Characterizing the Effects of Ionospheric Divergence and Decorrelation on LAAS

Transcription

1 Characterizin the Effects of Ionospheric Diverence and Decorrelation on LAAS Boris Pervan *, Sam Pullen, John Andreacchi *, and Per Ene * Illinois Institute of Technoloy Stanford University BIOGRAPHIES Boris Pervan received a BS from the University of Notre Dame (986), MS from the California Institute of Technoloy (987), and PhD from Stanford University (996), all in Aerospace Enineerin From 987 to 99, he was a Systems Enineer at Huhes Space and Communications Group Dr Pervan was a Research Associate at Stanford from 996 to 998, servin as project leader for GPS Local Area Aumentation System (LAAS) research and development He was the 996 recipient of the RTCA William E Jackson Award and the 999 M Barry Carlton Award from the IEEE Aerospace and Electronic Systems Society Currently, Dr Pervan is Assistant Professor of Mechanical and Aerospace Enineerin at the Illinois Institute of Technoloy in Chicao Sam Pullen received two SB derees (in Aeronautics/ Astronautics and History) from the Massachusetts Institute of Technoloy (989) and received MS (99) and PhD (996) derees from Stanford University in Aerospace Enineerin Since raduatin, Dr Pullen has served as Research Associate and as Technical Manaer at Stanford, where he has supported GPS Local Area Aumentation System (LAAS) and Wide Area Aumentation System (WAAS) research and development and now serves as the project leader for LAAS His work in these fields and his support of the Johns Hopkins University Applied Physics Laboratory (JHU/APL) GPS Risk Assessment earned him the ION Early Achievement Award in 999 John Andreacchi received a BS in Mechanical Enineerin from Northern Illinois University (996) and MS in Mechanical and Aerospace Enineerin from Illinois Institute of Technoloy () Mr Andreacchi was a desin/process enineer in the automotive industry from 996 to 999 From 999 to he was a Research Assistant in the Naviation and Guidance Laboratory where he studied the effect of Ionospheric Diverence on Differential GPS implementations of codecarrier smoothin filters ABSTRACT In the Local Area Aumentation System (LAAS), as well as other local area DGPS systems which use sinlefrequency (L) measurements only, differential ranin error due to the ionosphere is the result of two effects: the temporal diverence of the code and carrier and spatial decorrelation of delay The effect of diverence is most sinificant when round and air filter implementations are different; but even when filter implementations are identical, transient differential error can exist due to the different filter start times The effect of spatial decorrelation is caused by variations in the delay between the ionospheric pierce points for the aircraft and the round receiver The effective between round and aircraft antennas that defines pierce point is larer than the physical of the two antennas by an amount proportional to the filter time constant and the horizontal velocity of the aircraft In this work, both ionospheric spatial decorrelation and diverence are analyzed with the oal of definin conditions for safe interoperability of round and airborne systems ION GPS, 9- September, Salt Lake City, UT 653

2 INTRODUCTION In the Local Area Aumentation System (LAAS), L pseudorane and carrier phase measurements are brouht toether by means of a smoothin filter The filter exploits the accuracy of the pseudorane (raw code phase) and the hiher precision of the carrier phase to mitiate multipath and other receiver-associated noise Amon several errors embedded in the smoothed pseudorane, the one of interest in this paper is the filtered output of the ionosphere-induced roup delay and phase advance The carrier phase advance and pseudorane code delay are equal and opposite Thus over time, the effect is realized as a diverence between the code and carrier measurement error When such a diverin error is filtered, there will exist, in eneral, a trackin error in the output of the smoothin filter relative to the raw code pseudorane The nature and manitude of the trackin error is a function of the filter used and the time history of ionospheric diverence [] For example, the LAAS Ground Facility (LGF), which will use sinle-frequency measurements passed throuh a first-order filter, will exhibit