Ionospheric Scintillation Effects on Single andDual Frequency GPS Positioning

S. Datta-Barua, P. H. Doherty, S. H. Delay, Boston CollegeT. Dehel, FAA Technical Center, National Satellite Test Bed

J. A. Klobuchar, Innovative Solutions International, Inc.

BIOGRAPHY

Seebany Datta-Barua is a research engineer studying lowlatitude ionospheric phenomena at the Boston CollegeInstitute for Scientific Research (ISR). She is also aPh.D. candidate in the Aeronautics and AstronauticsDepartment at Stanford University.

Patricia Doherty is a Senior Research Scientist with theBoston College ISR. Her prime research activitiesinclude studies of ionospheric effects on GPS signals andworldwide systems and in analytical and theoreticalmodels of the earth’s ionosphere.

Susan Delay is a Senior Research Analyst with the BostonCollege ISR. Her work includes data and numericalanalysis, programming and graphics development.

Thomas Dehel is lead engineer on the National SatelliteTest-Bed (NSTB), a prototype and test tool for the FAA’sWide Area Augmentation System (WAAS). He currentlysupports WAAS testing and related international andionosphere test efforts.

John A. Klobuchar is a Chief Scientist for AtmosphericResearch at Innovative Solutions International supportingthe FAA in their development of the GPS Wide AreaAugmentation System. He is also a Fellow of the IEEE.

ABSTRACT

The low latitude ionosphere poses a challenge to bothGPS users and Satellite-Based Augmentation System(SBAS) providers. Single and dual frequency GPSreceivers used in low-latitude regions can suffer fromrapid amplitude and phase fluctuations known asscintillation. Scintillation occurs when the GPS or SBASsatellite signal travels through small-scale irregularities inelectron density in the ionosphere, typically in theevening and nighttime in equatorial regions. Frequentscintillation and high rates of change in Total ElectronContent (TEC) can cause loss of lock to dual frequencyand even single frequency receivers. At these times, GPS

users in low latitudes can experience decreased levels ofaccuracy and confidence in stand-alone positioning.

We present observations of scintillation and its effects onstand-alone positioning at a station in Rio de Janeiro,Brazil, during a two-week span in February of 2002, apost solar maximum year. A GPS Silicon ValleyIonospheric Scintillation Monitor (ISM) is colocated witha dual frequency MiLLennium receiver. The ISMprovides measurements of amplitude scintillation at L1once per minute via the S4 index of normalized standarddeviation of signal intensity. Multipath can inflate S4,falsely indicating ionospheric scintillation activity, and isremoved with the use of a multipath/scintillationdiscriminating technique.

Positioning is performed post-process by iterativelysolving a linearized model of the range equations. Forsingle frequency measurements, the ionosphere isestimated using the GPS broadcast ionospheric model.Dual frequency positioning has the advantage ofexploiting direct measurements of TEC. We use carrierphase leveled measurements of TEC, when available, toestimate position accuracy available to a dual frequencyuser experiencing scintillation. For these TECmeasurements the satellite and receiver inter-frequencybiases have been estimated.

We present nighttime observations of TEC in Brazil andthe relationship between high rates of TEC and amplitudescintillation. The effects of scintillation on both a singlefrequency receiver and dual frequency receiver’savailable constellation for positioning are shown. Inaddition, a dual frequency user’s L2 availability is shown,as this impacts one of the main advantages of a dualfrequency receiver: the ability to directly measure andremove the error due to the ionosphere. We aim toillustrate what kinds of effects the single frequency userand the dual frequency user can expect to experience, andwhat kind of result this can have on the accuracy andconfidence in their position solutions.

INTRODUCTION

The ionosphere is a region of the atmosphere at analtitude of several hundred kilometers whose definingfeature is the presence of free electrons stripped fromatoms by solar ultraviolet radiation. As a dispersivemedium that lies on the signal path between the orbitingGPS and Satellite-Based Augmentation System (SBAS)satellites and the users, the ionosphere refracts thebroadcast RF wave by an amount proportional to the totalelectron content (TEC) along its path and as a function ofthe signal frequency. This error term is on the order ofmeters and affects GPS users worldwide.

Observed ionospheric behavior varies over the earth andcan be generalized into auroral, mid-latitude, andequatorial areas. The geographic bands 10-15° north orsouth of the magnetic equator are referred to as theequatorial anomaly region, due to the occurrence of theAppleton anomaly. This anomaly is a daily evening-timepeak in TEC that follows the local midday peak. Theanomaly peak is both spatially and temporally highlyvariable and may reach higher magnitude than the middaypeak. Small spatial irregularities in the ionospheretypically develop during and after the Appleton anomaly.

