as the wave number (a func-tion of the material properties of the matter contained inthe space) changes along the path.

Variational methods of calculus of may be used to deter-mine a dominant path but the physical principle is that allpaths providing first order invariant phase to the receivedsignal will contribute to the received signal. Both theelectric and magnetic fields of the wave are modulated bythe interference. Conventional receivers respond to cur-

rents induced in the antenna by the electric field. So t“ω” component a Fourier resolution of the radiation eletric field becomes:

(3)

where is electric field at the transmitter. Thsummation is really taken over all available paths. Thterm is a complex valued phase envelope thmodulates the received signal and is a function of timand position.

Velocity Augmentation

We believe that the spacecraft velocity, being roughly 1times greater than velocities encountered in terrestrapplications contributes to the scintillation effect. Tstudy this, we linearize with respect to its spaciagradients and extract information about how velocicontributes to modulating . If the velocity is largecompared to the secular motions of the geophysical pcesses (which we believe to be the case) then we propthat essentially all the noise is a result of the motionthe spacecraft. Consider a velocity dependence resultfrom the spacecraft velocity and spatial gradients in tenvelope:

(4)

We would like to identify the velocity perturbation withcomponents parallel and perpendicular to the linesight to the scintillated satellite. The dot product in thintegral in equation 4 is then expressed:

(5)

Where we have used the obvious notation to indicate tparallel (||) and perpendicular ( ) components of thspacial gradient and is the angle between the velocvector and the line of sight to the satellite.

We argue that satellite directed components of the graent are negligible since the accumulation of paths that acontributing to the first order variation are, in that casnearly parallel to the line of sight. Certainly, paralle

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components of velocity contribute to doppler shift but thereceiver is already adapted to measure this for the rangerate observation. Neglecting the parallel component andsubstitution into equation 3 allows us to see how varia-tions in the radiation electric field are modulated by thevelocity and the phase envelope.

(6)

Equation 6 provides us with a means to support the the-ory by examining distributions of scintillated signal rela-tive to the angle the line of sight makes with thespacecraft velocity vector which we here identify aswith denoting forward direction.

Speculation about Faraday Rotation

Since the ionospheric plasma is magnetized, Faradayrotation, a preferred phase advance of right hand circu-larly polarized component of the electric field in a mag-netized plasma, is a candidate for contributing to L bandscintillation. Klobuchar6 reports that the circular polar-ization of GPS signals protects against Faraday rotation.On the contrary, there is no physical basis for the circularpolarization of the GPS signal to protect against Faradayrotation as it still represents a phase advance of the elec-tric field. Rather, the high frequency of the L band com-pared to any conceivable cyclotron frequencies in theionosphere protects against first order effects from Fara-day rotation. Contributions to range rate noise fromrapid modulation of a Faraday rotated electric field vec-tor resulting in scintillation is not ruled out. This mightmanifest as enhanced noise for lines of sight parallel tothe local magnetic field.

VELOCITY ANGLE DISTRIB UTION

Identifying a null hypothesis that the signals are ran-domly distributed with respect to spacecraft velocity, thedistribution of events with respect to angle from thevelocity vector must then be proportional tobecause the solid angle available to intercept randomlines of sight scales according to this factor. On the otherhand, if signal events are proportional to the perpendicu-lar component of velocity in accord our theory then dis-tribution must be further scaled by another factor of

since is the component of velocity per-pendicular to the line of sight as seen in equation 6.

To test this, we accumulate statistics on the line of sightof scintillation events (σ > 2) compared to contempora-neous un-scintillated measurements (σ < 2). These datawere prepared by calculating the angle between the GPSsatellite line of sight and the spacecraft velocity vector.

Nominally, 4 satellites are tracked simultaneously. Ditributions of angles are divided into two sets basednoise level. On STS 99 for example, we found 1030scintillation events characterized by noisy delta rangeσ> 2). In this set we also found 25266 satellite trackinintervals which exhibiting just nominal signal level. Figure 2 presents the results. These histograms are normized to unit integral with respect to angle. Normalizedistributions of and are presented foreference.

