High Integrity Multipath Mitigation Techniques forGround Reference Stations

Donghai Dai, Todd Walter, C.J. Comp, Y.J. Tsai, P.Y. Ko,Per Enge and J. David Powell

Stanford University

Biography

Donghai Dai is a Ph.D candidate in the Departmentof Aero-Astro at Stanford University. As a member ofthe GPS Laboratory at Stanford, his research is cur-rently focused on the study of multipath mitigation,integrity monitoring, optimization and integration ofWAAS.

Dr. Todd Walter is a Research Associate in the De-partment of Aero-Astro at Stanford University. Dr.Walter received his Ph.D in 1993 from Stanford and iscurrently developing WAAS integrity algorithms andanalyzing the availabilityy of the WAAS signal.

Dr. C.J. Comp is a Research Associate in the De-partment of Aero-Astro at Stanford University. Dr.Comp received his Ph.D in 1996 from University ofColorado and is currently developing WAAS integrityalgorithms.

Y.J. Tsai is a Ph.D Candidate in Department of Me-chanical Engineering. He is working on real-timeephemeris/clock estimation and integrity monitoringfor WAAS.

P.Y. Ko is a Ph.D Candidate in Department of Aero-Astro at Stanford University. His research is cur-rently focused on advanced LAAS algorithms, in-tegrity monitoring and GPS/INS integration.

Dr. Per Enge is a Research Professor in the De-partment of Aero-Astro at Stanford University. Prof.Enge’s research currently centers around the use ofGPS as a navigation sensor for aviation.

Dr. J. David Powell is a Professor in the Depart-ment of Aero-Astro at Stanford University, where hehaa been on the faulty for 26 years. Prof. Powell’sresearch deals with land, air, and space vehicle nav-igation and control. He is a coauther of two controlsystem textbooks.

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Abstract

There is an increasing demand for accuracy, integrity,continuity and availability in the ongoing develop-ment of differential GPS (DGPS) techniques. DGPSperformance relies on the elimination of errors thatare common to both users and ground reference sta-tions. A multitude of error sources affect DGPS mea-surements. Most of them can be effectively eliminatedwith dlfferencing techniques. Unfortunately, multi-path and receiver thermal noise cannot be canceledin this manner. Code phase noise is reduced very ef-fectively by carrier smoothing, however, this methodis less effective against multipath. The bias-like mul-tipath remains the dominant error source for differ-ential GPS.

This paper presents a spectral decomposition-basedmultipath mitigation technique, which combines car-rier smoothing, carrier Signal-to-Noise Ratio (SNR)and repeatability. Multipath stochastic modeling,SNR and repeatability aiding schemes are investi-gated in detail from an integrity viewpoint. Applica-tions in WAAS and LAAS reference station receiversare demonstrated through analysis and data from Na-tional Satellite Test Bed (NSTB) reference stations.

1. Introduction

As the development of differential GPS (DGPS) tech-niques continues, there is an increasing demand foraccuracy, integrity, continuity and availability. Amultitude of error sources affect the DGPS systemoperation performance. Fortunately, most of thesecan be effectively eliminated using difference tech-niques. DGPS performance relies on the eliminationof errors that are common to both users and groundreference stations. Unfortunately, multipath and re-ceiver thermal noise cannot be canceled in this man-ner. Code phase noise is reduced very effectively bycarrier smoothing, however, this method is less effec-tive against multipath. The bias-like multipath re-

3

mains the dominant error source for differential GPS.

Multipath mitigation techniques have been an openquestion for half a century. Much effort has been putinto solving this problem. Th majority of achieve-ments could be summarized as follows:Siting Siting is considered as the most critical issuefor ground reference stations due to the highly geo-metric related nature of multipath.Antenna Ground plane and choke ring are mostwidely used by survey and ground reference stationreceivers. Adaptive antenna array beam-forming isanother effective way to mitigate multipath and in-terference as well.Delay Lock Loop (DLL) Several successful DLLdesigns have been demonstrated to date. Narrowcorrelator, Multipath Elimination Technology (MET)and Multipath Estimation DLL (MEDLL) are typicalstrategies.Signaling Technique Some improvement could bedone by signaling, for example, longer C/A codecould do a better job in alleviating multipath errors.Data Processing Even though most users can takeadvantage of above techniques, there is still multi-path error in the measurements. Further improve-ments have to be done by data processing schemes.There are a wide variety of mitigation techniqueswhich employ data processing schemes. Carriersmoothing takes advantage of the fact that car-rier phase measurement errors typically are negligi-ble compared to code multipath. Optimal combina-tion of carrier and code phase measurements can effi-ciently reduce the code multipath to centimeter leveland are widely used. Other schemes have been in-vestigated to mitigate multipath. Typical methodsare focusing on taking advantage of SNR measure-ments [Com96, Bre96], repeatability y of multipathat ground reference stations or multiple receiversused for canceling spatial correlated multipath. Per-formance improvements are limited and it is difficultto guarantee robust performance in practical applica-tions.