These small-scale irregularities in electron density candiffract the signal, leading to rapid fluctuations in signalintensity, known as amplitude scintillation [Skone 2000].Amplitude scintillation can be severe enough that thereceived GPS signal intensity drops below a receiver’slock threshold, forcing the receiver to reacquire the signal[Doherty 2000]. Amplitude scintillation is measured bythe S4 index, which is essentially a normalized standarddeviation in the signal intensity over 60 seconds.

Figure 1: Ionospheric amplitude scintillation ascaptured by S/N, S4, and TEC measurements.

Figure 1 illustrates the characteristics of amplitudescintillation described above. The uppermost plot ofdetrended signal-to-noise ratio over time demonstrates

that the receiver experiences a great deal of scintillationon this line of sight around 01:00 UT, and to a lesserextent at 02:00 and again after 03:00. The correspondingS4 values, shown in the middle plot with the periods ofscintillation highlighted in red, confirm these findings.The measurements of TEC are in the bottom plot, wheredistinctive ionospheric structure that coincides withperiods of scintillation may be seen. The data shown inthis plot are from the data set analyzed further in thispaper, whose content and processing are described insubsequent sections.

Figure 2: Effect of amplitude scintillation onavailability of L1 and L2 data.

The effect of ionospheric amplitude scintillation on a GPSreceiver is illustrated in Figure 2. The S4 value at L1along one line of sight is plotted across the top, withperiods of scintillation highlighted in red (see descriptionof S4 data processing below). Epochs for which L1measurements are unavailable, henceforth referred to as“dropouts” or “outages”, are marked with black circles, asare L2 data outages. These dropouts are importantbecause the loss or gain of a satellite’s measurementseffectively changes the available constellation of a userwho wishes to perform stand-alone positioning. There isa correlation between periods of scintillation measured atL1 and the occurrence of dropouts on L2. This figuremakes clear that scintillation can even be severe enoughto cause data outages on the civilian L1 frequency. At itsworst, scintillation can cause the very receiver designed totrack it and provide the S4 measurements to lose lock.

Another form of scintillation, known as phasescintillation, occurs from rapid phase variations in thesignal after traveling through these same small-scaleionospheric irregularities. Phase scintillation may lead tocycle slips and loss of lock for receivers as they track thesignal. Phase scintillation is quantified by σ∆ϕ, thestandard deviation of the detrended phase over an intervalof up to 60 seconds. Phase scintillation is not addressedin this paper.

Figure 3: Fading depths at L-band worldwide for solarmaximum and solar minimum.

Scintillation activity is both geographically andtemporally dependent. The 11-year solar cycle, localseason of the year, and geomagnetic location all play arole in degree of activity [Basu 1988]. Figure 3 showsthe worldwide occurrence of worst-case fading at L-bandfrequencies during the peak of the solar cycle (left), andduring solar minimum (right). The figure of the earth isoriented with the sunward-side on the left, and thenighttime side on the right. The strongest signal fadingoccurs for a few hours after sunset in the equatorialanomaly regions north and south of the magnetic equatorand is more severe during heightened solar activity.

DATA AND IONOSPHERIC MEASUREMENTPROCESSING

The data analyzed and discussed in this paper come fromtwo colocated stationary receivers in the equatorialanomaly region during a post-solar-maximum year. Onesource is NovAtel’s dual frequency MiLLenniumreceiver, which tracks L1 and L2 (semi-codelessly) toprovide pseudorange and carrier phase measurements at30-second intervals. This receiver is part of the BrazilianTest-Bed (BTB) being developed by the FAA in SouthAmerica.

The other receiver is the Ionospheric Scintillation Monitor(ISM) manufactured by GPS Silicon Valley (GSV). Thisreceiver provides measurements of amplitude and phasescintillation at L1, in the forms of S4 and σ∆ϕ, updated atone-minute intervals. The ISM has wide-bandwidthtracking loops to maintain lock longer during the highrates of scintillation, and samples at a rate of 50 Hz tocalculate the scintillation statistics S4 and σ∆ϕ [VanDierendonck 2001]. The wide bandwidth provides aconsiderable improvement in monitoring, but the ISM isstill somewhat susceptible to extremely severescintillation. In these cases it is forced to reacquire andaccumulate data for four minutes before resuming output.

