GEOPHYSICAL
RESEARCH
LETTERS,VOL. 17, NO. 3, PAGES199-202, MARCH
1990
AN AUTOMATIC
EDITING
ALGORITHM
FOR GPS DATA
Geoffrey Blewitt
Jet PropulsionLaboratory,CaliforniaInstitute of Technology,
Pasadena
Abstract. An algorithm has been developed to edit
automatically Global Positioning System data such that
outlier deletion, cycle slip identification and correction
are independent of clock instability, selective availabil-
CASA Uno experiment made it clear that manual intervention in the data analysis had to be minimized since the
task would have required many analysts,with a variety
of non-reproducible editing styles.
This paper presents a reliable, automatic algorithm for
editing dual-frequency GPS carrier phase data from receivers with P code pseudorange capability. The technique is especially attractive because,unlike most algorithms, it does not require any differencing of data between receivers or satellites. The algorithm could, therefore, be implemented in real time by receiversin the field.
In addition, a model of the geometrical delay is not necessary,thus the algorithm is applicableto kinematic GPS
ity, receiver-satellitekinematics,and troposphericconditions. This algorithm, called TurboEdit, operates on
undifferenced,dual frequency carrier phase data, and re-
quires(1) the useof P codepseudorange
data and (2) a
smoothlyvarying ionosphericelectron content. The latter
requirementcan be relaxed if the analysissoftwareincorporatesambiguity resolutiontechniquesto estimate unresolvedcycle slip parameters. TurboEdit was tested on
the large data set from the CASA Uno experiment, which
containedover 2500 cycle slips. Analyst intervention was
requiredon 1% of the station-satellite passes,almost all
of theseproblemsbeing due to difficultiesin extrapolatingvariationsin the ionosphericdelay. The algorithm is
presentlybeing adapted for real time data editing in the
Roguereceiverfor continuousmonitoring applications.
(however,as will be explained,certain antenna effects
mustbe accounted
for).
The algorithm has been incorporated into the GIPSY
softwareas a module called TurboEdit. The principles
of the algorithm are described here in some detail, followed by a discussionof its performance,and possible
adaptation to codelessreceiversand ionosphericconditions which causeseverevariationsin phasedelay.
Introduction
Carrier phase data from the Global PositioningSystem (GPS) have been used in recentyears to measure
regional
scalegeodeticnetworkswith sub-centimeter
pre-
Observable
Model
and Definitions
Many of the conceptsoutlined here were developedin
Blewitt[1989]for purposes
of carrierphaseambiguityres-
cision[e.g.,Dongand Bock, 1989]. Resultsusingthe olution, which is the task of determiningthe integernumGIPSY(GPS-Inferred
Positioning
System)software
show ber of wavelengthsassociatedwith the first phase mea-
sub-centimeteragreement in the horizontal baselinecomponentswith solutionsinferred by very long baselinein-
surement of a pass. Subsequentphase measurementswill
have the same associatedinteger, provided the receiver
tefferometry
in California[Blewitt,1989].Threedimen- maintains lock on the G PS signal. Lossesof lock cause
sionalbaselineaccuraciesof 1.5 parts in 10s have been
integer discontinuitiesin the phasemeasurements,which
demonstrated
overdistances
of 2000km [Lichtenand
BerHõer,1989]. A prerequisiteto suchhigh precision in this paper axecalled "cycleslips.• (As a cautionary
GPS-based
geodesy
is the reliabledetectionof and,where
remark, some engineersdo not use this term if the discontinuity is caused by a low signal to noise ratio. For
possible,
correction
of integerdiscontinuities
(cycleslips) convenience,
paper makesno suchdistinctions).A
in thecarrierphasedata,causedby receivers
losinglock time seriesof this
phase data which has no cycle slipsis called
onGPSsignals.Withoutan adequatedata editingcapa- a "phaseconnectedarc."The objective of GPS data editb]!ity,
furtherprocessing
of GPSdatato extractgeophys- ing is to (1) deletedata outliers,(2) identifycycleslips,
ical results would be futile.
GPS data editing has generally involved a variety of (3) correctcycleslipswhereverpossible,and (4) introheuristicmethods,most of which operateon differences duce a carrier phase ambiguity parameter for eachphase
of data betweenpairs of stationsand pairs of satellites connected arc for further estimation using already estab[Blcwitt,1989;DongandBoek,1989].