a steady-state trackin error due to ramp-like (constant velocity) diverence and a continuouslyrowin trackin error in response to quadratic (constant acceleration) and hiher order diverence inputs In a differential system such as LAAS, the airborne user and reference (LGF) trackin errors due to diverence will cancel precisely only if the round and airborne filters are identical and sufficient time has elapsed since the initialization of each filter In this work, we characterize and quantify the resultin differential error in the realistic case when these two conditions are not precisely satisfied In this reard, ionospheric diverence has been modeled with ramp, quadratic, and harmonic (sinusoidal) structures Usin both time domain and frequency domain techniques, differential ranin errors due to round-air differences in filter time constant, order, and initialization time are characterized This paper also includes analysis and experimental data that shows the manitude of LAAS airborne error due to ionospheric spatial decorrelation Since LAAS round and aircraft receivers may be spatially separated by tens of kilometers, small variations in ionospheric delay between round and air ionospheric pierce points result in small but non-neliible differential ranin errors at the aircraft Furthermore, the effective between round and aircraft is increased relative to their physical by an amount proportional to the filter time constant and the horizontal velocity of the aircraft This paper derives the equation used to compute the standard deviation of this error at the aircraft and presents relevant experimental Wide Area Aumentation System (WAAS) data to estimate the standard deviation of the radient of vertical ionospheric delay that is to be broadcast by the LAAS Ground Facility (LGF) IONOSPHERIC DIVERGENCE At the LAAS Ground Facility (LGF), a first order (Hatch) filter with sec time constant is specified: where, N r ( k) = [ r( k ) + φ ( k) φ( k )] + p( k) N N r is carrier-smoothed pseudorane φ is carrier phase measurement output from receiver p is pseudorane measurement output from receiver τ is time constant of smoothin filter ( sec) T is sample interval (/ sec) N is τ / T The continuous analo to the Hatch Filter (takin limit as T approaches zero) is [] τ r! ( t) + r( t) = τ φ! ( t) p( t) + Takin the Laplace Transform yields τ sφ ( s) + P( s) R( S) = τ s + We now consider the effect of a diverence error e (t) such that φ ( t ) = e( t) and p( t) = e( t) The resultin transfer function ffrom diverence input to the smoothed pseudorane output is τ s R( s) = E( s) τ s + If a first order filter with a different time constant (τa) is used at the aircraft, the resultin differential ranin error is ( τ a τ ) s R( s) = E( s) τ τ s + ( τ + τ ) s + a a 654

3 Ionospheric Diverence (m) In the frequency domain, this is a band-pass filter with center frequency and peak ain ω = peak τ τ τ a τ H ( jω peak ) = τ + τ Because of the band pass nature of the effective differential filter, it is clear that the differential ranin error due to hih and low frequency diverence inputs will be suppressed Fiure (left plot) shows an example time history of ionospheric delay collected over one hour period usin dual frequency GPS carrier phase measurements (The initial ionospheric delay, which has been arbitrarily set zero in the plot, is not relevant since it does not contribute to differential ranin error) Also shown (riht plot) is the Fourier Transform of the ionospheric delay overlaid on an example differential filter assumin a sec time constant on the round and a 5 sec time constant in the air An example of observed ionospheric 3 4 Time (sec) Manitude Fiure Diverence in the Frequency Domain a a Time Constant Mismatch: τ= sec and τa = 5 Iono Diverence Differential Filter Hertz flexibility possible, this requirement does not represent a sinificant desin constraint It is also important to note that these results also apply to carrier aided Delay-Lock Loops (DLLs) within round and air receivers However, the time constants are much smaller in this case For example, at the LGF the minimum noise equivalent bandwidth of a carrier aided DLL is 5 Hz (which corresponds to a time constant of less than sec) When the round and air DLL time constants are individually small, their difference will also be small, resultin in neliible