The receivers were placed in Rio de Janeiro, Brazil,which is located at 15° south magnetic latitude. Thesereceivers recorded data from 15 – 28 February 2002, less

than two years after the 2000 peak of the solar cycle. Inthe Americas, “scintillation season” takes place fromSeptember to March [Sobral 2002], so February is areasonable time to expect to experience and measurescintillation.

TEC measurements are derived from the dual frequencydata of the MiLLennium receiver. The carrier phasemeasurement of total electron content, expressed inmeters at L1, is Iφ:

121

−−

=γφ

kkk LL

I

Equation 1

112

−−

=γρ

kkk PP

I

Equation 2

2

2

1

=

ff

γ

Equation 3

In these equations, P1k and P2k are the receiverpseudorange measurements, in meters, to the kth satelliteat the L1 and L2 frequencies, respectively; L1k and L2k

are the carrier phase measurements to the kth satellite, inmeters; and f1 and f2 are the frequencies of the L1 andL2 bands, in Hz. The ionosphere is dispersive, and higherfrequencies (i.e. L1 and L2 carrier signals) are advancedwith respect to lower frequencies (i.e. chipping rates ofcode P1 and P2), so the signs for Iρ and Iφ are opposite.

The code measurement of the ionospheric delay Iρ isnoisy but accurate. The carrier phase measurement Iφ isprecise but ambiguous and subject to cycle slips. Forthese reasons, a cycle slip detector is used to identifylikely cycle slips. The detrended third-order difference ofthe linear combination L1-L2 is iteratively tested forpoints beyond the larger of |±4σ| or |±1| (where |*|indicates absolute value of the quantity enclosed) becausecycle slips manifest themselves as extremely high rates ofchange in phase. Triple-differencing 30-second datarequires continuous segments at least 2 minutes long;slips in anything shorter will remain undetected. Once thecontinuous segments of Iφ longer than 2 minutes areidentified, they are piecewise leveled to the codemeasurement of the TEC, Iρ. The broadcast satelliteinterfrequency bias known as TGD is removed. Themeasurements may remain as slant delay for removalfrom the pseudorange measurements or be converted toequivalent vertical delay through use of a thin-shell

mapping function M that assumes a shell height of 350km:

)))cos(

(cos(

1)(

1

ionoe

ke

k

hRelR

SinelM

+

=−

Equation 4

The mapping function M used is a thin shell model that isa function of the elevation of the kth satellite. In thecalculation of the obliquity factor M, Re is the meanradius of the earth and hiono is the assumed height of theionospheric shell, in this case, 350 km. An estimate of thereceiver L1/L2 interfrequency bias is made by exploitingthe fact that unbiased TEC measurements have veryconsistent early morning equivalent vertical values acrossdifferent lines of sight. We make use of this spatialuniformity by choosing the receiver interfrequency biasthat minimizes the variance of the vertical TECmeasurements each morning between UT 08:00 and10:00, or 05:00-08:00 local time (LT).

Amplitude scintillation measurements S4 were obtained atone-minute intervals from the ISM. These outputmeasurements S4 are given by:

2 24 4 4

22

4 2

T N

T

S S S

SI SIS

SI

= −

−=

Equation 5

S4T is “total S4” measuring fluctuations due to any causeand S4N is a measure of amplitude fluctuations due toambient noise described in more detail by VanDierendonck [2001]. SI is signal intensity, measured at afrequency of 50 Hz, and <> indicates expected value ofthe quantity enclosed over a full minute. Since thevariance of the signal intensity SI is normalized by thesquare of the average value of SI, and then the componentof S4 due to noise S4N is removed, the resulting S4 is adimensionless number with a theoretical upper limit of 1.

Not only scintillation but also multipath interference canproduce fluctuations in signal intensity. The periodswhen scintillation dominates the S4 value aredistinguished through the use of a scintillation/multipathdiscriminator. This test makes use of the fact that thevariance of the code-carrier divergence over 60 seconds ishigher for multipath than for ionospheric phenomena.Conker et al. [2002] summarize a definition of multipathas occurring when the ratio of σccd to S4 is greater than 5.With the additional step of requiring that at least onequarter of the epochs in the previous 5 and subsequent 5

minutes must return a decision of “scintillation” for anygiven epoch to be considered a “scintillation” epoch itself,we are able to obtain more consistent results. Thisadditional step is taken because the discriminator test hastrouble distinguishing low elevation satellites whosesignals are suffering multipath from ionosphericscintillation, so that at some epochs it mistakenly returns adecision of “scintillation” when there is no small-scaleionospheric disturbance visible in a plot of TEC. In plotsof S4 such as Figure 2, the periods when scintillation isdetermined to dominate the S4 measurement are shown inred, and epochs when multipath is the main contributor toS4 are shown in blue.