]norderto reduceinstrumentalbiases.Visual inspection lishedtechniques
Consider the following model for the GPS carrier
of the data usinginteractivegraphicsor printoutshave
beenroutinelyusedby analyststo find and correctprob- phaseand pseudorangeobservablesspecificto a receiverdata)
le• wherealgorithmshave failed. Suchlabor-intensive satellitepair (i.e., for undifferenced
dat•preprocessing
hasbeenthe majorobstacleto improvingbaseline
production
efficiency,
uniformity,andrepro(la)
ducibility.
The > 2500cycleslipsin the data setfromthe
(lb)
•pyright 1990 by the AmericanGeophysicalUnion.
Pa,•r n•r
90GL00294.
(D94-8276/90/90GL-00294503.00
where • and •2 are the recorded carrier phases, L•
and L• are the carrier phases expressed as raz•ges, P•
199
200
Blewitt: An Automatic Editing Algorithm for GPS Data
and Pz are the P code pseudoranges,c is the speed of
light, the carrier frequenciesf• = 154 x 10.23MHz and
To solvefor wide-lane cycle slips the following pseudorange combinationis subtractedfrom L,-
fz = 120 x 10.23 MHz, and the wavelengths ).• - 19.0cm
and Az • 24.4 cm. The term p refers to the non-dispersive
delay, lureping together the effects of geometric delay,
tropospheric delay, clock signatures, selective availabil-
--pq-I f,f•/(f•--f2)
+ A)
(a)
ity (rapid variationsof the 10.23MHz GPS referencefrequency)and any other delaywhich affectsall data types
identically.The term I in equations{1) is an ionospheric
(4)
(4)
b•= •
delay parameter; b• and b• are phase biases which can
changespontaneously
by integervalues{cycleslips).
Termsignoredby equations{1) includedatanoise,mul-
The •rboEdi% algorithm calculatestimeaveragesof •
in equation(5) both beforeand after a cycleslip, •d
tipath, phase center effects, and higher order ionospheric
effects. The differential delay between the Lz and Lz an-
the difference is required •o be close to •
integer An• •
(b•-b,) = A• - An•. The actualdecision
• •o wha•
tenna phasecenterscouldbe easilyaccountedfor [e.g., constitutesa cycle slip, •d whether ph•e conn•tion '•
Blewitt, 1989]. Providedthe L• and Lz phasecenters successful,will be describedla•er.
are less than about 2 cm apart, this term can be safely
ignoredfor editing data from stationary antennas(but
may be requiredfor movingantennas).
The Ionospheric Combination
The ionosphericph•e combinationis defined• lollova:
Another term missing for kinematic GPS applications
is due to antenna rotation causing a phase advance in
the circularly polarized wavefront. This effect must be
L• • L• - L•
= I + Axbx- A•b2
removedeither by (1) externalcalibration,(2) differencing the data betweentwo satellites,or (3) usingonlythe
wide-lanephasecombination(• -(•z), which is rotationally invariant, but by itself is not suitable for regional
geodesysince it is uncalibrated for ionosphericdelay.
A cycle slip in L•, denoted An•, is defined as an integer
discontinuity in the value of b•, and similarly for Ariz.
Thus a cycle slip in dual frequencydata can be described
by the expression
= (hi -
-
(2)
=• +• (• -O•)+(X•- •)•
(•)
= I + A•b• - Xlb2
where the ionosphericwavelength),z =- (,•z - ,•x) --- 5.4
cm. The correspondingpseudorangecombinationis
Pz = P• - P• -- I
(7)
Unlike the wide-lane combination, the ionosphericcarrier
phasecannot be successfully
calibratedby the pseudorange, since it would require that multipath be controlled
at the centimeter level. The approach that will be de-
where b[ and b• are the new valuesof the phasebiases scribedassumesthat the ionosphericparmeter I behaves
•fter the cycle slip. Most often, cycleslips occurconcuras a reasonably smooth function.
rently and differentlyon the L_•and Lz channels,so that
non-zero values of An• and An• must be independently
Cycle slip Detection and Correction
detectable.
