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40Journal of Siberian Federal University. Engineering & Technologies, 2019, 12(1), 126-131
yflK 629.7.05:53.089.6
GLONASS Receivers Calibration
Dmitry S. Pecheritsa*
Russian Metrological Institute of Technical Physics and Radio Engineering Mendeleevo, Moscow region, 141570, Russia
Received 25.06.2018, received in revised form 29.06.2018, accepted 13.07.2018
The research presents the method and the results of calibration of GLONASS receivers in the pseudorange measurement error (bias). The method is based on the application of the instruments providing traceability to national primary standards of values. The influence of pseudorange biases to positioning error are described in the work.
Keywords: GNSS, GLONASS, receiver, GNSS simulator, navigation signal.
Citation: Pecheritsa D.S. GLONASS Receivers Calibration, J. Sib. Fed. Univ. Eng. technol., 2019, 12(1), 126-131. DOI: 10.17516/1999-494X-0078.
Калибровка навигационной аппаратуры потребителей ГЛОНАСС
Д.С. Печерица
Всероссийский научно-исследовательский институт физико-технических и радиотехнических измерений Россия, 141570, Московская область, Менделеево
Представлен метод и результаты калибровки НАП ГЛОНАСС в части систематической инструментальной погрешности измерения псевдодальности (задержки). Метод основан на применении средств, обеспечивающих прослеживаемость измеряемых величин к первичным государственным эталонам единиц величин. Показаны результаты учета результатов калибровки на погрешность определения координат.
Ключевые слова: ГНСС, ГЛОНАСС, НАП, имитатор сигналов, навигационный сигнал.
© Siberian Federal University. All rights reserved
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). Corresponding author E-mail address: [email protected]
1. Sntroduction
Th^c msin purpose of GLONASS navigation equipment (receiver) is to receive and process nnvignSion satsllits's fNS) signals inorLee toids^e sonsnmer s spafCotempLtaC data, his velocity vectLr, efCcOude esfesencs, etc.
The most common method of solving satellite navigation problem is a pseudorange method. It is based on pseudorange measurement up to NS with the given position and subsequent calculation of its rpaikctem1,) rdcoordinntes. PrsudorannL ismeae.e msacuredudShpheuseofnon-mquiry method, i.e. She sum of propagation time and difference of a signal source and a receiver timescales.
TheCctclpositierur errceuscng usenVoravua melhoditdefined by the:
APOS = AR ■ PDOP i
AR is the pseudorange measurement error, PDOP (Position Dilution of Precision) is the attitude geometric factor.
Pseudorangemeasurement errorin itsturn includesseveralessential components and might be describedlike thefollnwine [2]:
AR = Aeph + Ktm + Kel +AM + AREC + SR ,
Aeph is the contribution to pseudorange measurement error due to ephemeris error, i.e. signal-in-space range error (SISRE), Aatm is the contribution due to navigation signal delay in the atmosphere, Arel are the contribution due to relativistic and gravitational effects (RGE), AM is the supply due to NS multiple propagation, AREC is the contribution due to instrumental pseudorange measurement error, eR are the other error components.
Table 1 contains all the above described components. The residual values of each errors are given inaccordancewith [3].
One can see from Table 1 that considering GLONASS system development prospects receiver's instrumental error makes the most significant contribution to the total pseudorange measurement error.
2.Problemdefinition
In order to reach potential precision of location (time) definition that a consumer is able to get by receiving GLONASS signals one must provide crucially small value of instrumental receiver's pseudorange measurement error comparing with the SISRE (minimum 3 times smaller). Thus, the
Table 1. Components of pseudorangemeasurement error ofGLONASSreceivers
Source of error Residual error Comment
SISRE 0.7 by 20 18
Atmosphere 0.4 Dual-frequency measurements, application of models [1], [2], [3]
RGE 0.1 Application of models [3]
Multiple propagation 0.5 Antenna sgructuee, processingalgorithm [1], [2], [3]
Instrumental error >2
requirements for instrumental receiver's pseudorange measurement are possible to describe with the value of 0.2 m (requirements for the system of the year 2018).
The main reason of instrumental receiver's measurement error is a navigation signal delay in receiver's path. Receiver's radio-frequency path includes frequency-dependent elements the navigation signal propagation delay of which depends on the signal spectral characteristics. GLONASS system applies signals frequency division in several frequency band that is why the delay of all received signals will be different. This fact explains the presence of instrumental receiver's pseudorange measurement error. The values of this error might reach some meters values for different letters within the one frequency range and exceed 10 meters for signals from different frequency ranges. Due to its nature, instrumental receiver's measurement error has a systematic character that means it might be defined according to calibration results and used in measurements. Calibration here and elsewhere means a procedure of systematic component of instrumental pseudorange measurement error (bias) definition.
