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Study of Improved Observation Modelingfor Surveying Type Applications

in Multipath Environment

Bernhard RichterHans-Jürgen Euler

September 2001

Published in ION GPS 2001 ProceedingsSalt Lake City, Utah, September 11–14, 2001

30 40 50 Real-Time Processing Strategies

Publikation_en_Sept_2001 30.11.2001 14:08 Uhr Seite 1

rapid static and kinematic applications, Nolan et al. (1992).The SNR translates directly into how long the receiverneeds to integrate or average, e.g., the time it takes for thetracking loops to match the incoming signal. If the SNR ofone receiver would be 10 times larger compared to anotherreceiver, this would mean that the time for integration oraveraging is reduced by 90 per cent.

Under ideal conditions the SNR plotted over elevationangles unveil the strong correlation between both. A pureelevation dependent weighting model might be interpretedas a different way of using a SNR dependent weightingmodel. In the case of a distorted SNR elevation correlation,simple elevation dependent models are no longerappropriate. The benefit of using mixed weighting modelsenhanced with an SNR dependency is already shown byBrunner et al (1999), where the so-called SIGMA-DELTAmodel has been presented. The basic information of theSIGMA-DELTA model is the SNR, but additionally thedifference between a template and the actual SNR is takeninto account. This means for a certain elevation angle, acertain SNR will be expected. The expected true SNRs arerepresented by a template, usually described by a poly-nomial of degree 2 or by the envelope of the values. How-ever, if the actual value deviates from the expected value by∆, the observation will be further down-weighted. Equation1 describes how the variances of phase observations for theSIGMA-DELTA model are derived. The factor Ci consists ofthe carrier loop noise band-width and a conversion termfrom cycle2 to mm2. The factor alpha has been included toequation 1 to allow empirical scaling of the effect of ∆.

(1)

The above-mentioned relationship between the elevationangle and the SNR is illustrated in figure 1. The outlinedactual measurement deviates from the expected value by ∆.

Fig. 1. SNR characteristics of the Leica AT504 choke ringantenna.

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ABSTRACT

Besides ionospheric and tropospheric effects, multipathand diffraction are the factors which can most limit theaccuracy of real-time applications. Phase observationscontaminated by diffraction may have unwanted effects inkinematic applications and this would limit the suitability ofmonitoring systems based on GPS as well as pure GPSsurveying real-time applications.

The concept of a self-calibrating weighting model ispresented which can be used to weight down or completelyeliminate poor signals from processing. The Signal-to-Noise ratio (SNR) is highly correlated with signalscontaminated by diffraction. The problem with using theSNR for the weighting model is that the SNR is dependenton the setup, which means that different receiver/antennacombinations and cables with varying resistances showdifferent elevation dependent SNR patterns. Even adifferent location would have an influence on this pattern.

For real-time applications it is therefore necessary toautomatically calibrate a weighting model, which is basedon the SNR. Our paper describes the advantages of such aself-calibrating weighting model compared to purelyelevation dependent weighting models. The efficiency ofthe used model is demonstrated for a kinematic real-timeapplication as well as for a typical static survey. Thekinematic test was conducted on the world’s largestsuspension bridge in Hong Kong. Such monitoringapplications, where the place of mounting a GPS-antenna is almost given, benefit strongly from this approach.

INTRODUCTION

GPS is becoming a standard measurement tool for both alarge number of standard surveying applications andmonitoring applications. Independence of visibilityrequirements and the ability of GPS to work under severeweather are often reasons to use GPS in preference tosystems involving theodolites. GPS positioning accuracy iswell understood in the user community and only inlocations with limited sky view a degradation is expected.Some of the degradations might be the result of signaldiffraction. Signal diffraction is an expression for anobstructed satellite where the signal is not completelymasked and can still be tracked by the receiver.

