Calibration of GNSS positioning receivers

Karim Elglmadya,Hatem Hussein,Osama Terra,Mohamed Medhat

(1. National Institute of Standard (NIS),Giza 12211,Egypt； 2. Faculty of Science,Ain-Shams University,Cairo 11435,Egypt)

Abstract：Nowadays global navigation satellite system (GNSS)receivers are the primary tool not only for precision surveying but also for geodesy,geophysics and many other industrial applications worldwide.The only way to assure the accuracy,universality and longevity of GNSS measurements is by calibration of its receivers.The parameters affecting the calibration accuracy of a single GNSS receiver are discussed in this paper.And a geodetic basepoint is established according to previous empirical studies to serve as a reference for calibration.Additionally,the traceability to the systeme international (SI)unit of such kind of calibrations is discussed.Stability of the base point is also verified through long-term measurements over three years.Eventually,a calibration of a sample single GNSS receiver is performed and the uncertainty budget is derived.

Key words：global navigation satellite system (GNSS);global position system (GPS);receiver calibration

0 Introduction

Global navigation satellite system (GNSS)technology has found plenty of useful commercial applications in many fields including navigation,port automation,machine control,precision agriculture,construction,surface mining,aerial photogrammetry,ground mapping,geospatial information systems,unmanned vehicles,defence and time applications.Also,it is now a primary tool in precision surveying and large-scale studies such as geodynamics and geophysics.The rapid development in these fields increases the demand for evaluating the accuracy of GNSS technology.Accuracy evaluation for large scale metrology has become an interesting field for their wide applications.By utilizing our laboratory capabilities for measuring distance with accurate and traceable optical methods,the accuracy of GNSS techniques as a distance measurement tool has been evaluated[1-7].However,for absolute positioning,accuracy needs to be further investigated.

The International Organization for Standardization (ISO)has published in 2015 the ISO 17123-8:2015 “GNSS field measurement systems in real-time kinematic (RTK)”.The ISO standard discusses the precision of the system,identifies the common sources of errors in satellite positioning methods,but it does not shed the light upon the matter of how to determine the measurement accuracy[8].However,the scientific community uses two approaches for the calibration of GNSS receivers.In the first approach,researchers deal with the GNSS receiver as an electronic device,and consequently evaluate the accuracy of its electronic components.For example,zero baseline (ZB)test is used for evaluating the receiver hardware noise and absolute antenna calibration is used for determining the antenna phase center offset and variation[9-10].

In the second approach,they perform a field calibration of the GNSS receivers against a reference base point.In the United States,the Federal Geodetic Control Sub-committee (FGCS)establishes test networks consisting of a number of first-order geodetic control points to help GNSS manufacturers verify the quoted accuracy of their receiver hardware and software positioning systems[11].

In Australia,initial tests were implemented on the proper functioning related to the receiver’s electronic circuits.After that,the verification procedure can be carried out at a larger control base where network adjustment is implemented using several pillars placed at different positions[12-13].

In China,they establish a number of base station pillars at a high building,bound them to the international terrestrial reference frame (ITRF)coordinates of IGS stations,then obtain the coordinates by least squares adjustment of GNSS networks and finally derive the uncertainty budget.These points are used as a reference system in the calibration of GNSS receivers[14].

However,in addition to the hardware noise and antenna phase center errors,GNSS accuracy is also affected by delays of satellite signals due to its propagation through troposphere and ionosphere layers,and interference of the satellite signals reflected from the near-field or the far-field objects[15].Therefore,to estimate the calibration uncertainty budget of GNSS measurement,it is necessary to consider all these sources of uncertainty.So,in the field calibration approach,all the factors affecting the GNSS measurements are evaluated including GNSS equipment,observation procedures,data analysis steps and processing software.

In this paper,the field calibration approach is adopted.The establishment of a field calibration for GNSS receivers is discussed from how to choose the suitable field site to the procedures of performing the calibration and the traceability to the SI units is achieved.

1 Field calibration of GNSS receivers

The field calibration depends on the existence of a reference base point with accurate and well-known coordinates.The under-test receiver measures the coordinates of the reference points.By comparing the measured coordinates with the reference coordinates,the accuracy of the under-test receiver can be evaluated.However,the establishment of a reference base point faces many challenges.GNSS measurement is affected by several error sources such as atmospheric error,multi-path error,instrument offset and satellite geometry which must be investigated to get reliable calibration results.

However,using the high precise static GNSS technique can be very helpful in this case,which is considered as the most precise technique for GNSS measurements.It depends on the differential technique by using the difference obtained from observation results of two or more GNSS receivers simultaneously tracking a common set of four or more satellites.This difference is free from most of errors since by knowing the accurate position of one of the two receivers,the position of the other one can be easily determined.