One must provide a residual receiver's error not bigger than 0.2 m. Consequently combined standard receiver calibration uncertainty must not exceed 0.1 m (with a sweep ratio equal to 2).
3. Theory
As it was said above the measured pseudorange has a systematic error the value of which depends on operational frequency of navigation signal and is caused by group delay (GD) dependence in receiver's radiofrequency path. Radiofrequency path might be divided in two basic components: antenna feeder device (AFD) with a cable and receiving-measuring device path. It is evident that each component contributes to the total systematic pseudorange measurement error. Thus receiver calibration in the part of systematic component of instrumental pseudorange measurement error (bias) means the calibration of separate components.
AFD calibration comes down to GD measurement in antenna path as well for different operational frequencies values, different elevation and azimuth. The measurements are effected with the help of specially developed equipment set for AFD parameters measurement. The set includes a standard unit of group delay in receiver's antenna within the frequency range from 1.1 GHz up to 1.7 GHz, that is traced to the primary special standard length unit National Standard 199-2018 and to primary standard of wave resistance in coaxial waveguide NS 75-2011.
The calibration method of receiving-measuring device is based on seminatural modeling of navigation signal with the use of GNSS signals simulators which serve as standard navigational signal source. The measuring diagram is presented at Fig. 1.
As one can see from the diagram the simulator and the receiver uses the same reference frequency and their timescales are synchronized. That means that the simulator timescale (TS) simultaneously is both a TS of a system and a TS of a consumer. This fact allows eliminating pseudorange component caused by the difference of these timescales.
One set up formation of navigation circumstances on the simulator with the following parameters:
• traffic model - solid point;
• shaping signals - all that can be received by receiver's-measuring device;
• atmospheric effects shaping - off;
• formation of ephemeris-temporal supply - off.
DmitryS. Pecheritsa. GLONAhS Rpceivors Calibration
Fig. l.Measuring diagram
Considering she above mentioned c ircumrtancee tlie; mo del ofshaping ^euderan.c for every time moment isresaesentod in ihe foUoceuw wny:
RM,i bee) = pi (j)+ CLM,i N SIM , (1)
wlipre:t is thvstandr bor aha combmnlion of a certain NS and s(gnal types pforinsbancu, -tandard precision signal within the fcee[ueocy eangeLl NS .№1 ofGLONAfi( system),y'isnhf epoch number sn whk;h ttemeasuremant hsie bpea recen^d, j^,- (j) is tiie shapinR oieudapanne, p,- h)sa ihp shaping rer^ptsneeanoo, fPlg it llte systematif cempenenl of instrumenta) assadoraage measueemenl error by GNSS signals simulator expresseol in meters, £/M etn else eandom con^pneni) n. pseMorange mnasurement error. normally riatrrtrnbei1 random Reopess.
tseuPdraogo mearuredwitd tSnr recetving-mearurtnc <b^csp^<s (n stp tern (s deraribed like
this:
R^ OS = P (b) + Vi +etH + Ka 0)
where Rreci (j) is the pseudorangpmyesure.with she eeceivmg-me^¡^^t1!^ deakae, C^, se the systomatin component of instrumental pseuderange measueement esofr muasureh with tie receipinn)mep)uring metees, Erec is t^d:^^ rEeecilom comppnant of sseudoeange mepsurement error, normal ly d(sSriMited pondom procesi.
"Thesce mpbsurrments aer eSfeated wcreing the pwriod o:f r^ot less then 24 hnurs iei osldei" to nrovide measurements mf allN^Sl. Tleemeasurements must bdj)e4Fo^r^edwi^h^^n 8daysin (eederto estimate natality bsm fordhe peases that during this period GNTSS GLONA°S sateUite constrllation will be entieePo tesseyiS^^d SO
The ceiSd^nrtote bsetfs4efi5t^ui^ctangf of tise retei-oins^ Sdviae and datd from the
simulates id nccardanae wsSp equatienp (S)s (2f ;ate ^e^isrt.i^^d m the ixtllewmg en-:
Kec.i (j) " eR)(n,i ex) = "Vi - Crecp - * ,
where e is the total random simulator pseudorange error and receiving-measuring device, normally distributedrandom process.