Diffracted signals usually show higher residuals, becausethe signal’s travel path is extended compared to the directsignal path. Therefore, a purely elevation dependentweighting model does not represent the stochastic modelproperly. Diffraction weakens the GPS signals, indicated bylower SNRs. This indicator can be used in an improvedweighting model. SNRs represent the power of a satellitesignal and are measured for L1&L2 independently. Thehigher this ratio, the better the receiver will perform in

Study of Improved Observation Modeling for Surveying TypeApplications in Multipath Environment

B. Richter, H.-J. Euler, Leica Geosystems AG, Switzerland


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To make use of the advantages of the SIGMA-DELTAweighting model for real-time applications as well as forpost-processing applications, templates would benecessary for each antenna/receiver combination. But thereare more aggravating factors, which make it difficult toprovide standard templates for different antenna/receivercombinations. It is not only the antenna and the com-bination of antenna/receiver which influences the SNRcharacteristics, but even the attenuation of the coaxial cablebetween the antenna and receiver effects the SNR patterns.The relationship between antenna, cable and sensor isdescribed in the next section. Apart from hardware specificparameters the location where the antenna is mounted canalso influence the SNR patterns. Similar to antenna phasecenter (PCV) correction files, which are needed to model thephase center variations, the template information of theSNR characteristics would have to be available on thesensor for all used antennas. This would result in anadditional logistic effort on the manufacturer’s side as wellas a deep technical understanding on the customer’s side. The handling of the whole equipment would become quitecomplicated, if all these factors had to be observed. In orderto keep the use of real-time GPS for surveying typeapplications as simple as they are today, but neverthelessprofit from an advanced weighting model, a study of animproved observation modeling was carried out. Two self-calibrating models will be described, which automaticallyadjust the SNR templates according to the antenna-receiversetup and according to the predominant conditions on thechosen location.

ATTENUATION EFFECTS

NOISE FIGURE OF THE ENTIRE SYSTEM

Apart from multipath, the total noise figure of the wholesystem determines the amount of noise being added to theincoming signal. If the signal strength is expressed in dBthere is a simple relationship between the signal strength ofthe incoming signal and the total noise figure of thesystem, which is obtained by simply subtracting thosefigures. Figure 2 illustrates how the noise figure can beused to calculate the SNR at the output port from the noisefigure and the SNR at the input port.

Fig. 2. Noise figure example

The total noise figure of the system NFtotal itself comprisesof the noise figure of the antenna NFAnt and the noisefigure of the sensor NFSR divided by the antenna gainGAnt. Figure 3 and equation 2 illustrate this relationship.

Fig. 3. Second stage noise figure

(2)

INFLUENCE OF THE ANTENNA CABLE

As mentioned in the introduction even the cable length mayinfluence the SNR measured by the sensor. The generalunderstanding that the resistance of the antenna cableattenuates the actual GPS-signal and the noise by the sameamount and therefore does not influence the derived SNRis only true to a certain extent. The impedance of theantenna cable directly influences the gain at the sensorinput. A small overall gain value results in a higherinfluence of the noise figure of the sensor and consequentlythe total noise figure of the system is increased. Figure 4illustrates the attenuation in dependence on frequency of acommonly used RG223 antenna cable. The unit of theattenuation in this figure is dB/100m. To derive theattenuation e.g. for a 10m cable, the value of the table hassimply to be divided by 10, because of the linearrelationship between attenuation and cable length.

Fig. 4. Attenuation values of a double screened antennacable (RG 223) at 20°C.

Fig. 5. SNR scatter diagram with a 1.5m antenna cable andwith a 30m antenna cable.

The derived SNR in the sensor does not exactly follow thelinear behavior of equation 1. Providing the gain at thesensor input is above a certain value (dependent on thereceiver), there will be little difference seen in the SNRswhen using different antenna cables with different


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attenuation characteristics. But if the gain at the receiverinput is low, long antenna cables will influence the derivedSNR by almost 1:1. This means that at a certain gain level afurther attenuation of 1dB from the cable will additionallyinfluence the SNR by 1dB. Such behavior is illustrated byfigure 5, where the SNR scatter diagram of a 30m longantenna cable with high attenuation is plotted versus a1.5m long antenna cable. As clearly seen in figure 5, onerigid SNR template used for all setups cannot cover allcombinations.