We assert that scintillated events follow a distrbution consistent with our theory while the “randomline of sights conform closely to the . Althoughwe have not ruled out other possible selective factosuch as latency in acquiring lock on satellites in the foward direction for example. The same analysis for ST88 supports the theory. The same analysis for the tother missions studied have less statistical confidencedo not contradict it.

We are aware that the satellite selection algorithm for tGPS receiver is not strictly random. The receiveattempts to track 4 satellites with an optimal geometrThis puts an emphasis on selection of one high elevatsatellite and 3 other low elevation satellites. We are nable to rule out an accidental clustering of scintillatioaccording to a distribution, but we would nounderstand how to reconcile this with the of thnon-scintillated satellite tracks. We would expect ththese latter events would be depleted near 90 degreewe were accidentally selecting high elevation satellitthat were also scintillated. We should also point out ththe selection logic permits satellites to track over signi

δE x t,( ) E0eiωt– ∇⊥Φ x( )V αsin td

0

t∫=

αα 0=

α( )sin

α( )sin V α( )sin

sin α( ) sin2 α( )

sin2 α( )

sin α( )

sin2 α( )sin α( )

α, angle from space craft velocity vector/degrees

radi

an-1

scintillation

not scintillation

sin2(α)

Figure 3. STS 99 data. Distribution of line of sight to GPsatellite vectors and local spacecraft velocity vectNot-scintillated events should scale according tosin(α)

sin(α)

9American Institude of Aeronautics and Astronautics

Kramer

ullctton

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cant arcs of the sky so that a high elevation satellite even-tually becomes low elevation.

MAGNETIC FIELD

Plasma instabilities contributing to the spread F anomalyare restricted in motion to co-rotating flux tubes that areoriented along geomagnetic meridians. The importanceof the magnetic field to mobility of ions and our sugges-tion that transient Faraday rotation contributes to scintil-lation encourages us to consider examining eventdistribution with respect to the angle of the line of sightusing the same kind of analysis we performed for thevelocity. Figure 4 represents our effort in this regard.Here, we have accumulated a histogram of number ofevents in bins of angle of the line of sight from the geo-magnetic field at the location of the spacecraft. As wehave mentioned previously, solid angle measures of ran-dom distributions are weighed toward perpendicular as aresult in the increase in available solid angle as the per-pendicular direction is approached. To compensate forthis in figure 4 we have weighted the histogram bins sothat the width of bins are proportional to the arc-cosineof the solid angle. The histograms are also normalizedto unit integral with respect to angle.

There were 3635 scintillated of 12889 total events withdip angle magnitude less than 45 degrees. STS 99 andthe other missions are similar. Although there is sometendency to elevated levels at 0 and 180 they are not sup-ported statistically and we have not ruled out other coin-

cidental reasons for that effect. We therefore report a nresult for substantial clustering of the events with respeto angle between the magnetic field and line of sightGPS satellites. We would like provoke further discussioin this area.

CONCLUSION

The essential physics of radiation through the ionosphepredicts that the medium will not attenuate at L band frquencies. Scintillation occurs because there exists muple available paths of propagation that are geometricafar apart and rapidly varying. Thus, amplitude fadinand phase scintillation are not distinct phenomenon brather reflect individual idiosyncratic receiver responsto the same interference envelope.

The GPS receiver slated to be used on the Space Shuis subject to a spacecraft velocity augmented modulatiof the interference envelope affecting range rate obseables. The interference occurs in the geographic regioand at solar hour angles consistent with previously idetified ionospheric instabilities that cause scintillation.

The incidence of observed scintillation is highly variableEquatorial events occur at night and cluster to within 2to 30 geographic degrees of the magnetic equator corsponding to a dip angle boundary between + or - 4degrees except for a few excursions outside that zonethe south central equatorial Atlantic ocean. The equtorial zone coincides with the location of ionospheriplasma instabilities identified with equatorial spreadLocal time occurrence is consistent with that conclusioalthough we see it occurring at later hours in the nigthan the most of the literature. Polar events correspondthe auroral regions and exhibiting known asymmetriconsistent with the polar auroral oval systems.