This paper will investigate multipath mitigation tech-niques from the data processing viewpoint. De-tailed analysis of carrier smoothing techniques areprovided for more insight on optimal combination ofcode and carrier measurements. Furthermore, start-ing from physical mechanisms and spectral analysisof GPS multipath errors, a spectral decompositionbased multipath mitigation strategy, taking advan-tage of SNR and repeatability is proposed. Statis-tical and integrity analysis of SNR and repeatabilityare investigated carefully. Applications in WAAS andLAAS reference receivers are demonstrated in detail.

594

Figure 1: Carrier-Code Combination scheme block dia-gram.

2. Carrier Smoothing Schemes

Dual frequency pseudorange and carrier phase mea-surements are:

Ionosphere-free measurement could be obtained bycombining dual-frequency measurements:

~TLI – TL2r~ = = P + ME.,.

‘y-l

The code measurement is noisy, while the carrierphase is precise but biased due to the integer ambi-guity. So-called carrier smoothing schemes representways to take advantage of both.

The most intuitive explanation for combination ofboth measurements is shown in Figure 1, where a lowpass filter (LPF) and a high pass filter (HPF) are con-ceptually used from the “Complementary Filtering”viewpoint. Ftmdamentally, all the carrier smoothingstrategies are based on this concept using differentlow pass and high pass filter structures.

2.1. Hatch FilterThe Hatch filter is one of the most well-known andsimplest schemes. It estimates the carrier phase bias,NAC, averaging the difference of code an~ carrier mea-surements [WU92]:

N-i.(n) = ; ~[dc(a)–T.(i)] (1)*=1

where, n is the length of the data set. This time av-eraging is just a LPF. If A ME were white, zero-meangaussian, N]. would be the maximum likelihood es-timator (role) of the carrier bLas. Then pseudorange

0.0

;..7~06

‘8

; 0.4

02 .

O.t -..+..---- ---

---- ------- ____ ----

‘otmmoxobmmm em700em9c0ua0Wls Cal,twl (.04

Figure 2: Carrier smoothing code performance as afunction of time constant in presence of ran-dom errors (receiver noise and multipath) andbias error (ionospheric divergence).

could be estimated recursively by:

(n-1, ‘(n -1)+ A@c(n)] + +~.(n) (2)j(n) = yb

where, A&(n) = @c(n + 1) – #.(n). This is the well-known Hatch filter.

For the single frequency case, the same concept givesa similar equation:

‘k -1) [@(n -I)+ A@LI(n)] + ;~M(n) (3)p(n) = ~

Here, this smoothing scheme is actually a movingaverage window of width k. Code and carrier iono-spheric delay divergence causes the carrier bias to beunobservable from ionospheric effects. The perfor-mance of this scheme changes with the time constant(moving average window width). The estimation er-ror of pseudorange as a function of the time constantis shown in Figure 2. The random errors include re-ceiver noises and multipath components. Bias errorsare introduced by the ionospheric divergence effects.Obviously, trade off is necessary for optimal perfor-mance.

The Hatch filter is an efficient carrier smoothingscheme. Unfortunately, error covariance information,which is critical for DGPS correction generation algo-rithms, is not defined. To compensate for this draw-back, other filtering schemes are investigated here.

2.2. Multipath Stochastic Modeling and Fil-tering SchemesAs mentioned above, the critical point of code andcarrier combination is to resolve the carrier integerambiguity. Unfortunately, the carrier bias observ-able are corrupted by receiver noise and multipath,

59

which are bandlimited, non-zero mean and changewith elevation, azimuth angle and SNR measure-ments. It is well-known that the efficiency of anyfiltering scheme strongly depends on the nature ofdisturbances, dynamics of the process and error mod-els. Here, different filtering schemes implemented fordifferent stochastic multipath models are investigatedto solve the same bias estimation problem for perfor-mance and integrity comparison.

2.2.1 Recursive - Least Square (RLS):RLS method here is just a weighted version of theHatch filter, a special case of Kalman filter. The im-provement of RLS over the Hatch filter is that errorcovariance bounds are clearly defined. The estimateserror of carrier bias and covariance bounds of RLS(Weighted Hatch filter) is shown in Figure 3. RLSact as a maximum likelihood estimator (role) if thedisturbances are white gaussian and zero-mean, andthe error covariance bound shrinks down extremelyfast and tight, as shown in the figure. Unfortunately,the multipath is a typical colored disturbance, so thecovariance bounds given by RLS fall short from theintegrity viewpoint due to the incorrect assumptionin the disturbance model.

2.2.2 Kalmau Filter (KF): Now we formthe standard Kalman Filter. The system states in-clude carrier bias, which is modeled by a random con-stant, augmented with the multipath model: a priortime-invariant second order Gaussian-Markov modelor Autoregressive (AR) model.