IMPROVED STOCHASTIC MODELING

THE WEIGHTING MODEL

Observations at low elevations are much more corruptedby tropospheric and ionospheric refraction and multipatheffects than those at high elevations. The systematic errorswhich cannot be modeled increase the root mean squarevalue of the GPS-processing. In order to optimize the usageof low-elevation observations, elevation dependentweighting of the observations has become a standard in allreal-time and post-processing software packages.

The improved weighting model, worked out for this study,is a combination between Leica’s standard elevationdependent weighting model and the use of the difference ∆between the expected true SNR and the actual SNR. Thequestion arises how to combine the elevation dependentweighting model with the information ∆. Empirical testsresulted in an exponential relationship between phasevariance and SNR. This exponential relationship betweenSNRs and the residuals of a diffracted satellite can be seenin figure 6. The exponential relationship is described indetail by e.g. Ward (1996).

Fig. 6. Example of the relationship between L1-phaseresiduals of a diffracted satellite and the SNR.

(3)

Equation 3 describes how the a priori standard deviationsare derived in our studies. The term F(z) stands for Leica’sstandard elevation dependent weighting model, where z isthe zenith angle. The factor a is a scale factor less or equalto one and ∆ is the difference between the measured SNRand the template value at the appropriate satelliteelevation. In addition to the weighting function, a limit ofthe maximum allowed difference ∆ between the actual SNR

and the template value can be set. If the computed value ∆of a certain observation exceeds this limit, this observationwill not be used for processing.

AUTOMATIC CALIBRATION OF TEMPLATES

Returning to the problem that the correct template for thecorresponding antenna-receiver combination has to beavailable to make use of the benefits of our modifiedweighting model. As mentioned in the introduction, thisproblem would be similar to the problem of providing thecorrect PCV calibration files for the antennas. Although thematching of all standard antennas is done automatically inLeica’s post processing software SKI-Pro and PCV-files canbe downloaded from the internet and directly imported intoSKI-Pro, Leica has found many errors are still made by theuser. The automated generation or adjustment of an SNRtemplate during processing is the only way to avoidcomplication on the user’s side, who would otherwise haveto ensure that the correct template is provided. As may beimagined the additional logistic effort of providingtemplates for a weighting model for all possibleantenna/receiver combinations would be huge and is themain reason that similar weighting models have not yetbeen implemented in commercial GPS processing softwarepackages.

Fig. 7. SNR characteristics of the Leica AT502 antenna.

To point out the differences of templates of various antennamodels we compare the scatter diagram of figure 1 with thescatter diagram of figure 7. A distinct difference can berecognized in the slope of the template, but also the pointsat which the signal strengths become almost constant vary.Looking at only these two examples we experience, again,that only one standard template would not fulfill the needsfor the self-calibrating SNR weighting model. In the nexttwo sections two different approaches are described whichshow how templates are generated.

Template generation – Method I

Assuming that a sufficient amount of data has beencollected, a purely statistical method can be implemented.The generation of the template is done in discrete steps, by counting the number of SNR measurements falling intoa certain signal strength interval. This is done for eachelevation interval at an interval width of a few degrees. Theinterval width can be adjusted. Figure 8 illustrates thecounted SNR measurements for elevation angles between30° and 35°. As to be expected, the majority of counts areconcentrating on some classes where the most, pre-sumably good, observations were collected. Observationswith SNR values further away from this cluster, one would


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want to down-weight or even exclude in the dataprocessing, since these observations will probably showhigher deviation from the truth. To derive the representativeSNR, used as the template value during the calculationslater, for such an interval, the median count value of allSNRs within the defined interval plus an additionalcorrection is computed (see figure 9).