Linear Combinations
Cycle Slip Detection in the Wide-Lane Combination
of Data
The wide-lanebias,equation(5), is estimatedindepenFor purposesof estimatingcycleslip parameters
An•) we are free to choose2 linearcombinations
of the dently at every data epoch. An a priori RMS scatterof
in at4 observables,
expressed
in equations(1), whichare inde- 0.5 wide-lanecyclesis assumed(a goodassumption
pendentof the term p. This will guaranteethat the data most all cases),and the algorithm sequentiallyupdates
editing algorithm will be insensitiveto clock instability, (b,), the meanvalueof b,, and rr, the RMS scatter,using
selectiveavailability, and receiver-satellite kinematics.
the following recursive formulae:
The Wide-lane Combination
i
As was shown for the problem of ambiguity resolu-
tion [Blewitt,1989],the wide-lane
phasecombination
ß, -- (•x - •z) canbe adequately
fit usingpseudorange
data of the qualityproducedby TI-4100 receivers.From
equations
(1), thewide-lanephasedelaycanbewritten
= ai_•+ •
-
}
The calculationof the mean is exact; the calculationof
the RMS is a good approximationto simplify the code,
andhasthe diminishing
errorterm of O(1/i•), where
i
is the current number of points in the data arc. Subsequent epochestimatesb•+• are requiredto lie within 4a•
of the runningmean<b•)•.Isolatedoutliersare deleted.,
and any two consecutiveoutliers lying within 1 cycle are
consideredto indicatethe possibilitythat a cyclesliphas
where the wide-lanewavelength,k, _-- c/(L86.2cm,and the wide-lanebias,b• ---_
(b•- b,.).
f•) -•
occurred. Starting with these two points, a new aver-
ageisstarted,andcontinues
until a potentialcycleslip
B!ewitt: An AutomaticEditing Algorithmfor GPS Data
201
againencountered.
The values(5•) and crfor eachphase Equation(ga) is alsousedto identifyoutliers.The value
connected
arc are computedusingequations(8), andare of k defaultsto 6 cycles,but can be set to a more ap-
storedfor further analysis.
propriate value should ionosphericconditionsbe unusual.
Wid½-lan• Phase Connection
The reasons
for havingsucha hightolerance
(6 x 5.4ca)
for ionospheric
discontinuities
arethat (1) therearequite
The storedvaluesof (b•) for eachphaseconnectedarc
oftenlargephasevariationsfor receiversat highlatitudes
aredifferencedwith the value which has smalleststandard
due to ionospheric activity which are not to be confused
error
inthemean
crN/v/(N
- 1),where
N isthenumberwith cycleslipsand (2) the chancesof havingidentical
of data in the arc. The integer offset between the two
slips,An• = An2,of lessthan6 cyclesareveryslim,based
arcs is determined by rounding of[ this difference if the
on to our experience with the TI-4100 receiver. Note that
standard
error in the difference
is lessthan 0.15 (~ 1/6)
cycles,
andthe fractionalpart of the differenceis lessthan
0.30cycles(2 standarddeviations).
As data arcsare phaseconnected,the time-average(56)
equation
(gb)ismuchmorestringent
than(ga),because
of the aggregatearc is computed at each step to statistically enhancesubsequentphase connection. For multiple
lossesof lock which cause a sequenceof cycle slips to occur in a short period of time, the approach taken is to
deleteall the data between the first and last cycle slip,
andto subsequentlyconnect phase acrossthis gap, which
the initial point in a data arc is oftenspuriousdue to the
receiverhavingnot completelyrecovered
fromlosinglock.
œonosphericPhase Connection
If wide-lane phase connection is successful,a polyno-
mial fit is madeto /,• of equation(6) beforethe cycle
slip, then extrapolated to data just after a cycle slip. Using our knowledge of An•, it is then straightforward to
istypically
a fewminutes.
resolve
An2= (b•- b•) by subtracting
the extrapolated
Usually,
fortheTI-4!00 receiver,
15minutesofcontinu- fit fromthefirstfewdatapointsafterthecycleslip.The
ousphase
databeforeandaftera cycleslipisadequate
to orderof thepolynomial
ischosen
byincreasing
theorder
satisfythe criteria for wide-lane phase connection. For the
until the subsequentreduction in post-fit residual scatter
Roguereceiver[Thomas,1988]with a choke-ringback- is consistentwith that due to random noise. This proce-
plane, 1 minute of data is sufficient. The critical factor dure most often selectsa quadratic fit.