The Kalman Filter estimation error and covariancebounds are also shown in Figure 3. Different fromthe RLS case, a Kalman filter with above multipathmodel gives more reasonable definition of the confi-dence interval. Obviously, a better statistical knowl-edge of the system disturbances is critical for bothintegrity and performance. The Kalman filter givesthe closed form optimal solution in Hz sense, whichwill be treated as a benchmark for comparison be-tween different filtering schemes.

2.2.3 Extended Kalman Filter (EKF):An enhanced version can be implemented by usingthe Extended Kalman Filter(EKF), wfiich takes thetime-variant effects of multipath error into account.In EKF, the model parameters are adapted and ori-ented on-line. The EKF provides excellent adaptiveperformance when the process and measurement dis-turbance models are reasonably close to physical sys-tems. Carrier phase bias estimates using this algo-rithm are given in Figure 3. The performance iscomparable with KF results with more conservativecovariance bounds, which is desirable from the in-

5

.1: J0,2 0.4 0.6 0,8 1

Thn m)

.1: I0.2 0,4 0.6 0.8 i

mm (h”)

- FM. vs.H.M1

~ ..xc WI,.. . ,...

-1: I0.2 0.4 0.8 0.0 1

ml. m“)

Figure 3: Comparison of different carrier smoothingschemes: RLS (Weighted Hatch filter), KF,EKF and H- flter

tegrity viewpoint, but may be too conservative andnumerically less robust to support sufficient availabil-ity.

2.2.4 Hm Filter: The optimum observers de-scribed above all require an accurate knowledge of thestatistical properties of the disturbances. However,practical model uncertainties and lack of statisticalinformation on the exogenous signals lead to inter-ests in minimax estimators, with the belief that theresulting so-called Hm algorithms will be more ro-bust and less sensitive to parameter variations andmodeling assumptions. Based on Hm framework, acarrier bias estimation result is shown in Figure 3.Obviously, robust Hm filter designed for worst casegives most conservative covariance bounds with theoverall performance degraded as expected.

2.2.5 Comments for R~k-Sensitive Filter-ing Schemes: From the risk-sensitive viewpoint,the above filtering schemes, including RLS, KF, EKFand Hm, are ordered by increased noise model un-certain y, or increased risk-averse preference. RLSmodels the noise as white gaussian, which is one ofthe most ideal and cooperative disturbance and rarelyhappens in reality. Under this assumption, the errorcovariance shrinks too fast to hold integrity when col-ored multipath error dominates the disturbance bud-get. KF models the multipath as a time-invariantGaussian-Markov process, which gives more reason-able covariance bound with integrity. EKF becomes

596

more conservative, and time-variant multipath modelis used. Hence the increase of risk-averse gives a widerconfidence interval. For Hw case, the multipath andnoise are assumed to work as exogenous disturbances,and can be combined in the worst case, which makesthe filtering most conservative, the risk-averse pref-erence expressed in extreme. Trade off between op-timality and integrity is critical in practical applica-tions. Multipath AR model with KF implementationis a reasonable choice.

3. Spectral Decomposition Based MultipathMitigation Strategy

Differing from the above filtering schemes which modethe multipath from the stochastic viewpoint with in-tegrity guaranteed, the following section investigatesdeterministic knowledge about multipath error seek-ing for optimality improvement. Based on spectralanalysis of multipath error, a spectral decompositionbased mitigation scheme is proposed. SNR and re-peatability information could be combined naturallywith carrier smoothing schemes in characterizing andmitigating multipath error based on this platform.

3.1. Spectral Analysis and Multipath Decom-positionSpectral analysis of multipath error is the fundamen-tal concept for thk technique. As described before,multipath errors are bandlimited and can be subdi-vided into bias-like and noise-like components. Thefrequency bands for those components are different.Time constants of multipath errors can have valuesfrom 1 sec to hours. The scheme to deal with variousbandpass errors should be quite different to guaranteeefficiency. Hence, effective decomposition of multi-path error in the frequency domain is critical in mul-tipath mitigation techniques.

An effective decomposition is illustrated in Figure 4.The multipath errors are decomposed into three com-ponents:(1) High Frequency (HF) Component: Noiseand fast fading mainly due to diffuse multipath,fast fading and receiver tracking errors. Its energyranges about 40’% of total residuals, w“ith time con-stant 1 see< ~ <1 min.(2) Medium Frequency (MF) Component:Multipath dominated component mainly dueto specular dominated multipath errors. It usuallycontains another 4070 of total energy, with time con-stant 1< ~ <8 min.(3) Low Frequency (LF) Component: Slow fad-ing due to long-term bias-like multipath and drift er-rors, usually contains 20% total energy, ~ >8 min.