Fig. 8. Example of a statistic of all measured SNRs ofsatellites between 30 and 35 degrees.

Fig. 9. Example of a template derived with method I.

During the actual calculations when an enhanced SNRweighting model is used, an observed SNR value would becompared with the derived template value in a particularelevation range. The difference between both is used thenin the weighting model described in equation 3.

The method works perfectly as long as the majority of SNRvalues in all elevation classes are those for uncorruptedobservations. This can be ensured when long observationintervals are being analyzed in post-processing or when thesystem was running already several hours for real-time. Ifnot enough data is available, one problem of method I willbecome obvious. As long as information has only beencollected for a certain elevation angle class from adiffracted satellite, the template value will reflect thisdiffraction. A weighting model based on that informationwould not down-weight the diffracted observations duringprocessing. In some situations it may even amplify theinfluences of diffracted observations by down-weightingundisturbed observations.

For method I it is crucial to provide sufficient data over a

long period, so that the template values would no longerchange. This is clearly a disadvantage of method I and,therefore, it is more practicable for post-processing andonly if a sufficient coverage of the sky is provided duringthe survey.

Template generation – Method II

The approach of using the median values for definedelevation intervals turned out to be not applicable for real-time surveying applications. Because GPS post-processingseems to be a dying breed for pure surveying applications,post-processing will often only be used if the real-timeradio link fails. One requirement for these studies was todevelop a model which is also appropriate for real-timeapplications.

Independent of the antenna/receiver combination, all SNRpatterns show the same characteristic. Up to a certain point- the point of inflection - the SNR follows a linear curve witha positive gradient. Elevation angles larger than the point ofinflection show ideally constant values. Method II is basedon the observation that all analyzed SNR/elevation patternsshow similar shapes for template values within the sameantenna type models. Under the assumption that theprinciple shape of the SNR/elevation pattern does notchange, a different approach can be used for the generationof a template. We describe a characteristic master templatefor every antenna type model by two straight lines. One linehas a positive gradient and the other line is horizontal. Themaster template needs to be adjusted for representing theactual SNR data by finding suitable coefficients of thesetwo straight lines. One way would be, for instance, to use aleast-squares adjustment in conjunction with the statisticaltable generated as in method I. However, to avoid outliershaving too much influence on the derived template thisapproach is not recommended, especially when aconsiderable amount of data is corrupted. The median ofthe residuals between the master template and thestatistical table as produced for method I is calculated andthe master template is shifted by this amount to reflect theactual conditions.

With this approach the amount of data being necessary toderive a template is significantly reduced and already aftera few epochs of data, a representative template can begenerated. Predefining the slope and the elevation angle ofthe point of inflection for different antenna types isadvantageous for short observations, especially whendiffracted signals would influence the gradient of thetemplate.

For static surveys all SNRs of all satellites are retained andused to generate the template. Over time the values wouldapproximately converge to template values as beingderived with method I. For kinematic applications a socalled ring buffer is advantageous. Such a ring buffer storesthe relevant SNR information only for a certain period oftime and permanently updates the template.

TEST RESULTS

KINEMATIC TESTS ON TSING MA BRIDGE

Hong Kong’s Tsing Ma Bridge (see figure 10) is the world’slargest span suspension bridge with 1,377 meters acrossthe Ma Wan shipping channel. A real-time kinematic GPSmonitoring system was installed to provide the centimeter-level accuracy to detect bridge movements beyond normalranges, Wong (2001).


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Fig. 10. Tsing Ma Bridge (Hong Kong)

The trigger for the studies to integrate the SNR dependencyin Leica’s weighting model function was the analysis ofproblematic data of this monitoring application. Always atthe same time of the day peaks in the height componentswere noticed. These peaks are highly correlated with anabnormal decrease (figure 11) of the signal strength of onesatellite in each case. One example of these unexpecteddrops in the SNR is given by figure 11.