Figure 4: Summary of equivalent vertical TEC and S4

measurements during scintillation from UT 15-28February 2002.

Figure 4 shows equivalent vertical TEC measurements,derived as described above from the MiLLenniumreceiver, along every line of sight over the entire two-week period of the data set, which spans 15-28 February2002. Below that curve, in red and not to scale, are the S4measurements from the ISM, after filtering out allmultipath-dominated measurements.

A number of general conclusions that we will use inlooking at effects of scintillation on positioning can bedrawn from this plot. First, in this region of the world atthe equatorial anomaly during the stage of the solar cyclefollowing peak activity, during the local scintillationseason, we see that ionospheric scintillation happensalmost nightly, generally from 00:00-06:00 UT (21:00-03:00 LT). The notable exception to this is 19 February,which is free of scintillation from 00:00-06:00 UT, andprovides a quiet night for comparison of positioning.

A typical day of equivalent vertical TEC from this two-week data set is shown in greater detail in Figure 5. Theperiod during which scintillation occurs, 00:00-06:00 UT,is characterized by wide variations in TEC from line-of-

sight to line-of-sight. Small-scale structure is also visibleas more rapidly alternating periods of low TEC and highTEC. The period of scintillation follows the second dailyequatorial anomaly peak. It occurs in the early eveningafter the midday peak, and is highly variable along eachline of sight as well; notice that the anomaly peak ishigher in magnitude than the midday peak, and happens atdifferent times (from 19:00-24:00) on different lines ofsight.

Figure 5: Equivalent vertical TEC on all lines of sighton a typical day with scintillation.

OCCURRENCE OF DATA OUTAGES

Amplitude scintillation can lead to data dropouts, as wasseen in Figure 2. This is of concern to the GPS userbecause his constellation for positioning is affected by thegain or loss of satellites that apparently flicker in and outof visibility when scintillation or fading causes temporaryloss of lock. The existence of a scintillation-free night inour data set, 19 February 2002, allows for the directcomparison of the total number of outages on that nightbetween 00:00-06:00 UT versus all of the other nights.

Figure 6: Number of data outages at L1 (top) and L2as a function of mask angle.

The upper plot of Figure 6 shows the total number ofoutages (epochs during which the satellite was withinview and healthy, but the receiver provided noinformation from it) at L1 from 00:00-06:00 UT as afunction of mask angle, with one curve per night. Themask angle is the threshold elevation angle below whichno data is considered.

The night on which there was no scintillation, 19February, is drawn in blue. Notice that in spite of beingscintillation-free, there are a significant number of dataoutages on satellites all the way up to an elevation el =15°. For these low elevation satellites (el < 15°) on thisquiet night, multipath was the likely culprit in causingdata dropouts. However, on nights when there wasscintillation in addition to this basic amount of multipath,there were outages on satellites at elevations up to 30° oreven 40°. The curve that extends farthest to the right isinflated due to a single line of sight on 15 February forwhich the satellite was broadcast as healthy but was nottracked by the receiver for a few continuous hours while itwas in the sky.

The lower plot in Figure 6 demonstrates the effect ofscintillation on the number of outages at L2. On the quietnight, the receiver is still susceptible to outages up to 15°elevation. On the nights with observed scintillation, it isclear that high elevation satellites are even more likely tohave L2 data drop out than L1, with outages existing onsatellites almost as high as 70°.

The key features of this plot show that as baselinebehavior in this data set we may expect outages up to 15°that may be due solely to multipath. Beyond that,scintillation is the dominating factor in dropouts.

Table 1 lists percentages of dropout frequency at L1. Auser who is estimating position with a receivercomparable to the MiLLennium and is subject toscintillation may be interested to know how often she mayexpect to have dropouts on 1, 2, or 3 satellitessimultaneously. For comparison we offer the samestatistics calculated over the quiet night 19 February from00:00-06:00 UT, as we do over all other nights from00:00-06:00 UT combined.