2

0-

-2-0 02 0.4 0.6 0.8 1

0

-21 Io 0.2 0.4 0.6 0.8 1

2iMediumFrewemwUdUtMii I

o

-21 I02 0.4 0.6 0.6 1

2°sow FadrKI‘

o ~

-2I Io 02 0.4 0.6 0.8 1

Time (hr)

Figure 4: Meiwrement Residual Decomposition intothree components: (1) Noise and fast fading(due to diffuse, scattering, atmosphere andunknown error sources, r <1 rein) (2) Multi-path dominated component (due to specu-lar multipath error, which is correlated withSNR, 1< T <8 rein) (3) Slow fadkg (due tolong-term bias-like multipath and drift errors,T >8 rein). Data from Stanford University,PRN15, January 15, 1997

Thk decomposition is based on the physical mecha-nisms of multipath errors and presents a simple wayto combine the strengths from different schemes inmitigating multipath: carrier smoothing, SNR andrepeatability. The following section will further de-tail this decomposition and the mitigation strategyfollows naturally.

3.2. Multipath Calibration StrategyNow we will further characterize each component ex-tracted from the above decomposition scheme, andpropose corresponding calibration strategies.

3.2.1 High l%equency Component (Noiseand Fast Fading): Noise and fast fading aremainly due to ground and atmosphere introducedfast fading, scattering and diffuse multipath, receivertracking errors etc., with time constant 1 see< 7<1min. This component presents noise-like statistics,which can be effectively averaged out by carriersmoothing schemes. Due to its bandlimited butzero-mean properties, AR model or Gaussian-Markovmodel is used to guarantee both performance and in-tegrity.

3.2.2 Medium Frequency Compo-

nent (Multipath Dominated Component) and

59

0

Figure 5: Multipath dominated error components vs.SNR calibration profile. Data from StanfordUniversity, PRN14, January 15, 1997

SNR Calibration: Medium frequency componentis mainly due to specular multipath dominated error,which is Klghly correlated with SNR variation, withtime constant 1< ~ <8 min. A typical correlation be-tween this component and SNR is further illustratedin Figure 5, where both multipath error and SNR val-ues are extracted within the same frequency windowand put together for comparison. Obviously, the SNRbandpass components and multipath components aremost in phase and present similar patterns. The re-lationship between them can be modeled as a linearsystem, but with time-variant property.

The reason we highlight the correlation between SNRvalues and multipath errors within this specific fre-quency window band is also based on the spectralanaJysis of SNR. The higher frequency SNR compo-nent is corrupted by quantization errors, while thelower frequency component is dominated by antennanominal gain pattern. The SNR at these frequenciescan not be used as a reference to calibrate code mul-tipath errors. By comparing multipath errors andSNR variations with specific frequency region, thecorrelation becomes clear. After identifying the lin-ear relation between SNR and multipath error, wecan effectively calibrate out this multipath compo-nent with benefits to the filtering sckeme bandwidth.High bandwidth filtering is also highly desired for in-tegrity purposes. .

3.2.3 Low Frequency Component (SlowFading) and Spline Function Calibration:Slow fading is mainly due to long-term bias-like multi-path errors, with ~ >8 min. Stochastic filter schemesfall short due to the long time constant of distur-bances. An effective solution could benefit from themultipath repeatability at the ground reference sta-tions.

7

GPS satellites are semisynchronous, with a period ofone half sidereal day. Ground track geometry of eachsatellite at a reference station repeats with a fixedtime shift of 236 seconds every day, due to the differ-ence between sidereal day and mean sun day.

The spectral analysis shows that the most repeatablemultipath errors are the low frequency components.By taking advantage of repeatability, most slow fad-ing error can be reduced systematically. To model therepeatable multipath, spherical harmonics [Coh92], aset of linearly independent, orthogonal (without loss-ing generality) spline function in spherical coordinate,are specified as base functions for the reconstructionsubspace, with the form:

5(8, f)) = ~ [maw1=1

+$&cos(0)(clkcos(~#) + SMsin(k#))]&=l

where, 6, # are the elevation and azimuth angle, theaccuracy is governed by the model order, n.

The effective result is because the base functiononly depends on satellite geometry and is less sen-sitive to exact orbit time shift than that in [Bis94].This scheme provides more flexibility and robustness,which are critical for automatic data processing.

3.2.4 Synthesize Spectral DecompositionBased Multipath Mitigation: Based on spec-tral decomposition, carrier phase measurements, SNRmeasurements and repeatability are naturally con-nected to different multipath components. Frequencydomain interpretation is illustrated by a typical ex-ample in Figure 6. This gives the fundamental plat-form for synthesizing multipath mitigation scheme,which can be readily implemented within a Kalmanfilter framework.