steady state differential ranin error Given that the round and air filters have the same time constants, transient differential error due to diverence must still be considered Transient error will always exist since, in eneral, round and air filters will start trackin (and smoothin) a iven satellite (SV) at different times In the examples which follow, we assume that the reference receiver starts at time t =, while aircraft starts trackin at some later time t = t (Note that the choice of which receiver starts trackin the SV first is arbitrary) Diverence and Smoothed Pseudorane (m) to Filters initialized with raw pseudorane Ionospheric Delay Initial Error Time (sec) Ground Smoothed Pseudorane Aircraft Smoothed Pseudorane Fiure Example Response to Ionospheric Ramp In the time domain, the steady state differential ranin error with respect to a constant rate diverence input I! t is easily shown to be ( τ a τ ) I! For example, for an input rate of cm/sec, ranin error will exceed m if the two time constants differ by more than 5% (5 sec) Clearly, iven the specified LGF time constant of sec, only a small marin for aircraft desin flexibility exists The problem is made worse when hiher order filters are used at the aircraft where, unlike the round, ionospheric ramp inputs are tracked without steady state error For these reasons, the LAAS Ground Based Aumentation System (GBAS) Standards and Recommended practices (SARPS) specifies that the round and airborne filters must be identical Because of the minimal desin Fiure shows an example input ionospheric ramp of cm/sec Because the filters start at different times, differential error initially exists, but decays exponentially with time Fiure 3 shows parameterized curves of transient differential ranin error for a number of air filter start times (t ) In this fiure the parameter a represents the ionospheric ramp slope I! The worst-case differential error occurs when the round filter is at (or near) steady state when the aircraft filter beins trackin the satellite 655

4 δr/aτ Start Time Offset Top to bottom t o /τ = " = 3 " = 5 " = 5 " = " = 75 " = 5 " = 5 Fiures 4 and 5 show the results for quadratic inputs (with a = ) I! analoous to those of Fiures and 3 for ramp inputs In this case, no worst-case value of t exists (and only results up to t /τ = 7 are shown in Fiure 5) Therefore, no specific wait time is sufficient However, it is important to note that quadratic inputs due to the ionosphere cannot be sustained indefinitely A more realistic model is needed to characterize the effects of hiher order inputs (t-t)/τ Fiure 3 Normalized Transient Ranin Error (Ramp Input) δr/aτ 5 Top to bottom to/τ = 7 " = 6 " = 5 " = 4 " = 3 " = In Fiure 3 the curve labeled (t /t = ) corresponds to this case In this scenario, for a cm/sec input ionospheric ramp, transient differential error will be larer that cm unless a 3 sec wait time has elapsed before the aircraft smoothin filter output is used 5 " = (t-t)/τ It is worth notin that if diverence rate is known, the filters can be started at steady state In this case, there will be no transient response to ramp inputs Unfortunately, estimation of diverence rate from the sinle frequency (code-minus-carrier) data available to LAAS will also require smoothin over time to mitiate effect of multipath In this context, the wait-time is not avoided, but instead simply passed over to another process It is also desirable to consider the effect of hiher order inputs In this reard, it is natural to next consider to the case of a quadratic input However, the first order filters to be implemented in LAAS will not track quadratic (or hiher order inputs) with a steady state error; the error will instead continue to row with time Ionospheric Delay Fiure 5 Normalized Transient Ranin Error (Quadratic Input) Quadratic Model Time Harmonic Model Imax I( t) = cos ( ωt) Fiure 6 Inonospheric Harmonic Input Ionospheric diverence Diverence and Filter Output Ionosphere Ionospheric diverence vs Time Filter Outputs Time Time Fiure 4 Example Response to Ionospheric Quadratic Input As illustrated in Fiure 6, a harmonic model (sine/cosine input) implicitly includes quadratic and hiher order effects while simultaneously maintainin the bounded maximum amplitude of ionospheric delay In this case, the transient differential error depends on two factors: the phase shift (time offset) between initialization of the two filters and the input ionospheric frequency In Fiure 7, an example ionospheric input with 5-second period is shown toether with resultin the round filter response and several potential air filter responses correspondin to different initialization times It is clear that over time the round and air filter outputs will convere and the resultin differential ranin error will approach zero In the transient reion, however, differential ranin error will exist 656

