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Analysis of propagation effects from GNSS - gAGE

1. Source File 2 Plot Nr 1 Plot Nr 3 Plot Nr 4 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 21 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Example 1 HPE plot gLAB out gLAB Version 2 0 0 gLAB Version 2 0 0 Horizontal positioning error SPP 1 Nolono corr ou n ver 15 e Fullmodel H ium Se a as 10 9 wma E be m c 4 7 mu DES e 8 i A xp c Preferences E ai 1 P Positioning Analysis Preferences Templates Positioning Analysis NEU positioning error Horizontal positioning error Zenith Tropospher Templates nem NEU positioning Dilution Of Precision Satellite skyplot Carrier phase amt x eee P mS MIN Y min Y max r Model components Prefit residuals Postfit residu piton pi pre P iS Meaxur Multipath Noise Model components Prefit rg iduals Postfit residuals Orbit and k comparison Global Graphic Parameters Title Horizontal positioning err East error m Y label No 9o oo XV 1 Global Graphic Parameters lf i 20 Y min 20 Title Horizontal positioning err Zbel East error m Y label NOx Rc Plot Nr 2 y onospheric combinations
2. O Automatic Limits B X min X max Plot Nr 2 Plot Nr 3 amp Plot Nr 1 ndividual Plot s Configuration Source File guAB out Plot Nr 1 Plot Nr 3 Plot Nr 4 DSTAE 19 Column DSTAN v 18 X Columf DSTAE y 19 Y Column DSTAN M Label Full Model d N vun Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 22 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 1 Klobuchar iono corr plot gLAB out gLAB Version 2 0 0 i Model lono corrections SPP 33 g F ed E e ge CSS httpi www gage es ESE NENNEN j ENA 7 Preferences About s a s t a AVA Y Positioning Analysis C ZEN Templates NEU positioning error Horizontal positioning error Zenith Tropospheric Delay lonospheric combinations Dilution Of Precision Satellite skyplot Carrier phase ambiguities Measur Multipath Noise Model components Prefit residuals Postfit residuals Orbit and Clock comparison Global Graphic Parameters Title Model components X label Y label Clear Automatic Limits X min X max Y min Y max meters advance 10000 20000 30000 40000 50000 60000 70000 80000 90000 time s Individual Plot s
3. Save Config Show Config SPP Template PPP Template RungLAB how Output Save Config Show Config SPP Template PPP Template RungLAB Show Output Equivalent command line sentence gLAB linux input cfg gLAB p1 Full cfg 5S ESAC Madrid Spain 15 17 Oct 2012 Slide 59 input obs amc3030 030 pain E Tutorial associated to the GNSS Data Processing book input nav brdc3030 03n J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 1b Iono disabled 2 Reprocess the same files with the iono corrections disabled gLAB Version 2 0 0 About l Preferences Positioning Analysis Positioning Analysis Modellirg Options Satellite clock offset correction Consider satellite movement during signal flight time Consider Earth rotation during signal flight time _ Satellite mass center tc antenna phase center correc Disable Ionospheric corrections 1 SPP Template PPP Template _ Receiver antenna phase center correction _ Receiver antenna reference point correction NB 3 Nominal Simple Mapping RINEXNavFile v Flexible Wind up correction Carrier phase only Sl Pl P2 correction Sj F1 Cl correction Solid tides correction Relativistic path range correction Save Config Show Config Run gLAB Show Output Equivalent command line sentence
4. Ex 1 Assessing Iono effects on single freq pos NEU positioning error SPP Full model Execute in a single line or use the gLAB GUI graph py f gLAB out x4 y18 s c 1 OUTPUT 1 North error f gLAB out x4 y19 s c 1 OUTPUT 1 East error f gLAB out x4 y20 s c 1 OUTPUT 1 UP error yn 40 yx 70 xl time s yl error m t NEU positioning error SPP Full model graph py f gLAB out x4 y20 s c 1 OUTPUT 1 Full model f gLAB1 out x4 y20 s c 1 OUTPUT 1 No Iono cl r yn 40 yx 90 xl Time s yl Up error m t Vertical positioning error SPP graph py f gLAB1 out x19 y18 so c 1 OUTPUT 1 No Iono cl r f gLAB out x19 y18 so c 1 OUTPUT 1 Full mod cl b xl East error m yl North error m xn 40 xx 40 yn 40 yx 40 t Horizontal pos error SPP P2 P1 shifted 4 m s c 1 INPUT j1 MODEL cl r xl time s yl meters 6 yn yx 80 t Ionospheric Combination T T T PI P2 P1 shiifted 4m Klobuchar STEC graph py f gLAB out x4 f gLAB out x4 J Sanz Subirana J o 10000 20000 30000 40000 50000 60000 70000 800 00 90000 1 Assessing Iono effects on single freq pos Vertical positioning error SPP ee p i Horizontal ee error SPP 3 BEI e No lono corr ONT RE ee PN ee b e e Full mo