determiningthe required length of time is the accuracy
Before attempting ionospheric phase connection, howof the pseudorangemeasurements, which is both a funcever, the validity of polynomial extrapolation is tested on
tion of receiver precision and the effectivenessof antenna a set of at least 20 data which are free of cycleslips,immebackplanesin controlling multipath. Sample rate is not diately before the cycle slip in question. The procedure
an importantfactor (assumingreceiversinternally aver- is consideredvalid if the backward extrapolation givesan
agethe pseudorange
signal), neither is the carrier phase estimate of the imaginary cycle slip of less than 0.25. If
measurement accuracy.
valid, then extrapolation acrossa biasbreak is attempted.
If the cycleslip has an estimatedvalueof An2 • 0.5, then
CycleSlip Detection in the Ionospheric Oornbination
the cycle slip hypothesisis discarded. If An• > 0.5, then
a cycle slip is asstuned, and the nearest integer value is
First, the hypothesisis made that there are cycleslips taken if the deviation of the estimate from this integer is
intheionospheric
combination
(L, of equation(6)) when- < 0.215.If the fit fails to connectphase,a secondattempt
everthereare wide-lanecycleslips. We should,however, is made using twice as many points in the fit.
bepreparedfor the extremelyunlikelyeventthat a cycle
slipoccurssuchthat the widelanediscontinuityAn• = 0, Integer-Cycle Adjustment of Data
ß
i.e.,An• = An2. To guard againstthis, a polynomialfit
Each carrier phase data point is correctedby aminteger
• to Pt of equation(7) is subtractedfrom L•, and then
number
of cycles, and the 'phase connected ranges• are
wesearchfor discontinuities
in the residual,(L•- Q).
(Thisfit to the pseudorange
spansall the data, sincethe formed:
pseudorange
doesnot haveintegercyclediscontinuities).
Standardstatistical techniquesfor optimizing the or-
derof the polynomialfit are not applicablein this case
because
the pseudorangemultipath errors can be very
correlatedwith high order polynomials. We have empiricallyfound it more effectiveto use the followinginteger arithmetic to compute the polynomial order: m
The integer valuesof m• and rn2 for the first data epoch
are arbitrary, but for reasons of convenience are chosen
such that Ri and P• agree as closelyas possiblewith the
min[(N/!00+l),6]. Undoubtedly,
better algorithms pseudoranges,P1 and P•. Subsequentchangesin the bias
couldbe developedfor fitting the ionosphere,but only values are calculated using the above algorithms:
a crudefit is necessaryto search for discontinuitiesand
•
fit is not usedto infer the valueof the cycleslip.
If we denotethe valueof the polynomial(• at epoch
asQi, thenwe identifyi as the first gooddata pointafter
theoccurrence
of a cycleslip if bothof the followingtwo
conditions are met:
(L,,--Q,)-
(L.r,_l- Q,-x) ;> k cycles
- (L,, - Q,) <
(6m, am) = (-am -
(11)
In the event of an unresolvedcycle slip, the best available
valuesfor (Z•rnl,Am•) areusedand,as.described
by Blewitt [1989],they are eventuallyresolved
usingambiguity
resolution techniquesafter Ks!man filtering all available
data (assuming
a sufficiently
well-designed
network).
202
Blewitt: An Automatic Editing Algorithm for GPS Data
Discussionof the Algorithm
Under conditionsof high ionosphericactivity, an •ternafire approach to using the ionosphericcombina-
Properties
tion is to usethe well-knownionosphere-free
combination
The algorithm is completely insensitiveto variations in
non-dispersivedelay,whether they be due to clockbehavior, frequencyvariationsof selectiveavailability,receiversatellite relative motion, troposphericdelay, etc. However,the algorithmcan be sensitiveto ionosphericactivity
and multipath environments. In addition, sincethe algorithm relies on time-averaging, it may not work too well
if the receiver never maintains
lock for more than about
Lo -Assuming
thatwide-laxm
phaseconnection
hasbeensuccessful,
cycleslipsintheLc
linear combination are integer multiples of 10.7 cm wave-
lengths[c.f. Blewitt,1989].Unfortunately,
this appro•
is very sensitiveto clock variations. A possiblesolution
to thisisto usehighqualityreceiver
clocks.Differencing
Lc databetween
pairsof satellites
mayalsobe effective;
however, this increasesthe variability in the data due to
satellite
clocks and measurement
noise.