5 Delay (m) δr (m) Ionospher Errors Ground Filter Time (s) Air Filters results it seen that errors less that cm are achievable with a maximum wait time of approximately 5 sec By comparison, the results for the ramp input case are more conservative While the results from the models considered are clearly sensitive to the specific quantitative assumptions made reardin ramp input manitude and amplitude vs frequency characteristic, the methodoloies are useful for determinin acceptable wait times for first use of LAAS filter outputs It is also important to note that the wait time can be circumvented by appropriate inflation of the measurement error standard deviations used to compute vertical and horizontal protection levels for LAAS In this case, an exponentially decayin error component may be included in the overall LAAS error model to compensate for the transient differential error resultin from ionospheric diverence δr (m) Fiure 7 Example Resonse to Harmonic Input The phase (time) offset between the round and airborne filter initialization that leads to maximum transient differential error will depend on the input frequency It is also important to consider the fact that the amplitude of the ionospheric input (Imax) should become smaller as frequency (ω) increases In this analysis, we assume a maximum ionospheric delay amplitude of 3 m applicable to the diurnal frequency (~-5 Hz) Amplitudes of ionospheric inputs at hiher frequencies are modeled as proportional to /ω This model is reasonably consistent collected data Top to Bottom freq = " = " = 3 " = " = t t Fiure 8 Worst-Case Transient Response to Harmonic Input Fiure 8 shows the worst-case transient differential ranin error for several input frequencies In these 3 IONOSPHERE SPATIAL DECORRELATION In addition to residual differential ionosphere errors from diverence (temporal decorrelation), LAAS users will also encounter small errors due to spatial decorrelation, or the chane in ionspheric delay between user and reference receiver ionospheric "pierce points" In order to insure that computed user protection levels bound actual errors throuhout the LAAS coverae volume, the LAAS VHF data broadcast includes a standard deviation of ionosphere spatial variation, σvert_iono_radient (or σvi), in the Type messae This parameter has an 8-bit messae field with a least-sinificant-bit resolution of mm/km, allowin a maximum value of 55 mm/km to be transmitted User Error due to Ionospheric Spatial Gradient The followin equation relates vertical ionospheric spatial decorrelation (di v /dx) to pseudorane error for a iven GPS satellite: ˆ ˆ dι v Ι v ( t, x) = Ι v a Ι v, [ xa + τ av dx, a where τa is the airborne smoothin time, va is the aircraft lateral velocity, and xa is the LGF-to-aircraft This equation ives the vertical ionosphere chane, which must be multiplied by an obliquity factor (F PP ) to convert to actual (slant) rane error [3]: F pp ( θ ) Re cos = Re + hi ] 657

6 where R e is the approximate radius of Earth ( km), and h I is the approximate ionosphere shell heiht (taken to be 35 km) Note that this factor varies from for satellites directly overhead to reater than 3 for lowelevation satellites These equations are used in the followin fiures to relate σ vi to σ iono, which is the onesima differential user rane error These plots assume τ a = sec (to match the LGF) and a constant τ a = 7 m/sec for a jet aircraft durin approach Fiure 9 shows the resultin vertical ionosphere error for three different values of σ vi as a function of LGF-user For σ vi = mm/km, the one-sima error at a conservative approach-threshold distance from the LGF (x a = 75 km) is 43 cm, which is neliible compared to multipath and other LGF error sources At the ede of LGF VDB coverae (x a = 3 nmi, or about 43 km), the error is about 8 cm, which