Fig. 11. Example of an abnormal decrease of the signalstrength of satellite 11.

The correlation between double difference L1-phaseresiduals and the measured SNRs is illustrated by figure 12.The double difference L1-phase residuals are computedwith reference to satellite 2, a satellite with a large elevationangle. The extremely high and unexpected drop in thesignal strength of satellite 11 coincides with an increase ofthe residuals of satellite 11. Satellite 11 has still a relativelymoderate elevation angle of more than 20 degrees whenthe satellite signal is distorted and the SNR immediatelygoes down. According to the template the signal strengthshould be about 46dBHz at an elevation angle of 20° in anundisturbed environment.

The benefit of using the enhanced SNR weighting model,which reflects the stochastic of the observations muchbetter, can be clearly seen in figure 13. The top row offigure 13 was created by using a standard processingscheme without an additional phase check. By using theenhanced SNR weighting model the observations of thediffracted satellite PRN 11 are down-weighted and theimproved result is illustrated by the middle row of figure13. To generate the SNR template method II was used,which has been explained in the previous section. Ifmethod I were applied, exactly the same results would be

produced provided there is enough information to generatean appropriate template. In this case about one hour of datawould be necessary to have a sufficient coverage of the sky.For processing, the scale factor a in equation 3 was set to1.1 and the maximum deviation from the template value toeliminate single satellites was 5dBHz. The diffraction effecton the height component is completely removed andadditionally the a posteriori rms is reduced from 3.1mm to2.9mm. The diffraction effect on horizontal components isin most cases not as severe. In addition to the improvementof the positioning accuracy, the ambiguity fixing process isconsiderably supported, if the stochastic model fits thetruth more realistically.

The bottom row of figure 13 shows the height componentover a period of nine hours. The light-gray curve is com-puted by using the standard elevation dependent weightingmodel and the black curve is derived by using the enhancedSNR weighting model. Every time a satellite comes close toan area between 23 and 25 degrees of elevation and be-tween 38 and 40 degrees of azimuth, peaks repeatedlyappear in the height component in the light-gray curve,whereas the black curve is not influenced by these diffrac-tion effects. It is important here to distinguish betweenmultipath and diffraction, where the effects analyzed hereare diffraction effects and not caused by multipath.

Fig. 12. Correlation between double difference L1-phaseresiduals of a diffracted satellite and the SNRs of the samesatellite.

Fig. 13. Top row Standard elevation dependent weighting. Middle row Improved weighting model. Bottom rowElevation dependent weighting model versus improvedweighting model over a period of nine hours.


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It has to be noted, pseudorange multipath and carrier phasemultipath behave very much the same, except that thevariation of the pseudorange multipath is in phase with thevariation of the SNR variations whereas for the carrierphase multipath there is a phase shift of π/2, Braasch(1996). A phase shift of π/2 cannot be recognized in theexample data and is an indication that multipath is not thereason for the peaks in height. Furthermore, the enhancedSNR weighting model may have a counterproductive effectin the existence of true, pure phase multipath.

STATIC TESTS

Further static testing was performed on the roof of a Leicabuilding in Heerbrugg. The rover station was set up veryclose to a lift shaft, which can be seen in figure 14. Thereference was placed only 20 m away, but not maskedbelow an elevation angle of 15° and the observationduration was 4 hours. Exactly the same effects will beobserved as before if the data are processed in a kinematicmode. Every time when a satellite signal is partiallyobstructed by the lift shaft, this signal influences thekinematic position to such an extent that a peak of up to4cm in the height component can be seen (see figure 15).

Fig. 14. Rover station in multipath environment.

Fig. 15. Elevation dependent weighting model versusimproved weighting model over a period of 1 hour.

It is obvious that also static applications would benefit froma more suitable stochastic model. The rms a posteriori is anprecision indicator of how good the stochastic modelreflects the reality. In our example the rms is reducedconsiderably from 3.2mm to 1.2mm, when applying theimproved weighting model. Again both methods ofgenerating templates were used and delivered the sameresults (see table 1).