5. The same answer as in previous x lot 6500 BEEN METTE ui cama NNNM M buen MET Lecce MM p CE MEE MEUM UNI er O p Ts 0 10 20 30 40 50 60 70 80 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 106 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO Derivation of bending angle Q a from s Excess Phase Rate or Atmospheric KGPS 0 eem e Doppler Shift AAS KLEO ND wo Cos uo t x Ap occult Vaps Kop Vino Kino m Bending Angle a Apoa Apoca eaa A At AMf V Gps Kops 1 VLEO Ky 20 1 A n e UN O a Neps ops SIN Ol gpg Oops Myo zo SIN ro tOo 4 The Bending Angle a pa be derived iteratively from this equations system see R 6 A Usps T Ae Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 107 B k Tutorial associated to the GNSS Data Processing book aC U D J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO Comments From phase excess rate measurements the bending angle can be estimated From the bending angle the variations of the refractivity can be computed and from these one can then derive atmospheric quantities such as Pressure Temperature and the partial pressure of
6. Automatic Limits X min X max Y min 0 Ymax 40 J aay dre rV ESSO j n E E ad 3 E Ui i Individual Plot s Configuration o T Fa aris i Er H1 Plot Nr 1 Plot Nr 2 Plot Nr 3 Plot Nr 4 SEXO i e c A Source File gLAB out Examine Circles Condition INPUT A 1 INPUT Blue m X Column sec fa Y Column 10 9 Label PRN PI P2 P1 MP pes Piot AR LPS ast 4 aS Ae mt eus ess w uta 9 ue ee m4 j S 2 4 g se hg v un ee D if La e sua os e Ara o d a e ass d Baas s ae vy as w van ce iin PIG Lf we te a 2245 e fete et oes durs e eee oes ee Ce E DOR cisci P EA esen u zi Er se oe n k ii ees ETRE EU as ee tee tae Wig elis FEM Ese s 22 foe s HL LH et o as x cr Ln oem t a IIT ET d ee Drs faccecces ce tp ee fes pte d 5 o ui Ne PELA d d q hj ne t S eee ee 14 1 019 0 5 l 0 5 1 0 40 0 5 0 0 05 1 0 m O 1 rropagation errects cnannei moadeirs ana related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 41 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 3 Zenith Troposphere Delay estimation PPP Template static positioning with dual freq code amp carrier iono free combination PC LC post processed preci
7. 23 20718775 074 18605935 474 9 14498133 97346 20718775 6074 lt 17 20842713 610 19083282 892 9 14870090 55546 20842713 4814 lt s 6 Emission 300m Lot Reception Satellite clock offset 300Km Relativistic correction lt 13 m Pseudorange Sat instrumental delays TGD m P1 P2 C A Geometric distance p0 20000Km Ionospheric delay 2 50 m Tropospheric delay 2 10 m eceiver clock offset lt 300Km Receiver instrumental delays m Example 1 Iono effects on single freq Positioning 1 Compute SPP using files ramo1250 000 brdc1250 00n gLAB Version 2 0 0 gLAB Version 2 0 0 Pesa Er pry ee Peu Freferences About Horizontal positioning error SPP D eitinninn Ana 1 amp A priori receiver position Calculate 8 Use RINEX Position O Specify Use SINEX File RINEX Observation File home gLAB ramo1250 000 Show ANTEX Orbit and Clock Scurce North error m Broadcast Precise 1file Precise 2 files X m As z Y m Global Graphic Parameters RINEX Navigation File home gLAB brdc1250 C0n Examine m Z Im Title NEU positioning error p Automatic Limits X min max Ymin Ymax i i SINEX File oe S s seuls ou adnate m u Individual Plot s Configuration E show Broadcast same as navigation Broadcast spec
8. 9 e SPP config gLAB Version 2 0 0 MEAS messages es It provides the MEASurement values It is shown after an epoch is read and decimated It contains the measurements for each satellite for this epoch e Field 1 MEAS e Field 2 Year e Field 3 Doy e Field 4 Seconds of day M E AS e Field 5 GNSS System GPS GAL GLO or GEO e Field 6 PRN satellite identifier e e Field 7 Elevation of the satellite degrees f 1 l e e Field 8 Azimuth of the satellite degrees e Field 9 Number of Measurement s e Field 10 Measurement identifier as string e Field 11 Measurement s value m e Sample MEAS 2010 081 300 00 GPS 30 30 00 240 00 6 C1C L1C C1P L1P C2P L2P 20228715 3270 0 0000 0 0000 20228715 2722 20228714 8230 20228714 7005 Messages Print INFO Messages satellite clock offset correction Preferences Positioning Analysis E E B I I Station Data GNSS Satellite Selection Set data decimation to 1s pre dec 1 signal flighr rime Print CS Cycle Slip Messages amp Print MEAS Message Print EPOCHSAT Messages Si Consider Earth rotation during signliN light time C Satellite mass center to antenna phas center correction _ Receiver antenna phase center correctio Salellile Options ace Elevation Mask Degrees 5 Recel