Given two receivers A and B with known and unknown antenna coordinates respectively,and by assuming they are simultaneously tracking two satellites s and q,then the double difference carrier phase observables in length unitLencompassing two receivers (A &B)and two satellites (s &q)can be obtained by[16]

(1)

whereρis the geometric range between satellite and receiver;λis wavelength;Nis integer ambiguity;Iis range error due to ionospheric error;Tis range error due to tropospheric error;MPis phase multipath for each antenna;εdenotes the carrier phase observation noise and residual un-modelled effects.

There are two types of errors that cause GNSS measurement results inaccurate and unrepeatable,namely,systematic error and random error.With an appropriate observation model (e.g.,double difference carrier phase observable)and suitable processing algorithms (e.g.,ambiguity resolution,atmospheric modelling,clock corrections,precise orbits,etc.),systematic error can considerably be corrected.Hence,the remaining errors are most probably site-dependent errors such as multipath and local atmospheric effects[17].If we successfully correct the systematic errors by choosing a suitable site for the reference point,the most probable position value taken from the measurements of the reference point can be considered as the true value.

The research is started by searching for the most suitable site inside the campus of the National Institute of Standards (NIS),as shown in Fig.1.

Fig.1 Site location for ten points at NIS campus

The quality of the selected sites is evaluated based on four main tests,namely signal to noise ratio (SNR),multipath,occupation time efficiency and percentage of the cycle slips.Afterwards,concrete pillar is poured in-place in the selected location with a forced-centring stainless steel adapter.The second step is to select the continuously suitable operating reference stations for linking the base point to the ITRF.The selection depends on the nearest reference stations and the smallest height differences.Then long-term measurements on the reference base point are performed to evaluate the site terrain geological stability and coordinates reproducibility.Eventually,these reference coordinates are used to calibrate a under-test GNSS receiver.GNSS receiver calibration is performed according to the flow chart shown in Fig.2.

Fig.2 Flow chart for establishment of local base-points for calibration of GNSS receivers

2 Experimental work

2.1 Suitable site selection for base point

Ten locations at the campus of the NIS (NIS0-NIS9)as shown in Fig.1 are subjected to four different tests to check the site quality.Comparisons include SNR for the carrier frequenciesL1andL2,multipath onL1andL2,number of completed observations with respect to the expected number according to the occupation time and number of completed observations to the cycle slips founded.TEQC software is used for quality checking of GNSS measurements which are performed in each site.

2.1.1 SNR

Fig.3 depicts the four comparisons respectively for the ten locations mentioned above.Figs.3(a)-(b)show the SNR of the carrier frequenciesL1andL2for all ten base locations.The basepoint location must show low noise levels for calibration which means that it is less affected by any source of electromagnetic radiation,like high-voltage transmission lines.The mean values of SNR onL1andL2(SNR1 and SNR2)show very small noise values,which indicates that the environment around the base points is in good-quality.However,NIS1 shows the worst values among the ten points.

Fig.3 Experimental results for suitable site selection

2.1.2 Multipath

The second test is for the multipath which is an indication for the obstacles around the points either from near-field or far-field.TEQC software gives an indication about multipath error through values of moving average multipath parameters MP12 and MP21 in meter,the lesser the values,the smaller the multipath error.

Fig.4 Reference base point NIS0

Figs.3(c)-(d)show the moving average of the multipath parameter MP12 onL1and MP21 onL2in meter respectively for all ten base points.However,NIS1 shows the worst values among the ten points,and NIS0 shows the best suitable values which is also consistent with the values of quality checking for many IGS CORS stations[14,18].This result may be attributed to the proper selection of the roof of the Length Metrology and Precision Engineering Division building,NIS,as shown in Fig.4.This assures that there are no obstructions near the base to avoid GNSS signal multipath.

2.1.3 Occupation time efficiency

The third test is performed by checking the efficiency of the occupation time on the site which can be described by the ratio of the number of completed observations to the expected number associated with occupation time.Fig.4(e)exhibits the test for the ten locations.

2.1.4 Percentage of cycle slips

The last test is number of completed observations to the cycle slips founded.Fig.3(f)shows this ratio for all ten base points.Again,NIS0 shows the best value.From the four tests,it is clear that NIS0 is the best location site among the ten points with suitable values and also consistent with the values of quality checking for many IGS CORS stations.

High SNR indicates the absence of any source of electromagnetic radiation,like high-voltage transmission lines.The low multipath parameters values indicate that there are no obstacles (such as high buildings)around the points either from near-field or far-field.The PDOP and satellite visibility indicate the number of reachable satellites used for calculations for each pillar and they are discussed in the next section.