4. Statistical Analysis and Integrity

4.1. Multipath Mitigation Scheme Rkk Anal-ysisThe spectral decomposition based multipath mitiga-tion scheme models deterministic multipath errors bytaking advantage of their cooperative relationshipswith SNR and repeatability. The cooperative as-sumption is the baseline of this multipath mitiga-tion scheme. From the risk-sensitive viewpoint, bet-ter performance is a natural result of the above risk-seeklng assumption. The more we know about the

given property (deterministic modeling), the closerwe come to optimality.

59

~ 10

s

! o

‘1]“0-2U

-30:

4“104 -2 1o”’

Fr&ncy (HZ)10°

Figure 6: Spectral decomposition based multipath mit-igat ion scheme frequency domain interpreta-tion

The integrity of this multipath mitigation scheme re-lies heavily on the statistical analysis and integrityconcern of SNR and repeatability in practical appli-cations.

4.2. SNR Statistical Analysis and IntegrityReceiver SNR measurement reports carrier signal-to-noise ratio, which is highly receiver and environmentdependent. Receiver dependency is dominated by an-tenna gain pattern and receiver processing gain, whileenvironment dependency actually contains the infor-mation we want regarding multipath errors.

The high frequency component of SNR measurementsis corrupted by quantization, and the low frequencycomponent characterizes the receiver gain pattern.Only the medium frequency component is dominatedby environmental geometry effects, which have strongcorrelation with multipath error. Both statistical andphysical analysis support the concept presented in thedecomposition based multipath mitigation scheme.To justify SNR calibration methodology, there aresome questions that need answering.

.4.2.1 SNR Multipath-Correction Profile

Generation: SNR multipath-correction generationscheme includes the following procedures:

a. Bandpass Filtering Obtaining medium fre-quency SNR variation pattern is the first step. Band-pass filtering is needed to take off both nominal gainpattern and quantization error effects. Both infiniteimpulse response (IIR) filter or Kalman filter provideequivalent performance.

8

- FruwmcyMuMpdlcawcmmtwlsNRcdiki8ti

Cr0200403600803 Wmlm ,14CU

m Glm18!M(s.)

1.6,

Figure 7: Medium frequency SNR-multipath correctionregression coefficients and performance. Datafrom Stanford University, PRN06, April 15,1997

b. Linear Regression Ratio Correlation betweenSNR variation and multipath error is typically anon-collocated, non-unique time-variant function. Alinear regression model provides the most flexibilitywhile maintaining simplicity:

fi= c&@l&, SNR)

V-ir(slvl?)

In estimating C&( Me, SIVR) and V“&(SIVR), themean estimation of code multipath is of limited band-width, determined by the time constant. Performanceand regression coefficient range are shown in Figure7. A time constant of about 300 seconds gives opti-mal performance. Considering the time-variance, theratio is identified in real-time. Typical improvementsin multipath error versus elevation angles are shownin Figure 8. About 30-40% accuracy improvementsare commonly observed.

For the single-frequency case, on-line regression co-efficient identification is not available. A fixed priorSNR correction ratio should be selected and carefullyjustified. As shown in Figure 7, regression coeffi-cient mean value approaches steady state when timeconstant increased. This could provide the basis forsingle-frequency application.

c. Integrity Protection Threshold From the in-tegrity viewpoint, the SNR correction defined aboveshould be bounded by a specific protection thresh-old for the worst case. This threshold can usually beset from prior information. Prior standard deviationof the multipath error could be used as baseline forthreshold selection.

Sensitivity analysis, an example given in Figure 9,

599

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0,4 ‘.~ lo ‘..\

3:03-\<

$ ~(:””(0002 - -. ..: “ 0

‘..,... -.0. .Q ““0~“0“c..-L

.... . ,, . . ,.0.1-

,. . . ,.

00102034 eommEM..& A&w

1

Figure 8: Medium frequency multipath mitigationperformance by SNR-multipath correctionscheme. Data from Stanford University,PRN06, April 15, 1997

illustrates that consistent improvements are availablewithin wide ranges of integrity protection thresholdsand SNR correction ratios. Rule of thumb, the in-tegrity protection threshold can be set to about 3-uof multipath error, with SNR correction ratio aroundo ~.l,;,.,~ /u.~~ (approximately 0.8 in above examp-le).

4.2.2 SNR Integrity Monitoring: SNRmeasurements are generally not as robust as codemeasurements. An SNR quality control routine isnecessary to guaranteed integrity. Typical SNR mea-surements outages include: abrupt mean changes,outliers or breaks. Due to the high stability of SNRnominal measurements, these anomalous points canbe readily repaired or flagged autonomously basedon prior nominal SNR pattern calibrations. For highintegrity, isolated anomalous points are usually dis-carded and used as whole system protection alarms.This autonomous monitoring process could markedlyimprove both system and SNR calibration scheme ac-curacy and robustness.