9. Configuration Plot Nr 1 Plot Nr 2 Plot Nr 3 Plot Nr 4 sereme gunot P Examine ws di 7 ce ia X Column Y Column label Note Use the gLAB out file E In gLAB1 out file this model pep mS Select IONO component was switched off Ionosphere delays code and advances carrier measurements Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 23 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 1 Measur P2 P1 v s Model Klobuchar gLAB Version 2 0 0 Templates http www gagees Cesa Positioning Analysis NEU positioning error Horizontal positioning emor Zenith Tropcspheric Delay lonospheric combinations Dilution Of Precision Satellite skyplot Carrier phase ambiguities Measur Multipath Noise lonospheric combinations e o All PRN PIZ P2 P1 e e PRN 13 PIZ P2 P1 iie UJ Un UJ o 25 meters of L1 L2 delay m Model components Prerit residuals Postfit residuals Orbit and Clock comparison Global Graphic Parameters Yiobel neters of LI L2 delay im Title lonospheric combinations XJabel time s Clear Automatic Limits Incividual Plot s
10. Generating the input file gawk printf 9 5f 7 5f n 7 cos 6 3 14 180 15 ro tmp gt abl tmp Sort the file by impact parameter sort nr k 1 abl tmp gt abl dat Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 92 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares LWP 1 Electron Density Profile from RO 2 Run the program abel perl over the generated file abl dat to compute the electron density profile Ne p Sort the file by impact parameter cat abl dat abel perl gt Ne dat Ne COSMIC 4 Antenna 1 PRNO2 3 The output file abl dat contains the fields n p n L1 L2 n Ne n Plot the electron density profile Ne as a function the impact parameter p and as a function of height above Earth Ploti As a function of p graph py f Ne dat x4 y2 Xl Ne e m3 yl p km height km Plot2 As a function of height 10005 0 0 O05 1 0 15 20 25 30 35 490 Ne e m3 lell graph py f Ne dat x4 y 2 6370 xl Ne e m3 yl h km Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 93 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP 1 Electron Density Profile from RO Questions 1 Taking in
11. gLAB linux input cfg gLAB p1 NoIlono cfg input obs amc3030 030 input nav brdc3030 03n gLAB Version 2 0 0 Ses T ae gane ao http www ga Te MU LE Output Des Output File Examine Messages asju E SOOS amp Print INFO Messages Print CS Cycle Slip QNS Bj Print INPUT Messages C h an g e ou t D Uu t fi I e Print MEAS Message amp Print MODEL Messages name to gLAB1 out 3 Print EPOCHSAT Messages Print PREFIT Messages Print POSTFIT Messages Print FILTER Messages Print OUTPUT Messages Save Config Show Config SPP Template PPP Template Run gLAB 3ow Output AC Madrid Spain 15 17 Oct 2012 Slide 60 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Ex 1c 2 Freq processing gt 3 Reprocess the same files but with 2 freg Iono free PC gLAB Version 2 0 0 Preferences Positioning Analysis Modelling Options Satellite clock offset correction Consider satellite movement during signal flight time Consider Earth rotation during signal flight time Satellite mass center to antenna phase center cpm _ Receiver antenna phase center correction _ Receiver antenna reference point correction Disable Ionospheric corrections and P1 a_i nal v Simple Mapping P2 corrections C F1 P2 correction exible _ Wind up cor
12. print 3 15 ro dat Ploting L1 L2 graph py f ro dat xl time h yl meters of L1 L2 t RO L1 L2 COSMIC 4 Antenna 1 4 3 4 4 time h This file has been generated from files http cosmic io cosmic ucar edu cdaac podObs 2006 253 004 01 01 rnx leoOrb 2006 253 004 01 2009 2650 sp3 igs13920 sp3 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 67 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 2 STEC in a Radio Occultation RO RO L1 L2 COSMIC 4 Antenna 1 PRNO2 The previous plot shows only the variation of the Integrated Electron Content along the ray path STEC More information can be retrieved from occultation measurements For Instance e Electron Density Profile of the Ionosphere LWP1 Phase excess rate which is related to the bending of ray LWP2 41 4 2 43 44 45 4 6 time H meters of L1 L2 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 68 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Given that session time is limited to 2h participants who feel comfortable using gLAB can skip part of the next basic exercises Ex3 Ex6 and jump to the Laboratory Work Projects LWP