The scintillation we observe in the MAGR/S is appaently augmented by high velocity of the spacecrabecause events are preferentially distributed at rigangles to spacecraft motion, in accord with a theory wadvance holding that the component of spacecraft motperpendicular to the line of sight contributes to the inteference. This appears to be the case at least forMAGR/S receiver we are studying. If these observatioare repeatable and the theory further substantiatedwould like offer it as a selective factor in weighting measurements for future space rated receivers. The anbetween the velocity vector, and the line of sight to thGPS could be used to increase the formal measuremuncertainty of measurements when the angle is closeperpendicular. We propose that this can mitigate hierror in associated velocities.

not scintillated.

scintillated.

β, angle between line of sight and magnetic field.

Figure 4. Distribution of angles between satellite line ofsight and geomagnetic field at location of spacecraft forthe equatorial scintillation events from STS 88. Histo-gram bins are scaled according to equally spaced incre-ments of to compensating fordistribution of solid angle.

cos 1– β( ) β( )sin

radi

an-1

10American Institude of Aeronautics and Astronautics

Kramer

,

nl-

,

ea-

The widespread geographical distribution and apparentseasonal variability is striking and much greater than weare led to understand based on the current body of litera-ture. We submit that the known selective factors such asmagnetic activity are modified, even as Aarons1 pointsout, by seasonal or synoptic scale variability in the neu-tral atmosphere abundance and neutral winds as these arethe parameters least well understood.

ACKNOWLEDGMENTS

These materials are sponsored by the National Aeronau-tics and Space Administration under Contract NAS9-20000. The U.S. Government retains a paid-up, non-exclusive, irrevocable worldwide license in such materi-als to reproduce, prepare derivative works, distributecopies to the public, and perform publicly and displaypublicly, by or on behalf of the U.S.Government. Allother rights are reserved by the copyright owner.

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2. Anderson, D. N.,A Theoretical Study of the Iono-spheric F Region Equatorial Anomaly-II. Results in theAmerican and Asian Sectors, Planet. Space Sci., 21, 421-442, 1973.

3. Bishop, G., Basu, S., Holland, E., Secan, J.Impacts ofIonospheric Fading on GPS Navigation Integrity, Proc.of ION GPS-94, 577-585. 1994.

4. Doherty, P. H., Delay, S. H., Valledares, C. E., Klobu-char, J. A., Ionospheric Scintillation Effects in the Equa-torial and Auroral Regions, Proc. of ION GPS-2000,662-671, 2000.

5. Kelly, M. C.The Earth’s Ionosphere: Plasma Physicsand Electrodynamics, Academic Press, Inc., 1989.

6. Klobuchar, J.A.Global Positioning System: Theoryand Applications, Ch. 12, Ionospheric Effects on GPS,Eds. Parkinson, B.W, Spilker Jr., J.J. et al. AIAA, pp 485-515, 1996.

7. Klobuchar, J.A.Real-time Ionospheric Science: TheNew Reality, Radio Science, 32(5), 1943-1952, 1997.

8. Feynman, R. P.,QED: The Strange Theory of Lightand Matter, Princeton Univ. Press, Princeton, New Jer-sey, 1985.

9. Goodman, J. L. and L. Kramer,Scintillation EffectsOn Space Shuttle GPS Data, Proceedings of the NationalTechnical Meeting, Institute of Navigation, Long BeachCA, January 22-24, 2001.

10. Nichols, J., Hansen, A., Walter, T., Enge, P.,HighLatitude Measurements of Ionospheric ScintillatioUsing the NSTB, Proceedings of the National TechnicaMeeting, Institute of Navigation, San Diego, CA, January 25-27, 1999.

11. Pi, X, A.J. Mannucci, U.J. Lindqwister and C.M. HoMonitoring of Global Ionospheric Irregularities Usingthe Worldwide GPS Network, Geophys. Res. Let., 24(18)2283-2286, 1997.

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13. Whalen, J.A.Equatorial Bubbles Observed at theNorth and South Anomaly Crests: Dependence on Sson, Local Time and Dip Latitude, Radio Science, 32(4),1559-1566, 1997.

11American Institude of Aeronautics and Astronautics