4.3. Repeatability Statistical Analysis and In-tegrityThe spline functions used to model the repeatablemultipath will face the biggest challenge from envi-ronment changes due to strong dependence on localgeometry. On-line monitoring is difficult due to theunobservability of these changes. Integrity must stemfrom reference station environment maintenance andtimely calibration of the repeatable multipath splinecurves. Physical ground specular reflector range fromreference receiver is given in Figure 10. Conceptually,low frequency multipath component most likely relieson near-field (within meters) environment geometry,

El1<

..> 1.1.s \,, ... ,z 1s .+9 ‘. ....

!...., 0.73 ,0.8 ‘<.

5a0.5

2468

Slullold**W, I&&3, M1YD7

L-

Inw.adlyThmdlOHRedo

Figure 9: Sensitivity analysis of SNR correction ra-tio and integrity protection threshold ratio(relative to amu,ti,oth). Contour lines arethe multipath residual RMS after calibration,normalized by multipath RMS before cali-bration. Consistent improvements are avail-able within wide ranges of integrity protec-tion thresholds and SNR correction ratios.

and is low amplitude (usually with maximum levelless than 0.5 meters) for well-sited antennas. Thus,reference receiver environment maintenance is man-ageable and poses less of an integrity risk.

An example of the repeatability of low frequency mul-tipath component and spline function calibration per-formance is shown in Figure 11. For the commoncase, 80-90% improvement is reasonable. Long-termtemporal correlation of low frequency multipath er-ror, shown in Figure 12, encourages timely recalibra-tion for this scheme.

It is noted that this strategy can only be used byWAAS, as LAAS single-frequency reference stationscan not get the true ionospheric delay and full mul-tipath observability, rendering the repeatable compo-nents unavailable.

5. Applications for WAAS Reference Stations

The multipath mitigation strategy presented abovewas originally motivated for WAAS ground referencestations with dual-frequency receivers and well sitedantennas. Both code and carrier phase measurementson L1 and L2 are available for data processing, whichcan accurately characterize the ionospheric delay andprovide potential to reduce the multipath errors tocentimeter level in asymptotic sense.

600

10-’010203040s4 6070W90

Figure 10:

Ehntkm M

Ground specular reflector range (horizontaldistance) from reference station receiver as afunction of elevation angle of GPS satellite.Multipath is assumed to be reflected fromground reflection. Resulted multipath timeconstant is marked in the plot.

Figure 11: Repeatability of low frequ~cy multipatherror components and spline function cali-bration performance example with 4th or-der spherical harmonic fit. Data collectedat Stanford University, PRNO1 on April15,16,17.

‘“:~012345 878010

Figure 12: Temporal correlation of low frequency multi-path error components. Data collected hornStanford University and Dayton referencestations, including PRN1, 4, 5, 6

.; 1CL2 0.4 0.8 0.8 1

~ ml

Figure 13: Performance of multipath mitigation schemevs. Hatch Filter. Data from Stanford CA,PRN15, January 14, 1997

5.1. Implementation for WAAS applicationSNR and repeatability calibration can be easily in-tegrated into a Kalman filter scheme. Overall filterbandwidth can be two orders higher than Hatch filterwith about 3070 accuracy improvement. A typical fil-tering result is given in Figure 13. Faster convergenceand improved accuracy are obvious.

Further analysis on asymptotic behavior of carriersmoothing and performance of above multipath mit-igation techniques will give more insights of this syn-thesizing scheme.

5.2. Asymptotic Performance in WAAS Ap-plicat ion

5.2.1 Carrier Smoothing: The mechanicsof carrier smoothing stem from complementary filter-ing. Cutoff frequencies of code low paas and carrier

60

.F- (HZ) -

Figure 14: Fkequencybehavior of carrier smoothing andits asymptotic performance

high pass filters, determined by the width of the av-eraging window, are lower with time as more data isincoming. The frequency behavior of carrier smooth-ing and its asymptotic performance are conceptuallyshown in Figure 14. The carrier phase will domi-nate the strength of the combined measurements, ex-cept code DC component which is exactly the integerambiguity of carrier. Hence, carrier smoothing areusually assumed to be unbiased to the code asymp-totically.

5.2.2 Multipath Mitigation Scheme: Themultipath mitigation technique decomposes the mul-tipath error in the frequency domain. Figure 15illustrates this filtering scheme with frequency do-main behaviors. As shown, the filtered signal is ahigh performance combination of code, carrier, SNRmeasurements and daily-repeatable spline data. Thecarrier measurement strength still dominates the re-sulting high frequency response. Different from thepure carrier-smoothing method, medium and low fre-quency multipath error components of code measure-ments are notched out by SNR and spline curve. As aresult, the code phase always dominates the very lowfrequency response, but with a very narrow band-width. The whole system bandwidth is dominatedby the carrier smoothing parameter k(= n), whichdefines the cutoff frequency of the equivalent carrierhigh pass filter. The resulting system yrovides highperformance multipath mitigation with high band-width, which is greatly desirable to both integrity andaccuracy.