13. 3 Zenith Troposphere Delay estimation Tropospheric delay The troposphere is the atmospheric layer situated between the Earth s surface and an altitude of about 60 km The effect of the troposphere on GNSS signals appears as an extra delay in the measurement of the signal travelling from satellite to receiver The tropospheric delay does not depend on frequency and affects both the pseudo range code and carrier phases in the same way It can be modeled by A hydrostatic component composed of dry gases mainly nitrogen and oxygen in hydrostatic equilibrium This component can be treated as an ideal gas Its effects vary with the temperature and atmospheric pressure in a reasonably predictable manner and it is responsible for about 90 of the delay A wet component caused by the water vapor condensed in the form of clouds It depends on the weather conditions and varies faster than the hydrostatic component and in a totally random way For high accuracy positioning this component must be estimated together with the coordinates and other parameters in the navigation filter Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 45 B aC ku Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares 1 Introduction 2 The gLAB tool suite 3 Examples of GNSS processing using gLAB gt Laboratory session organ
14. Configuration Plot Nr 1 Source File 10000 20000 30000 40000 50000 60000 70000 time s 80000 90000 ab lonospheric combinations Condition Ly 1 INPUT Y min Y maxz40 X Cclumn Y Column 3 e e Klobuchar STEC 35 E ees NN Pog fe All PRN PI P2 P1 3 UJ eo meters of L1 L2 delay m N 00 10000 20000 30000 40000 50000 60000 70000 80000 90000 time s Example 1 Summary Klobuchar model perform l Full model 5 No lono corr Up error m North error m gLAB out 10000 20000 30000 40000 50000 60000 70000 80000 90000 5 0 East error m Model lono corrections SPP i M5 BEAB 0 Ionospheric correction J ld iubd4 ue acd ane broadcast Klobuchar Tonospheric delays are larger at noon due to the higher illumination meters if NE Large positioning errors mainly in vy VN vertical appear when neglecting nie ciel ME E WO come ionospheric corrections 10000 20000 30000 40000 50000 60000 70000 80000 90000 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 25 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M
15. ESAC Madrid Spain 15 17 Oct 2012 Slide 49 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Laboratory session organization 3 Advanced Labeled as Homework exercise The study ofcode carrier ionosphere divergence effect on single frequency carrier smoothed code is proposed as a complementary Homework Exercise These exercises are beyond the scope of this 2h laboratory session but can be selected as well instead of the Laboratory Work Projects LWP1 or LWP2 Hatch filter cl Single Frequency and Divergence Free smoothing 100 seconds Cl Rav Cl DFree smoothed where n k if k lt N and n Nit k N The algorithm is initialised with P 1 P 1 A minimum knowledge of UNIX e g awk is desirable for these homework exercises gawk BEGIN g 77 60 2 print 6 4 g 13 14 15 16 g 1 meas txt gt PC txt Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 50 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares 1 Introduction 2 The gLAB tool suite 3 Examples of GNSS processing using gLAB 4 Laboratory session organization LABORATORY Session gt Starting up your laptop e Basic Introductory lab exercises rono amp Posit SF storm TIDs e Medium Laboratory Work Projects LWP1
16. Hern ndez Pajares 1 Introduction gt The gLAB tool suite 2 Examples of GNSS Data Processing using gLAB 3 Laboratory session organization LABORATORY Session e Starting up your laptop Basic Introductory lab exercises Iono amp Posit SF storm TIDs e Medium Laboratory Work Projects LWP1 LWP2 e Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 5 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares The gLAB Tool suite A The GNSS Lab Tool suite gLAB is an interactive multipurpose educational and professional package for GNSS Data Processing and Analysis gLAB has been developed under the ESA Education Office contract N P1081434 A Main features e High Accuracy Positioning capability e Fully configurable e Easy to use um rdum e Access to internal computations deeem aer rers rg NC NEUES Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 6 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares The gLAB Tool suite 1 Students Newcomers a Easy to use Intuitive GUI b Explanations Tooltips over the different options c Guidelines Several error and