Table 1

# svs Without scint. (19 Feb) With scint. (all others)out 5-15° 15-90° 5-15° 15-90°1 11.7% 0% 14.7% 4.69%

#svsout

Without scintillation(19 February)

With scintillation(all others)

2 0.556% 2.50%3 0% 0.289%

The GPS user estimating position on a scintillation-freenight may lose exactly one low elevation (i.e. el < 15°)satellite just over 11% of the time. With scintillationexacerbating the multipath, the incidence of single lowelevation satellite loss increases to over 14% of the time.On February 19th, there were no observed incidences of asingle high elevation satellite being lost. Compare this tothe other nights, when one high elevation satellite was outof view almost 5% of the time.

The lower half of Table 1 shows similar trends for theloss of 2 or 3 satellites simultaneously. On the quietnight, there were only a few epochs during which twosatellites dropped out at the same time (corresponding to0.556% of the time). With scintillation, a user mayexpect to lose 2 satellites at the same time 2.5% of thetime, and some of them may be higher than 15°. Asimilar pattern follows for loss of 3 satellites.

The loss of L1 frequency data prevents the single- andalso the dual- frequency user from including thesatellite(s) in their constellation, and so is of concern toboth. Similar outage percentages are calculated on L2,and are shown later, since they are applicable specificallyto the dual-frequency user.

STAND-ALONE POSITIONING

The MiLLennium receiver dual frequency data are post-processed to estimate user position. The linearized modelof the position equations can be found in many texts, forexample, Misra [2001] or Strang [1997]. The techniqueinvolves iterating a weighted least squares solution on alinearized model of the position equations. Only satelliteshigher than 5° elevation are used for positioning. Prior toestimating user position, corrections must be applied tothe vector of measured pseudoranges P1 at each epoch toarrive at a corrected pseudorange ρ in meters:

1 ( )SP B c I T dt b cρ = + ⋅ − − + − ⋅

Equation 6

These corrections include the list of broadcast satelliteclock errors at the time of transmission B, converted tometers using the speed of light c; the ionospheric slantdelay I for each satellite signal ray path, to be discussed indetail later for the single and dual frequency user; thetropospheric slant delays T for which we have used thedry component of a simple empirical model only [Misra2001]; and the Sagnac correction dtS, which accounts forthe fact that the user is in a rotating reference frame - theearth - while using a clock [Parkinson 1996]. The userclock error b is one of the resulting estimates of the

solution, and can be applied subsequent to the firstiteration.

Beginning with an initial estimate of user location andclock bias x0 that differs from the true position by someamount dx, the unit vectors between the position of eachsatellite at its time of transmission and the user positionare arranged in the well-known geometry matrix G. Theweighted least squares error solution for dx is then:

ρ111 )( −−−= WGGWGdx TT

Equation 7

The weighting matrix W will be specified for the singlefrequency and dual frequency users below. The error dxis added to the old estimate of position, and the process isrepeated until the resulting errors are less than 10-4 m.

SINGLE FREQUENCY POSITIONING

The single frequency (SF) user solving for position mustapply an ionospheric model correction I = Imodel inEquation 6 above. The model broadcast by the GPSsatellites for SF users is described in detail in the InterfaceControl Document 200C. We apply as weighting matrixW in Equation 7 the one given by:

≠=

=−

−

jijielMelM

Wji

ij,0

,))()(( 11

Equation 8

Here, M(eli) is the obliquity factor for the ith satellitewhose expression is given in Equation 4.

Figure 7: Position error vs time (top) and DOP vs timefor single frequency user without scintillation.

The upper half of Figure 7 plots the single frequencyuser’s position error in meters on the scintillation-freenight, February 19th, from 00:00-06:00 UT. The

horizontal error is drawn in blue, the vertical error ingreen, and the 3-dimensional position error in red.

The lower plot of Figure 7 illustrates the correspondingdilution of precision (DOP) values. Dilution of precisionis a unitless scalar derived from the geometry matrix Gthat characterizes the goodness of the constellationgeometry. Lower DOP indicates better geometry formore precise positioning. The horizontal dilution ofprecision (HDOP) is shown in blue, vertical DOP(VDOP) in green, and 3-d position dilution of precision(PDOP) in red.

On this quiet night, the user’s position error is as much as30 m, and gradually decreases to about 10 m. Thebroadcast ionospheric model that the L1-only user mustuse does not account for the second daily anomaly peak inthe equatorial regions. The error in estimation of theionosphere at this time of night contributes to highmagnitude position errors. Notice that after 01:00 UT theuser position estimate and the DOP fluctuate rather thanvarying smoothly. An abrupt change in PDOP occurswhen the constellation of satellites used in the positionequations changes due to the rising or setting of asatellite. In this case, a low elevation (5° < el < 15°)satellite was setting, and as we have seen above, even onthe scintillation-free night, low elevation satellites aresusceptible to dropouts. The alternating loss and gain ofthis setting satellite cause the fluctuations in DOP andposition error.