The asymptotic performance of this multipath mit-igation presents consistency with carrier smoothing.With data coming in, the carrier high pass filter cut-off frequency will decrease and finally dominate mostfrequency span, and perform equivalent to carriersmoothing case asymptotically.

1

Figure 15: Frequency behavior of the multipath mitiga-tion scheme and its asymptotic performance

6. Applications in LAAS Reference Stations

Thk spectral decomposition based multipath mitiga-tion concept could also be applied readily at typicalLAAS ground reference station.

6.1. LAAS Algorithm and Multipath ErrorLAAS algorithm is a most exhaustive application ofthe differential concept. All the common errors be-tween users and reference stations, including iono-spheric, tropospheric, and satellite clocks are elimi-nated by single differencing. Quickly resolving theinteger ambiguity is crucial for accurate carrier po-sitioning of LAAS. The integer ambiguity is directlysolved by the following difference:

Ad – AT = ANA+ AME4,,

where, the reference station and user multipath andreceiver noise become the biggest error sources forLAAS. Physically, a static receiver, such as a ref-erence station receiver, multipath decorrelation timeconstant is generally longer than that of a dynamicone. Generally speaking, in aviation applications, theuser measurement errors are dominated by fast decor-related multipath and white noise. As a result, thereference station multipath becomes the dominantlimitation for LAAS accuracy. Effective mitigationof the multipath at the reference station could be onepossible solution to speedup LAAS carrier position-ing.

6.2. Multipath Mitigation Schemes6.2.1 Carrier Smoothing Hatch Filter:

Carrier smoothing Hatch filters are commonly usedfor the single frequency case. The basic equationis given by equation [ 3]. As mentioned before, thesmoothing performance is limited by code and carrierionospheric delay divergence, shown in Figure 2.

6.2.2 Ionospheric Dynamic Model: Inabove carrier smoothing case, no explicit assumption

602

is made regarding ionospheric dynamics. Further im-provement could result from deterministic knowledgeof ionospheric dynamics. A dynamic model used tocharacterize the physical time-variant ionospheric ef-fects has the form:

i(t) = F(t)x(t) + w(t)

where,

x = [zi5]Tw= [O OW]T

[1010

F(t) =OOl

o 0 –T(t)-l

Here, the acceleration of the ionospheric delay is mod-eled as a first-order Gaussian-Markov process. Thecorrelation time constant ~(t) and driving noise wcan be time-variant functions adjusting filter track-ing ability to get better performance.

The above ionospheric dynamic model should be aug-mented with colored multipath error model, as de-scribed earlier, to get reasonable covariance informa-tion. The augmented system can be readily imple-mented as Kalman Filter.

Numerical Results Some numerical results ofabove algorithm present about 30% improvement overcarrier smoothing. The true ionospheric delay is ob-tained from dual-frequency carrier phase difference,with subcentimeter level accuracy. Some numericalresults are give in Table 1 for comparison. Typicalionospheric delay estimation is shown in Figure 16.Only relative ionospheric delay change is observableand matters here.

Table 1. Results of Ionospheric Delay EstimationFilter Scheme I Error STD (m) I Peak (m)

I Hatch[

0.2064 ‘ ‘tI 0.6898 ‘

KF w/ Iono. Model 0.1327 0.5241Hatch w/ SNR 0.1824 0.6527KF w/ Iono. + SNR 0.1339 . 0.5059

Here, the Hatch filter time constant is 300 seconds.Obviously, the Kalman filter scheme with dynamicionospheric model can improve the accuracy as ex-pected.

6.2.3 SNR Aiding Multipath Mitigation:The decomposition based multipath mitigation con-cept can be readily applied here. Unfortunate y, only

0.5 I

Tim (h.)

Figure 16: Typical results of comparison of iono-spheric delay estimation between Hatchcarrier smoothing and Kalman filter withionospheric dynamic model and multipathmodel. Data from Stanford University,PRNO1, hmlary 15, 1997

SNR aiding multipath calibration is available for thesingle-frequency user. Unlike the dual-frequency case,the true ionospheric delay and true multipath errorcan not be accurately known, nor can the repeatabil-ity. Here, SNR calibration performance is verified bydual-frequency measurements.

Numerical Results Numerical results demonstratethe improvement by SNR correction method forsingle-frequency receiver. Figure 17 shows typical im-provement over simple carrier smoothing code by us-ing the SNR correction. Consistent improvements,tighter variance bounds and less mean drifts, areachieved with different time constant. SNR correc-tion profiles are generated using the simplified schemedescribe before. The SNR corrections are also appliedto the Kalman filter with dynamic ionospheric model.Results are also shown in Table 1. Improvement fromSNR calibration for Kalman filter case is not obvious.Ionospheric dynamic model scheme can reach a muchlonger time constant than the Hatch filter, which ef-fectively smoothes out medium frequency multipath,causing SNR calibration effects to fade out.