2.2 Suitable reference stations selection

Since 1994,the International GNSS Service (IGS)has ensured a high-quality open access GNSS data product.The IGS has a global network consisting of over 400 permanents,and is continuously operating for tracking GPS,GLONASS,Galileo,QZSS,BeiDou and SBAS.Observation data of these IGS CORS are collected,archived and published beside the data products including GNSS satellite ephemerides,satellite clock information,etc.,to the GNSS users through the internet.

However,there are also some considerations when selecting the IGS CORS stations involved in the measurement.These considerations include the selection of IGS CORS that has the closest distance to our reference base point,the smallest height difference,the smaller common PDOP values and the largest number of visible satellites.

The Sopac website is used to check the nearest IGS CORS and the preliminary processing gives their height difference with the base point.The predicted number of satellites and the dilution of precision (DOP)values for the selected IGS stations with the base point along the whole day are checked using the Trimble planning tool and depicted in Figs.5(a)-(b)respectively.

(a)Satellite visibility for all CORS with NIS0

There are five IGS stations chosen under the pre-mentioned considerations and listed in Table 1 below with their separation distances and height differences when compared with NIS0.

Table 1 IGS CORS involved in measurements

The effect of the involved number of reference stations on the final coordinates is also examined by studying all different possible combinations,starting from five stations and going down to only one station.Figs.6(a)-(c)show a small dependence on the northing and easting components but a significant effect on the elevation component.The study also gives an alternative plan for unfortunate situations when one or more of these reference stations are unexpectedly not available.

(a)Northing

2.3 Optimum occupation time

Many researchers have investigated the effect of several parameters on the GNSS measurement accuracy[19-22].Eckl et al.[19]discussed the accuracy for baselines with inter-station distances of 26 km ≤L≤300 km and observation durations of 4 h≤T≤24 h and found that the dependence of accuracy on inter-station distances is negligible and the duration of the observation is the dominating factor.Sanli et al.[20]deduced another formula for baseline distances ranging from 300 km to 3 000 km,tested out the Eckl’s model for longer baselines and observed dependence of accuracy on the baseline distances as the distance increased.

Ozturk et al.[21]focused on combining the work of Eckl et al.and Sanli et al.to obtain a uniform accuracy prediction model covering all scales (i.e.,from 3 km to 3 000 km).Sanli et al.[22]studied the effect of large inter-station height difference on positioning and improved the previous studies.

Based on the previous studies,standard deviation formulae that account for the effects of inter-station distance and inter-station height difference for range from 300 km to 3 000 km are obtained.

whereSn,SeandSuare expressed in mm;Lis separation distance between stations,km;his height difference between stations,m;Tis occupation time,h.

However,there are also parameters that affect the accuracy even using optimal time and length,such as the number and geometric configuration of the visible satellites (SVs)and the processing method being used.Soycan et al.[23]investigated the relationship between horizontal and vertical position accuracy versus baseline length (BL),the observation duration (OD),the number and geometric configuration of the visible satellites (SVs,PDOP)for baselines from 2 km to 250 km,and concluded the following two equations respectively.

2DRMS=27.117+0.163(BL)-1.897ln(OD)-

1.604(SVs)+0.927(PDOP),

(5)

VRMS=60.993+0.304(BL)-3.742ln(OD)-

2.288(SVs)+1.377(PDOP),

(6)

where 2DRMSis the root mean square error for the two-dimension position andVRMSis the root mean square error for the vertical position.

Figs.7(a)-(b)depict the propagation of errors with the occupation time for both horizontal and vertical dimensions respectively.The figures compare Sanli-Kurumahmut model with the second Soycan model on our study case.As shown from Fig.7,the optimum observation duration required to achieve submillimeter difference is about 12 h.

(a)2D error

2.4 Calibration traceability

To achieve calibration traceability to SI units,the coordinates should be traceable to the ITRF,to which all current national datums and satellite systems (i.e.,GPS,GLONASS,Galileo)are aligned.The ITRF is a realization of the International Terrestrial Reference System (ITRS).ITRS is an international standard which describes the procedures for establishing reference frames suitable for measurements made on or near the Earth’s surface according to the SI system of units.The ITRS and ITRF solutions are maintained by the International Earth Rotation and Reference Systems Service (IERS).Fig.8 depicts the GNSS calibration traceability chain to the SI unit of time[14].

Fig.8 GNSS calibration traceability chain

3 Results

3.1 Stability of NIS0 base point

In order to evaluate the coordinates of reference pillar NIS0,a receiver is installed on the pillar with a force-centring adapter.The utilized GNSS receiver unit is a dual-frequency Trimble R8s.Trimble’s post-processing commercial software package (TBC)is used to calculate the pillar coordinates.

Five different sessions are performed along a period of three years to determine coordinates of the reference pillar NIS0 with their corresponding standard deviations and verify the stability and reproducibility of the reference pillar coordinates as shown in Table 2 and Fig.9.