Meesurome nt noise ir ehmmats0 soiSh tsie h^lp of stati sii<s proenti1 ng [4]. Therefore ine value of bre e,c^ayO e tndeecording to SOe formula:
N
Crec,i = -CM,i - NL{Rrec,i (j)- RM,i (j)) •
j=h
Table 2.Receivercalibration uncertaintybudget
Source of uncertainty Absolute value, m Comments
AFD calibrationuncertainty 0.045 Standard measurements uncertainty ofequipment setforAFD parameters measuring. Symbol uB(A)
Systematic pseudorange formation uncertaintybysignals simulator 0.03 GNSS signals simulator uncertainty Symbol ub(IM )
Other errors 0.02 Standard uncertainty of A-type. Symbol uA
In total <0,06
earlier, systematicinstrumenMCNEerro Hs caused by the tota1 naiagatioo signal propagation deianrncheyathof the antenca-ceedetdeyicean/the re ceiyiiiy/Neacuringdevice. Thus systematic inslrumcntot CNEerrocis deimed withche foliowifyeouotioc:
N
b = bKJ ■ c - bu. - X (( (j) - Rim li (j)) 1 (3)
j=i
Where: c is the light speed, i?0] is the i-navigation signal propagation delay in AFD path multiplied by light, bIMJ is thesystematic instrumental errorofpseudorange formationbyGNSS signalssimulator [5].
Table 2 contains the calculated budget of calibration uncertainty in compliance with Formula (3) [6].
The final calibration uncertainty is calculatedusing the following formula (4) [6].
urec = a/tB(iNVA)+wB(A) + ae(lM) + cA . (4)
The final GLONASS receiver calibration uncertainty in the pseudorange bias does not exceed 0.06 m.
4.Experiments results
The influence of calibration amendments to systematic component of instrumental receiver's pseudorange measurement error on the error of navigation problem solution is shown in Fig. 2, 3. The figures describe the errors of coordinates definition in the plane in the statistic mode on geodesic site with given coordinates. The solution of satellite navigation problem was obtained using the least square method in dual-frequency mode within the period of 24 hours with 30 sec interval according GLONASS signals with open access applying ephemeris-temporal information. Fig. 2 explains the result of navigation task solution without calibration amendments, Fig. 3 - with them. The center is a truereceiver's position.
Standard error of estimate of coordinates definition error in the plane decreased from 3.6 m to 2.2 m, i.e.bymorethan 30%
5. Conclusion
The article represents the developed method of calibration GLONASS receivers in the pseudorange bias with traceability up to primary standard values of Russian Federation. Calculation method uncertainty does not exceed 0.06 m in case of direct calibration. Consideration of calibration
- 130 -
10
-10
* Y*Sfll
-10 »i. 10
Fig. 2. Coordinates definition error in the plane with- Fig. 3. Coordinates definition error in the plane with out calibration amendments in meters calibration amendmentsinmeters
amendments to GLONASS receiver's pseudorange measurement provides the increasing precision of location definition by more than 30%.
References
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[2] Hofmann-Wellenhof B., Lichtenegger H. and Wasle E., GNSS - Global navigation satellite systems. GPS, GLONASS, GALILEO and more, Wien, SpringerWienNewYork,2008.
[3] Janz Subirana J.M., Zornoza M.H.-P., GNSS DATA PROCESSING. Volume I, Fundamentals and Algorithm, Netherlands, ESA Communications, 2013.
[4] ГОСТ Р 8.736-2011 "Государственная система обеспечения единства измерений (ГСИ). Измерения прямые многократные. Методы обработки результатов измерений. Основные положения". [GOST Р 8.736-2011 "State system for ensuring uniform measurement (GSI). Multiple direct measurements. Methods of measurement results processing.Main principals"(inRussian)]
[5] Печерица Д.С., Федотов В.Н. Калибровка имитаторов сигналов ГНСС. Системный анализ, управление и навигация: Тезисы докладов, М., 2016. [Pecheritsa D.S. and Fedotov V.N., Calibration of GNSS signals simulator, System analysis, management and navigation, Lectures abstracts, Moscow, 2016 (In Russian)]
[6] ГОСТ 54500.3-2011-3 «НЕОПРЕДЕЛЕННОСТЬ ИЗМЕРЕНИЯ. Часть 3. Руководство по выражению неопределенности измерения», 2011 [GOST 54500.3-2011-3 "MEASUREMENT UNCERTAINTY. Part 3. Guide to the expression of uncertainty in measuring", 2011. (In Russian)]