6.3. Dual-frequency LAAS Reference StationsCompared with the single-frequency and dual-frequency receivers described above, obvious advan-tages of the dual-frequency receiver over its single-frequency counterpart are not only the observabilityof ionospheric delay, but also the potential to mitigatethe multipath errors down to centimeter level. If thedual-frequency receiver could be equiped at LAASreference station, so-called multipath-free pseudor-ange correction could be available to LAAS user with

60

0.15~ & ~ & ; I40a Ea06w7m8rm 900

rmo— (-)

i=0 1m2mx.34Lm6iw31m immmo

rhla - [SOc)

Figure 17: Typical results of performance comparisonof carrier smoothing with and without SNRaiding multipath correction scheme. Datafrom Stanford University, PRNO1, January15, 1997

enhanced performance and integrity.

In recursive form, in carrier smoothing sense,multipath-free pseudorange is given by

?Ll (n) = +n) ++;.l(n -1)+ A4L,(n) +

fi(A#w1(n) - A#.,(n))]

The above mechanics are the same aa those in WAASalgorithms, and spectral decomposition based mul-tipath mitigation techniques can be further appliedhere.

Furthermore, the ionospheric effects could be accu-rately estimated withh dual-frequency LAAS senar-ios. An independent ionospheric integrity monitoringfor WAAS could be readily available. In future im-plementations, dual-frequency LAAS stations couldalso be augmented as a reference station into WAASnetwork. And LAAS and WAAS system could be in-tegrated naturally to provide high performance andintegrity, serving as a primary means navigation sys-tem.

7. Conclusion

This paper presents a spectral decomposition basedmultipath mitigation technique, which combines car-rier smoothing, SNR and repeatability. Multipathstochastic modeling, SNR and repeatability aidingschemes are investigated from the integrity viewpointin detail. Applications in WAAS and LAAS referencestation receivers are demonstrated.

3

The conclusions based on this research include:

● Optimal combination of carrier and code mea-surements should be augmented with correctstochastic model of colored multipath error forreasonable covariance bounds with integrity.Investigations of different filtering schemes, in-cluding RLS, KF, EKF and H~ filter, providea good reference. Multipath AR model withKF implementation gives a reasonable trade offbetween performance and integrity.

● Multipath Spectral Analysis characterizes themultipath error by decomposing it into threeparts: high, medium and low frequency compo-nents. Spectral decomposition based multipathmitigation technique introduces the combina-tion of carrier smoothing, SNR and repeatabil-ityy.

. SNR and repeatability statistical analysis aredetailed from the integrity viewpoint. About30-40% of medium frequency and 80-90% lowfrequency multipath components can be re-moved by SNR and repeatability calibrationschemes with high integrity.

● In WAAS applications, this multipath mitiga-tion technique can improve both the filteringbandwidth by an order of two and 30-40% onaccuracy over Hatch filter. Asymptotic behav-ior analysis verifies the consistent performancewith carrier smoothing. Practical implementa-tion is detailed and demonstrated by numericalresults from NSTB TRS data.

● Multipath is the biggest error source at LAAS

reference receivers. Dynamic ionospheric modeland SNR aiding multipath correction schemesare proposed and verified by numerical results.About 30% accuracy improvement over theHatch filter is demonstrated.

● Dual-frequency LAAS reference station de-

sign can most effectively mitigate code multi-path corruptions. High integrity multipath-freepseudorange measurements/corrections couldbe available on such a platform. Potential in-tegrity check for WAAS corrections, serving asLAAS/WAAS dual-functional station, or futureintegration with WAAS networks would be nat-ural follow-on.

8. Acknowledgments

We are grateful for the support and assistant of theFAA AGS-1OO, the Satellite Program Office, the FAA

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Technical Center. We are also grateful for coopera-tion from our colleagues in Stanford WAAS lab.

To access this paper via internet, usehttp: //www-leland. Stanf ord. edu/- dhdy/ion97.

Comments or questions may be directed todhdy@leiand.Stan ford. edu.

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[Bre96] Kjetil Breivik. Estimation of multipath er-rors in GPS pseudorange measurements using signalto noise ratio. Master’s thesis, Norwegian Universityof Science and Technology, 1996.

[Coh92] C. E. Cohen. Attitude Determination UsingGPS. PhD thesis, Department of Aero-Astro, Stan-ford University, December, 1992.

[Com96] C.J. Comp. GPS Cam”er Phase Multi-path Characterization and Mitigation Technique Us-ing Signal-to-Noise Ratio. PhD thesis, Department ofAerospace Engr. Sci., University of Colorado, 1996.

[WU92] S. Wu. An optimal gps data processing tech-nique. IEEE 1992 Position Location and NavigationSy?nposiuna - PLANS ’92, pages 21-26, 1992.