is still small and is much less sinificant because the required protection levels at this distance from the LGF are much larer than those that apply at the approach threshold Fiure shows the impact of σ vi = 4 mm/km and σ vi = 55 mm/km (the maximum possible broadcast value) on the total user rane error for Ground Accuracy Desinator B3 and Airborne Accuracy Desinator A For σ vi = 4 mm/km, the increase in user rane error sima due to ionospheric effects is no reater than 5%; thus the impact on user availability is very small On the other hand, σ vi = 55 mm/km increases overall user error sima by a factor of 3 or more, which would dramatically impact user availability While it is not possible to determine the maximum possible ionosphere spatial radient that miht ever occur, it makes little sense to field a LAAS system with σ vi = 55 mm/km without usin some other means of ionosphere estimation (dual-frequency measurements, WAAS) to reduce the error Thus, a maximum messae field value of 55 mm/km for σ vi is sufficient One-sima User Rane Error (m) σiono,v 43 cm at threshold 5 mm/km 3mm/km mm/km σiono,v 8 cm at ede of coverae σ vi One-Sima Total User Rane order to examine the values of σ vi that may occur under worst-case conditions, we have used the Raytheon WAAS database of ionosphere "supertruth" data of delays at the pierce points of the 5 WAAS reference stations [5] This data has limited applicability to LAAS because most WAAS pierce-point s are well over km, whereas LAAS users are most interested in s well below km However, sufficient data exists for s of 4 km and less to allow us to "zoom in" and make reasonable inferences reardin very-shortrane ionosphere delay differences Sima increase is relatively small (< 5%) B3/A + resid + iono B3/A + residual SV Elevation Anle (de) Sima increase is very lare (> 6%) availability impact is dramatic SV Elevation Anle (de) Fiure Contribution of Ionosphere Errors to Total User Error (B3/A Case) Fiure shows the cumulative distribution function (cdf) of ionosphere delay differences between pierce points for CONUS reference stations on April 7,, when a major ionosphere storm took place Each line in the plot represents a specific pierce-point (the data were binned accordin to between and 4 km so that separate historams could be plotted) These distributions appear rouhly Gaussian but with slihtly fatter-than-gaussian tails This does not necessarily mean that the underlyin data is non- Gaussian Instead, it may be an artifact of "mixin" data from many different reference stations with slihtly different ionosphere delay distributions [4] Bin of furthest Lateral User-to-Reference Separation (km) Fiure 9 User Differential Ionosphere Errors Some bins have tails slihtly fatter than Gaussian Bin of closest Because LAAS uses sinle-frequency (L-only) reference receivers and does not observe ionosphere delays in real time, it must broadcast values of σ vi that overbound the true ionosphere radients under worst-case conditions In Fiure CDF of CONUS Ionosphere Gradients, 7 April 658

7 Fiure shows the values of σ vi estimated from the 68 th and 95 th percentiles of these cumulative distributions as a function of pierce-point Note that these values are non-zero even for zero because of errors in the obliquity conversion between vertical and slant errors for satellites tracked by different reference stations and residual L/L interfrequency biases These errors do not affect LAAS users because L is not used to correct for ionospheric delays and because obliquity differences between LAAS reference and user receivers trackin a iven satellite will be very small Therefore, it is the slope of these lines that is of interest to LAAS In this plot, the same slope is obtained for both percentiles and is consistent over pierce-point s between 75 and 375 km: σ vi 7 mm/km σ vi of 4 mm/km will be a sufficiently conservative overbound However, more recent storm data collected in CONUS on July 5-6, must be investiated to confirm that this value overbounds that event as well [5] st dist before storm onset Two Gaussian distributions appear here Bin of furthest Near-zero- offsets due to truncation at zero; limited data; obliquity errors these do not affect LAAS users Extreme values occur after storm onset nd dist Bin of closest Fiure 3 CDF of CONUS Ionosphere Gradients, 6 April