17. Hernandez Pajares Example 1 2 frequency onosphere free solution From previous configuration set following options gLAB Version 2 0 0 gLAB Version 2 0 0 esa mee Le aa amp UP esa Liga ee Preferences Positioning Analysis Modelling Options Measurements gl Satellite clock offset correction Positioning Analysis Troposhere Selection Consider satellite movement during signal flight time _ Estimate Troposphere Pseudorange Consider Earth rotation during signal flight time Pseudorange Carrier phasd Satellite mass center to antenna phase center correction e Receiver antenna phase center correction D 1 S a b l e Receiver antenna reference point correction Receiver Kinematics wi Relativistic clock correction orbit excentricity I O n O C O r r e C t e Static C lonospheric correction Kinematic gj Tropospheric correction UNB 3 Nominal Simple Mapping a n d Parameters Pl P2correction e Po Other options D1 p2 TGDS Coordinates 1e8 m2 1e8 m C Backward filtering P1 Cl correction Flexible Receiver Clock 9e10 m 9e10 m2 Wind up correction Carrier phase only Available Frequencies Solid tides correction _ Relativistic path range correction Save Config Show Config SPP Template PPP Template Run gLAB Show Output Save Config Show Config SPP Template PP
18. LWP2 e Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 51 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Starting up your laptop 1 Plug the stick into an USB port and boot your laptop from the stick 2 Access the Boot Device Menu when starting up the laptop Note The way to do it depends on your computer E121 you should press ESC or F4 F10 F12 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 52 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Starting up your laptop 3 The following screen will appear after about 2 minutes IMB The US keyboard is set by default Click on this icon to You can change it by right corner Q AA t g S 9 A 4 a D Q wu 3 m o g e o pj A e 3 u M E pa o a n I LE v LT ct oO or ED x w p et m 3 Q LAB Manual Terminal c in m n un un T Y 5 o Ac Co Ti w PP w Click on the gLAB icon to start up gLAB Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 53 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Jua
19. N path STEC has been y ge shown From these integrated measurements during an occultation it is LWP1 Target In this LWP we will retrieve possible to retrieve the the Ne h using a simple electron density profile numerical algorithm which i e Ne h of the is equivalent to the Abel ionosphere transform see R 6 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 88 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares LWP 1 Electron Density Profile from RO The basic observable of this technique is the additional delay due to the refractivity index of a radio signal when passing through the atmosphere e This additional delay is proportional to the integrated refractivity in such a way that we can obtain an estimation of the 5 vertical refractivity profiles using As it is know STEC and Ne are related by f F r observations at different elevation LEO angles by solving an inverse STEC p N dl problem A valent herical e Traditionally the solution of this inis ida m inverse problem is obtained by STEC p 2Y Np n i e 1 Ln using the Abel inversion algorithm assuming a refractivity index that only depends on the altitude R 5 where p stands for the impact parameter the closest point to the Earth centre along the optical ray path Propagation effect
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21. combination of GPS carrier measurements L L L Some authors distinguish between Large Scale TIDs LSTIDs with a period greater than 1 hour and moving faster than 0 3 km s and Medium Scale TIDs MSTIDs with shorter periods from 10 minutes to 1 hour and moving slower 0 05 0 3 km s The LSTIDs seem to be related to geomagnetic disturbances i e aurora ionospheric storms etc The origin of MSTIDs seems to be more related to meteorological phenomena such as neutral winds eclipses or solar terminator that produces Atmospheric Gravity Waves AGW being manifested as TIDs at ionospheric heights due to the collision between neutral and ionised molecules Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 82 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Ex 6 Travelling Ionospheric Disturb In R4 2006 a simple method to detect MSTIDs is proposed It consists of detrending the geometry free combination of GPS carrier measurements from the diurnal variation and elevation angle dependences applying the following equation OL t L t L t 7 L t 1 2 where a value of 300sec is suitable to keep enough variation of LI i e STEC Using the previous equation the detrending is done simply by subtracting from each value an average value of the previous and posterior measurements i e th