Since scintillation increases the likelihood of dataoutages, we expect to see more frequent fluctuationssimilar to this. In fact, Figure 8 shows exactly this. As anexample of positioning on a typical night withscintillation, we have plotted similar position error andDOP plots for a scintillating night.

Figure 8: Position error vs time (top) and DOP vs timefor single frequency user during scintillation.

On these nights the absolute position error may reach ashigh as 50 m. Notice that fluctuations in 3-d position andPDOP are much more frequent as satellites “flicker” inand out of view of the receiver. Higher rates of change inposition error occur during scintillation. The fluctuationsin position estimate can be on the order of 10 m. The lossor gain of low elevation satellites generally produce themost dramatic changes in position estimate, possiblybecause the SF model error estimate, which assumes athin-shell ionosphere, diverges from the actual behaviorof the ionosphere in the equatorial anomaly region.

The high rates of change in position estimate and DOPseen on this night are typical of all the nights on whichscintillation occurred. The data depicted in Figure 9 for15-28 February 2002 from top (red) to bottom (lowerblack curve) are: S4 due to scintillation (multipath epochsare not pictured), rate of change in 3-d position error, andrate of change in PDOP.

Figure 9: S4 due to ionospheric scintillation, rate ofchange of 3-d position error, rate of change of PDOPover time span (UT) of data set.

The high magnitude rates of change in position estimateare visible on a nearly nightly basis around 0-6 UT. Theexception to this is 19 February. On the 19th the standarddeviation of the rate of change of 3-d position error of allestimates made between 00:00 and 06:00 UT was 1.7.Over the remaining nights (all of which showedscintillation activity), the position error rate of changewas higher so that the standard deviation σ = 2.9. It isalso clear from the plot that this bound on the rate ofchange during scintillation periods (0-6 UT) issignificantly higher than at any other time of day. Therate of change of PDOP shows a less dramatic, but stillsignificant, difference in spread on the scintillating nightscompared to February 19th: compare σ=0.121 on the quietnight to σ=0.189 on the other nights. The nighttimefluctuations in DOP during scintillation happen with

higher frequency so that the variance from 00:00-06:00UT is higher on all other nights than it is on the 19th.

We have seen an increase in fluctuations in the availableconstellation of the L1-only user due to amplitude-scintillation-induced data outages. The single frequencyGPS stand-alone user relies on a thin-shell model of theionosphere that, at equatorial latitudes, may differ fromthe actual ionosphere by 10s of meters, particularly duringand after the second daily anomaly peak. As theionospheric model correction for a satellite is added andremoved from the position equations due to its fading inand out of view, the ionospheric error can translate into 3-dimensional position error as much as 50 m, and rapidfluctuations on the order of 10 m/epoch.

DUAL FREQUENCY POSITIONING

The dual frequency user has the capability to improve onthe accuracy and precision of the single frequency GPSuser through the use of the L2 frequency data for directmeasurement of the ionospheric delay I = Imeas . For ouranalysis we use Imeas = Iφ, which is calculated as describedin Equations 2-3. For use in Equation 6, Iφ is notconverted to equivalent vertical, but kept as a slantmeasurement. Measurement of the ionospheric groupdelay depends on the availability of L2. Duringscintillation, data transmitted on the L2 signal is morelikely to be dropped, just as with L1. Below in Table 2 isa list of L2 outage percentages on the quiet night (19February 2002) compared with all the other nights of thedata set.

Since the L2 frequency does not contain a signal freelyavailable to the civil community, commercially availablereceivers that employ codeless or (as with theMiLLennium) semi-codeless tracking to track L2 aremore susceptible to loss of lock on L2 than L1. As aresult, the overall percentages on both the quiet night andthe active scintillation nights are higher than thecorresponding values for L1. On the scintillation-freenight 19 February, low elevation satellites (between 5°and 15°) were dropped 12.4% of the time. Duringscintillation this increased by more than 40% to a 17.5%chance of losing one low-elevation satellite. Whereas onthe quiet night, L2 was never lost on any satellite above15°, during scintillation hours from 0-6 UT, there was a7.41% chance of losing exactly one high elevationsatellite.