Consistent slope estimate possible at larer s: σvi 7 mm/km slope est from 95th pct: σvi 9 mm/km Different sima values before/after storm onset Fiure σ vi for CONUS Ionosphere, 7 April Fiures 3 and 4 show the same results as Fiures and for April 6,, the day of onset of the ionospheric storm Fiure 3 shows very obvious tail fattenin due to mixin sets of data with very different variances: the pre-storm ionosphere delays and those occurrin after storm onset Fiure 4 shows that this mix of two sets of data causes the sima estimated from the 68 th percentile to be lower than that of the 95 th percentile However, both April 6 sima estimates (3 and 9 mm/km) are lower than the estimate for April 7 It should be noted that the radients observed on these two storm days are much larer than typical radients observed in CONUS on non-storm days, even durin solar maximum, when σ vi for CONUS is no reater than mm/km and is typically 5 mm/km or less However, as noted above, LAAS has no direct means of observin which days are nominal and which have ionosphere storms; thus the broadcast σ vi must reflect possible storm events in order to be an overbound at all times The data examined to date suests that in CONUS, a broadcast slope estimate from 68th percentile: σvi 3 mm/km Fiure 4 σ vi for CONUS Ionosphere, 6 April Fiures 5 8 show plots of ionosphere radient cdf's and resultin sima estimates for data taken by the sinle WRS in Hawaii on the same two days as shown previously for CONUS There are far fewer points in this data; thus the maximum bin has been increased to 8 km, and the results appear "noisier" The CDF plot in Fiure 5 for April 7 shows that the ionosphere radients are larer in Hawaii than in CONUS, which is expected because Hawaii is on the northern ede of the equatorial reion of the ionosphere, where delays and radients are sinificantly larer Note that the tails in Fiure 5 appear narrower than Gaussian, which may be because the data is taken from only one site and no 659

8 "mixin" is occurrin The sima estimates for April 7 in Fiure 6 are consistent and ive σ vi 4 mm/km Bin of closest Bin of furthest rouhly 8 mm/km would ive some marin over the worst results observed from this data, but more data needs to be taken, and the July 5-6 storm data should be investiated as well Even if 8 mm/km were sufficient for Hawaii, it is not at all clear that it would suffice for LAAS sites deeper in the equatorial reion For example, recent data from Brazil suests that the worst-case ionosphere spatial radients observed there may be sinificantly larer than 8 mm/km [6] If this is the case, broadcastin larer values of σ vi would sinificantly impact the user error budet and thereby reduce availability It would be better use of real-time dual-frequency data obtained locally or via SBAS to reduce the size of these radients Tails of cdf curves are narrower than Gaussian Bin of furthest Fiure 5 CDF of Hawaii Ionosphere Gradients, 7 April Fiures 7 and 8 are for Hawaii on April 6 The cdf plot in Fiure 7 is similar to that of Fiure 5 but shows slihtly fatter tails, which may be due to the impact of mixin pre-storm and storm data Fiure 8 shows that some tail fattenin is present in the data, as sinificantly different σ vi values (37 and 55 mm/km) are estimated from the 68 th and 95 th percentiles of the data, respectively The larer of these values sinificantly exceeds the 4 mm/km observed on April 7 Bin of closest Two distributions (before/after storm onset) less visible Tails of cdf curves are narrower than Gaussian except for larest s Fiure 7 CDF of Hawaii Ionosphere Gradients, 6 April Different sima values before/after storm onset slope est from 95th pct: σvi 55 mm/km Consistent slope estimate over most PP s: σvi 4 mm/km slope estimate from 68th percentile: σvi 37 mm/km Fiure 6 σ vi for Hawaii Ionosphere, 7 April Based on this limited set of data, it is very difficult to select a value of σ vi that we can confidently state to be an overbound for LAAS stations in Hawaii A value of Fiure 8 σ vi for Hawaii Ionosphere, 6 April 4 SUMMARY AND FUTURE WORK It has been shown that for safe interoperability of sinle frequency round/air smoothin filter implementations in the presence of ionospheric diverence, only very small 66