Weighting model Rms [mm]

Standard 3.2Improved weighting model (method I) 1.2Improved weighting model (method II) 1.2

Table 1. Rms values of different weighting models

CONCLUSION

Signal diffraction is a dominant technical problem in thewidespread use of GPS in real-time operations for generalsurveying and monitoring applications. Diffraction isdifficult to avoid when using GPS in a real world environ-ment. The efficiency of using weighting models whichmake use of the measured SNR has been proved severaltimes, e.g. Hartinger (1998). Errors caused by diffraction canbe reduced by more than 50% with this method. Instead ofmanually excluding satellites from the processing run, theweighting model automatically detects diffracted satellitesby analyzing the SNR.

This study showed the conceptual realization of integratingan enhanced SNR weighting model into commercialprocessing software. The described weighting model issimilar to the SIGMA-DELTA model. The phase noise iscomputed by using the elevation angle, but additionallydiffracted signals will be further down weighted if themeasured SNR deviates significantly from the expectedSNR. The expected SNRs as used for calculations aredefined by templates. The main reason that similar modelshave not yet been implemented in commercial GPSprocessing software packages is that the logistic effort ofproviding templates for all possible antenna/receivercombinations would be enormous. This problem would besimilar to the problem of providing the correct PCV-files forthe antennas, where Leica has found many errors are stillmade by the user. The solution to overcome this problem isa self-calibrating weighting model which updates the usedtemplates according to the predominant conditions.

The test results proved the effectiveness of such aweighting model to reduce signal diffraction effects.Independent of the antenna/receiver setup the model isself-calibrating. This means no user input would berequired, but the user would still benefit from a weightingmodel that fits the truth more realistically in cases whensatellite signals are diffracted.


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REFERENCES

Braasch (1996) Multipath effects. In: Parkinson and Spilker(Eds) Global Positioning System: Theory andApplications Volume I, American Institute of Aeronauticsand Astronautics, pp.547-568.

Brunner, F.K., Hartinger, H., and Troyer, L. (1999). GPSSignal Diffraction Modelling: the stochastic SIGMA-DModel. Journal of Geodesy, 73, pp. 259-267

Hartinger, H., Brunner, F.K. (1998). Variances of GPS phaseobservations: The SIGMA-ε model. GPS Solutions, 2/4,pp. 35-43

Leick, A. (1994). Satellite Surveying. 2nd Edition, New YorkMeinke, H.H., Grundlach, F.W. (1992). Taschenbuch der

Hochfrequenztechnik. Grundlagen, Komponenten,Systeme, Springer, Berlin

Nolan, J., Gourevitch, S., Ladd, J. (1992). Geodeticprocessing using full dual band observables. In: Proc. ION-GPS-92, pp. 1033-1041

Ward, P. (1996). Satellite signal acquisition and tracking. In: Kaplan ED Understanding GPS: principles andapplications. Artech House, Bosten, pp. 119-208

Wieser, A., Brunner, F.K. (2001). Robust estimation appliedto correlated GPS phase observations. In: Proc. 1st Inter-national Symposium on Robust Statistics and FuzzyTechniques in Geodesy and GIS, Zürich, pp 193-198

Wong K., Man K., Chan W. (2001), Monitoring Hong Kong’sBridges – Real-Time Kinematic Spans the Gap. GPSWorld, Vol. 12, No. 7, pp. 10-18

Leica Geosystems AGCH-9435 Heerbrugg

(Switzerland)Telephone +41 71 727 31 31

Fax +41 71 727 46 73www.leica-geosystems.com

Illustration, descriptions an technical data are not binding and may bechanged. Printed in Switzerland. Copyright Leica Geosystems AG, Heerbrugg, Switzerland, 2001727422en – XI.01 – RVA


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