The lower table summarizes the percent of time thatmultiple satellite outages were observed simultaneously.On the 19th of February, 2 satellites dropped outsimultaneously only rarely, and 3 never did. Duringscintillation 2 satellite outages happened at the sameepoch more than 6% of the time, and 3 happened morethan 1% of the time. In all, a dual-frequency user

equipped with a receiver comparable to the one used here,the MiLLennium, might expect to spend almost one-thirdof his time without dual frequency data for some satelliteor another in the constellation.

Table 2

# svs Without scint. (19 Feb) With scint. (all others)out 5-15° 15-90° 5-15° 15-90°1 12.4% 0% 17.5% 7.41%

#svsout

Without scintillation(19 February)

With scintillation(all others)

2 0.694% 6.73%3 0% 1.34%

A dual frequency user has a number of methods availablefor dealing with the inability to measure the ionosphericdelay. Two options that we consider here are: 1) limitingthe constellation available for positioning to only thosesatellites for which both L1 and L2 frequencymeasurements exist; 2) substituting the SF user’sionospheric error model for the satellites that have L1only available, and de-weighting these terms in theposition solution equations, since they are not likely to beas correct as the ionospheric measurement. We considerthese two scenarios one at a time here.

DUAL FREQUENCY USER TYPE 1

Dual frequency (DF) users who limit their constellationsto the satellites from which they are receiving bothfrequencies (“Type 1” users) solve the position Equations6 and 7 with the use of an ionospheric correction I givenby the code-leveled carrier phase measurement ofionospheric delay Iφ in Equation 2. In this scenario, thesame elevation-dependent weighting matrix as the SFuser’s, given by Equation 8, is applied.

The DF Type 1 users enjoy significant improvement inaccuracy, as is visible in Figure 10, which plots theirposition error over time on a scintillation-free night.Compared to the SF user, whose positioning for this samenight is shown in Figure 7, the Type 1 user has 3-dimensional position errors under 20 m during the entireperiod from 00:00-06:00 UT. There is minimalfluctuation in this estimate even while the constellationchanges. The constellation available to the Type 1 user isdifferent from the SF user’s, as can be seen by comparingthe lower plots of DOP in Figures 7 and 10. The Type 1user’s constellation changes more often on the quiet nightthan the L1-only user’s does, but this does not translateinto large changes in position error because the Type 1user measures the ionospheric delay error directly,whereas the SF user estimates it with a model that candiffer from the true ionosphere in this part of the world atthis time of night by 10s of meters slant.

Figure 10: Position error vs time (top) and DOP vstime for dual frequency (Type 1) user withoutscintillation.

The DF Type 1 user who is now subjected to scintillationruns into different issues from the SF user. This is shownin the plots of horizontal, vertical, and 3-dimensionposition error and dilution of precision (DOP) in Figure11.

Figure 11: Position error vs time (top) and DOP vstime for dual frequency (Type 1) user duringscintillation on 21 Feb 2002.

When a Type 1 user limits himself to satellites fromwhich he has received both L1 and L2 frequency data,dropouts and cycle slips will hurt his ability to calculate aposition at all. He may be often limited to too fewsatellites (less than 4) to solve for position. In general,due to cycle slips and data dropouts, we observed thatthere were fewer than 4 satellites available for positioning8.46% of the time during scintillation. This percentagewill vary with implementation of cycle slip detection,correction, and receiver capability.

In addition there are situations where there may be at least4 satellites in view, but due to the physical location of theactively scintillating ionosphere at that time, theremaining constellation provides such poor geometry thatthe position estimate cannot be reliably trusted. In ourpositioning software, we have required a geometricaldilution of precision (three spatial dimensions plus time)of GDOP < 10. From an error-propagation standpoint,DOPs are multiplicative factors for errors beingpropagated through from the range domain to the positiondomain. Hence lower DOPs are better, and beyond acertain threshold the receiver position cannot be reliablycalculated. With the caveat that such a number isdependent on the cycle slip detection and patchingalgorithms as well as the receiver’s tracking capabilities,we observed a GDOP > 10 about 17% of the time from 0-6 UT on the scintillating nights.

For direct comparison with the SF user, compare Figure11 with Figure 12 below. The SF user with a receivercomparable to the MiLLennium will be able to estimateposition during scintillation, but it may differ from thetrue position by 10s of meters. The dual frequency Type1 user has traded availability of a position solution foraccuracy of under 20 m.