9 (5- sec) differences in time constant are permissible Because of this relatively minimal desin flexibility, the existin GBAS requirement that smoothin filter time constants be matched at sec is not a sinificant additional desin restriction Carrier-aided DLL implementations are interoperable because minimum noise-equivalent bandwidth is typically lare A minimum bandwidth of 5 Hz is required by LGF specification; airborne implementations should use a similarly lare value To ensure the transient differential error due to diverence is small, both round and air filters should be near steady state The results of constant rate and harmonic diverence input models suest that wait times less than 3 sec are likely sufficient to keep ranin error below cm An alternative technique to accommodate transient differential error without waitin is to inflate the error standard deviation of the smoothed pseudorane The inflation factor implemented for this purpose would decay exponentially with time as the filters approach steady state Ionospheric spatial decorrelation induces small errors for LAAS users LAAS round facilities will broadcast conservative standard deviations (that reflect worst-case ionospheric-storm conditions) of ionosphere spatial radients at each LAAS site, and LAAS users will apply a simple equation to convert these radients to simas of user rane error due to spatial decorrelation based on their s from the LAAS round facility and their appoach velocities "Supertruth" data showin ionosphere delay differences between WAAS reference station has been studied to estimate the standard deviations of ionosphere spatial radients under recent ionosphere storm conditions While one-sima radients under nominal conditions are typically no reater than 5 mm/km, a sima of 7 mm/km was observed in CONUS durin the April 7 storm, and a sima of 55 mm/km was estimated from a smaller set of Hawaii data on the storm onset day of April 6 More work is needed to make more confident assessments of the spatial decorrelation simas that should be broadcast in CONUS and in equatorial reions Data from the July 5-6, storm will be examined to see if the spatial decorrelations durin that storm exceed those found durin the April 6-7 storm or the projected CONUS broadcast value of 4 mm/km For Hawaii and other equatorial reions, data from more reference sites is needed to make better estimates of the spatial-radient simas that occur durin worst-case conditions Another issue of interest is the structure of ionospheric correlation across different satellites visible to a sinle LAAS round facility The current method of computin rane error simas for individual satellites assumes that the errors are uncorrelated This may be conservative in the case of ionospheric spatial radients because the same stucture of ionosphere delay variation affects all satellites in view of a sinle location The component of ionosphere spatial variation that is common to all satellites in the user's position solution will not affect his or her position error because it will be absorbed by the user clock solution Accordinly, it may be possible to take credit for this correlation to reduce the values of σ vi that are transmitted by LAAS round facilities ACKNOWLEDGEMENTS The help of Todd Walter, Andrew Hansen, and the Raytheon WAAS team that supplied us with WAAS "supertruth" data is reatly appreciated, as is fundin support from FAA AND-7 The opinions discussed here are those of the authors and do not necessarily represent those of the FAA or other affiliated aencies REFERENCES [] P Hwan, G McGraw, and JBader, Enhanced Differential GPS Carrier-Smoothed Code Processin Unit Dual-Frequency Measurements, J of the Institute of Naviation, Vol46, No (999),pp 7-37 [] B Pervan, Code-Carrier Diverence Analysis for LAAS, Briefin to RTCA SC-59 WG-4, Washinton, DC, November 3, 998 [3] Minimum Operation Performance Standards for Global Positionin System/Wide Area Aumentation System Airborne Equipment Washinton, DC, RTCA, DO-9B, Oct 6, 999 [4] J Parker, "The Exponential Interal Frequency Distribution," J of the Institute of Naviation (London), Vol 9, No 4 (966), pp [5] A Hansen, etal, "Ionospheric Spatial and Temporal Correlation Analysis for WAAS: Quiet and Stormy," Proceedins of ION GPS Salt Lake City, UT, Sept 9-, [6] S Skone, "Wide Area Ionosphere Modelin at Low Latitudes: Specifications and Limitations," Proceedins of ION GPS Salt Lake City, UT, Sept 9-, 66