10 minutes. Ionospheric problems may be alleviated us-
ing a higher data sampling rate. We suggestthat bad
multipath conditionsand high cycleslip rates are better
addressedby an appropriate selectionof field equipment
and sitesrather than by data processingtechniques.
Performance
Studies with this algorithm applied to the vast CASA
Uno data set indicate that the need for additional
man-
ual editing has been virtually eliminated. Over 99% of the
station-satellite passesrequired no further analyst intervention. Almost all of the remaining 1% had incorrectly
determined integer discontinuitiesdue to rapid variations
in the ionosphericphase delay.
Subjectively, the algorithm sometimesappears to be
overly conservativein decidingwhether to correctfor cycle slips; however, experience has shown that the ana-
lyst can be easily misled by anomalousclock and ionosphericbehavior. Therefore, the general philosophyrecommended here is for the algorithm to insert extra bias
parameters when in doubt, leaving them to be resolved
later by ambiguity resolutiontechniques.
Conclusions
An algorithm has been developed for rapid GPS data
editing which can ultimately be implementedin real time
field software for dual-frequency P code pseudorangereceivers. Most importantly, the algorithm is insensitiveto
clock variations, satellite motion, and conditions of selective availability. Tests on the CASA Uno data sample
with TI-4100 receivers show that 99% of station-satellite
arcs require no further analyst intervention. The alg0rithm is adaptable to non P code receivers, or situations
with high ionosphericactivity, provided a stable receiver
clock is used. Developments are currently underway to
implement code based on this algorithm in the Roguereceiver for continuously operating arrays.
Acknowledgements. The research in this publication
was carried out by the Jet Propulsion Laboratory, California Institute of Technology,under a contract with the
National Aeronautics and Spa•e Administration. I thank
JaxnesL. Davis and Wi!!iaxn E. Strange for their reviews.
References
Ej•ciency
On a Digital MicroVAX II computer, the cpu time used
by this algorithm was approximately 20 sec per station-
Blewitt, G., Carrier phase axnbiguity resolution for the
Global PositioningSystem applied to geodeticbaselines
satellitearc (eachapproximatelyof 3 hoursduration,with
a 30 secdata samplingrate), whichturnsout to be about
up to 2000 km, J. Geophys.Res., 9j, (B8), 10,187-
I day for the entire, 3 week CASA Uno data set. This
number includes cpu time for various plotting computations to give a record of decisionsmade by the algorithm.
Dong, D., and Y. Book, GPS network analysiswith phase
ambiguity resolution applied to crustal deform•i0n
Adaptations
Lichten, S. M., and W. I. Bertiger, Demonstrationof submeter GPS orbit determination and 1.5 parts in 1•
10,203, 1989.
studiesin California,J. Geophys.Res., 9•, (B4), 394'93966, 1989.
The algorithmabovecanbe adaptedfor (1) non-Pcode
receiversand (2) bad ionospheric
conditions.In the case
of codelessreceivers, an alternative to using the pseudor-
angeto calibratethe wide-lanephaseasin equation(5) is
three-dimensional baseline accuracy, Bull. Geod., 65,
167-189, 1989.
Thomas, J. B., Functional descriptionof signal processing in the Rogue GPS receiver, JPL Pub. 88-15, jet
Propulsion Lab., Pasadena, Calif., 1988.
to fit the wide-lane phase using polynomials. The disadvantage to this is would be the algorithm's sensitivity to
to clocks, satellite motion, etc. Should receiver clocks be
insufficientlystable, the algorithm can still be applied to
G. Blewitt, MS 238-625, Jet Propulsion Laboratory,
differenceddata from a pair of satellites to a common re- 4800 Oak Grove Drive, Pasadena, CA 91109.
ceiver. This still allowsthe algorithm to be implernented
in real time on the receiver, but may fail under certain
conditions of selective availability. Note that the diffi(ReceivedNovember!0, 1989;
culty in editing wide-lane data for codeless receivers is
RevisedJanuary 18, 1990;
compoundedby half integer cycleslips.
AcceptedJanuary19, 1990.)