Figure 12: Position error vs time (top) and DOP vstime for single frequency user on 21 Feb 2002.

DUAL FREQUENCY USER TYPE 2

Another method by which the dual frequency user mayaccount for the loss of L2 data is by compensating for lostionospheric measurements by using the SF user’s modelof the ionosphere instead. We will refer to this user’sscenario as that of the Type 2 dual frequency user. TheType 2 DF user may thereby hope to combine the positionavailability of the SF user with a degree of accuracyapproaching that of the DF (Type 1) user.

In combining ionospheric measurement terms Imeas withionospheric model terms Imodel in the vector I in Equations

6 and 7, the Type 2 user accounts for the fact that themodel diverges from the true ionospheric delay, andplaces less emphasis on these terms when solving for theweighted least squares solution. The Type 2 user’s choiceof ionospheric correction term I is given by:

∃−−

===

otherwiseI

LandPifLL

III

el

kkmeas

,

22,1

21

mod

γφ

Equation 9

The expression for γ is given in Equation 3. Theweighting matrix W we implement is:

)))cos(

(cos(

1)(

,022,))()((

22,))()((

1

2

1

1

ionoe

ke

k

kkji

kkji

ij

hRelR

SinelM

jiexistnotLorPandjielMelM

existLandPandjielMelM

W

+

=

≠=

=

=

−

−

−

−

Equation 10

The resultant Type 2 position estimation on a night withscintillation can be seen in Figure 13 and compared to theSF position error and DOP plot (Figure 12) or the dualfrequency Type 1 user’s position error and DOP plot(Figure 11).

Figure 13: Position error vs time (top) and DOP vstime for dual frequency (Type 2) user duringscintillation on 21 Feb 2002.

Because the Type 2 user keeps in her constellation allsatellites for which any data is available (i.e. L1frequency data), the constellation which determines theDOP plots for the SF user and this Type 2 user areidentical.

The 3-dimensional position error reaches 40 m at times,almost as high as the SF user error, and at times decreasesas low as the Type 1 user error. During the period whenthe Type 1 user was entirely unable to make a positionestimate between 01:30 and 02:30 UT, the DF Type 2user has enough satellites and good enough geometry(GDOP < 10) to estimate position. The error at this timeis comparable to that of the SF user in magnitude andfluctuation. The Type 2 DF user has ceded somepositioning accuracy in order to increase availability tothat of the SF user.

CONCLUSIONS

Amplitude scintillation due to the early nighttimeionosphere impacts both single and dual frequency GPSusers in the equatorial anomaly region of the world.Scintillation increases the frequency of data outages onboth L1 and L2, both for low elevation satellites whosesignals are subject to multipath and for high elevationsatellites that are usually clear in the receiver’s view.This in turn changes the user’s available constellation forpositioning.

The single frequency user can expect high rates of changein position estimate due to loss of L1 data, combined withlarge absolute errors due to the secondary peak in TEC ofthe ionospheric phenomenon known as the “anomaly”.The dual frequency user has the advantage of being ableto measure the ionosphere directly, but is susceptible tomore frequent L2 dropouts and cycle slips since civilianreceivers track the L2 frequency codelessly or semi-codelessly. Type 1 dual frequency users, who limit theirconstellation to all satellites for which ionosphericestimates are available, have high accuracy but worsegeometry. At times they may even lack position estimatesaltogether during scintillation. Type 2 dual frequencyusers, who substitute the single frequency ionosphericmodel correction broadcast by the GPS satellites into theposition equations when the measurement is unavailable,and de-weight the model-corrected terms, haveavailability and DOP identical to L1-only users. Theirabsolute errors can be as low as the Type 1 users’, butmay also reach as high as the single frequency GPSusers’.

Further tuning of the weighting matrix W of the Type 2dual frequency user who solves for position by weightedleast squares estimation, may improve the overallaccuracy of this method when used during scintillation.Another technique that may be considered when anionospheric measurement is unavailable to the dualfrequency user is the reuse of the most recent ionosphericmeasurement, with filtering over time. One importantconsideration in this case would be the fact that amplitudescintillation often accompanies small-scale irregularities

in the ionosphere. The total electron content might berapidly changing just at the moment when the dual-frequency measurement was lost, which would put a limiton the duration that an old measurement might beconsidered valid or safe to reuse.

ACKNOWLEDGEMENTS

The authors would like to thank the FAA WAAS programfor funding this research. Thanks also to Dr. Todd Walterfor providing helpful feedback and comments.

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