Table 2 Reference coordinates

(a)Northing

3.2 Calibration of a geodetic GNSS receiver

Another Trimble R8s receiver is calibrated on the reference point NIS0.The difference between the derived coordinates and the reference coordinates of NIS0 is calculated.Table 3 below shows the calibration results for an under-test Trimble R8s receiver.

Table 3 Calibration results

Since no calibration results can be reported without uncertainty budget,the uncertainty in the calibration is calculated according to the ISO standard[24].Different methods are used for reporting absolute and relative accuracies depending on national accuracy standards for geodetic control positioning in each country[25].Here we choose the 1D combined standard uncertainty scheme being used in China[14].The uncertainty sources and their influences on the measurements are discussed below:

3.2.1 Reference receiver

A dual-frequency Trimble R8s GNSS receiver is utilized in the measurements of NIS0 basepoint with high-precision static accuracy is about 62.9 mm for horizontal and 243.3 mm for vertical.

3.2.2 Reproducibility of NIS0 basepoint

The reproducibility of the NIS0 coordinates are discussed in section 3.1.The standard deviations of the coordinates are stated in Table 2.

3.2.3 Centring and levelling

This uncertainty source represents any uncorrected errors due to the wrong centring or levelling of the GNSS receiver on the force-centring adapter of the NIS0 pillar.The 1D uncertainty cannot exceed the value of 0.5 mm due to the spiral of the rod and adapter used for fixing the receiver on the pillar.

3.2.4 Phase center offset and variation

This uncertainty source is due to the phase center offset and variation of antenna.The APC point depends on the direction of the incoming signal (i.e.,elevation and azimuth angles).The APC for all antennas with the same manufacturer model number have the same mean error.These type of mean values are adopted by the National Geodetic Survey (NGS)or International GNSS Service (IGS).The TBC settings allow the user to use either the NGS correction models or an alternative Trimble relative APC correction model.The 1D uncertainty error after using these correction models is stated to be 0.1 mm[10,14].

3.2.5 Satellite orbit

The IGS provides the user with the precise corrections of the satellite orbital errors which is called final orbit ephemerides.The accuracy of IGS final orbit is about 2.5 cm for GPS satellites and 3 cm for GLONASS.The 1D propagation of orbit errors into baselines and networks is around 0.002×10-6×D,whereDis the average separated distance between the IGS stations and NIS0[14,26].

Uorbit=0.002×10-6× 599 704 m =1.2 mm.

(7)

3.2.6 Atmospheric delay correction

The correction of the ionosphere delay depends on the signal frequency.Thus the dual frequency receivers as our own reference receiver use the carrier phase observations for both frequencies to stimulate and eliminate most of the ionosphere layer effects.Also,the tropospheric refraction delay can be eliminated by utilizing dual-frequencies receivers with a tropospheric correction model[24].TBC software uses the modified Hopfield model.Although most of the Atmospheric delay errors are corrected through differential GNSS measurements,there still remain small parts depending on the separation distance between stations of around 0.002×10-6×D,whereDis the average separated distance between the IGS stations and NIS0[14,26].

UAtm=0.002×10-6×599 704 m=1.2 mm.

(8)

3.2.7 IGS station coordinates

The IGS states that the accuracy of their tracking stations coordinates are within 3 mm for horizontal and 6 mm for vertical[14].We adopt the maximum value of 6 mm.

3.2.8 Calibration standard deviation

This corresponds to the standard deviation of the under-calibration receiver measurements on the reference basepoint NIS0,as shown in Table 3.

The calibration uncertainty budget for northing,easting and elevation components are given in Tables 4-6 respectively.The combined uncertainty is calculated by adding the different uncertainty contributions in quadrature form under the square root.While the expanded uncertainty is calculated using a coverage factork=2 at approximately 95% confidence level.

Table 4 Calibration uncertainty budget for northing component

Table 5 Calibration uncertainty budget for easting component

Table 6 Calibration uncertainty budget for elevation component

4 Conclusions

This paper discusses the calibration of commercial GNSS receivers.A full methodology was suggested based on the previous studies to provide a reliable calibration procedure of the GNSS receivers.A set of 10 pillars have been established at NIS campus to accomplish this task,all of them were erected on the ground level while pillar NIS0 was established on the roof the building of the Length Metrology and Precision Engineering Division.The suitability of base point site for high-quality GNSS measurements was investigated and verified.Then a list of five IGS CORS stations was selected under pre-mentioned considerations to be involved in tying the NIS0 point to the ITRF coordinates of IGS stations,which is used as a reference in the calibration of GNSS receivers.The stability of NIS0 coordinates over three years were checked.Eventually,these reference coordinates were used to calibrate a under-test GNSS receiver and an uncertainty budget was introduced.