22. contribution of ionosphere and E 2 2 troposphere The troposphere e 6500 Lee E SUR ionem A produces the large drift at the bottom e dL1 dLc cancels common effects in esu both signals like troposphere and ionosphere But as there is no 6300 ie cic 5 T 7 T T zo bending effect due to the iono on m s Lc see previous plot P2 thence the curves match for p gt 6420 km Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 103 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares LWP2 Atmospheric Bending in RO P4 Plot the impact parameter p as a function of dL2 dLc and DDdL2 DDdRho Discuss the results found graph py f bending dat x10 y4 1 dL2 dLc f bending dat x 13 11 y4 1 DDdL1 DDdRho xl m L2 s yl p km xn 0 4 xx 4 y4 COSMIC 4 Antenna 1 PRNO2 6800 Q4 Justify the discrepancy 6700 L TR tae eet ea PRENNE between the CWO plots 6600 A eine ER Sever nny Seren See Answer 4 E 3 The same answer as in previous lot 2 6500 n Sone eee e bee eee eee I1 plot 6400 6300 E 0 0 0 5 1 0 1 5 2 0 2 9 3 0 3 5 4 0 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 104 Tutorial associat
23. correcti VeTAaUil a u J Satellite mass center to antenna phase center C Receiver antenna phase center correction Receiver antenna phase center correction GU configuration 1 In Modeling panel m onospheric EE sor SPP disable the model L 7 E lt correction v P1 P2 correction 7 P1 P2 correction name a component to analyze C Wind up correction Carrier phase only C Wind up correction Carrier phase only Soli tides correction in this example disable stn erect Relativistic path range correction C Relativistic path range correction mn SS sae Ionospheric correction gLAB Vers Desa SLAB e Positioning Analysis 2 Save as gLAB1 out the associated output file m Notice that the gLAB out file v Print INFO Messages Messages V Print INFO Messages usns In the Defalil contains the processing zr soe He Set output file pee nn ds S E results with the FULL ee an mmm Configuration the model as was set in the a as v Print EPOCHSAT Messages v Print EPOCHSAT Messages oe output file was default configuration nian gLAB1 out 3 V Print POSTFIT Messages V Print POSTFIT Messages Print FILTER Messages gLAB out E Print PUTER Messages Print OUTPUT Messages v Print OUTPUT Messages Save Config SPP Template PPP Template Save Config SPP Template PPP Template Run gLAB ee z piura e Propagation effe
24. m Lc s yl p km t DDdLc DDdRho COSMIC 4 Antenna 1 PRN 2 6800 DDdLc DDdRho COSMIC 4 Antenna 1 PRNO2 Q2 Why there is no excess ray path for p gt 6420 km E 6700 L I1 4 gt E I eee Answer 2 A The ionospheric bending effect on 6600 be E i MEM MEE MM ME en L1 and L2 is proportional to the E inverse of squared frequencies a 6500 antes A S AEE bee cme A E E S E E E E A Ne E E E EE A A E E eee oes first order and cancels in the ionosphere free combination of carriers Lc There is only bending effect in Lc due to the troposphere which produces the path at the bottom mis of the figure Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 102 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO P3 Plot the impact parameter p as a function of dL1 dLc and DDdL1 DDdRho Discuss the results found graph py f bending dat x9 y4 1 dL1 dLc f bending dat x 12 11 y4 1 DDdL1 DDdRho xl m L1 s yl p km xn 0 4 xx 4 y4 6800 iaa LL 1 PRNO2 Q3 Justify the discrepancy between the two plots 6700 i eT eee HERE VETTER ECHOS PER Answer 3 e DDdL1 DDdRho accounts for the 6600 L el DES i X MEN FOON TM TY MER
25. module e RINEX observation v2 11 amp v3 00 e RINEX navigation message e Fully configurable model e SP3 precise satellite clocks and orbits e Satellite positions files e Satellite clock error correction e ANTEX Antenna information files e Satellite movement during signal e Constellation status flight time e DCBs files GPS_Receiver_Type files o E rotation during signal flight e SINEX position files e Satellite phase center correction Receiver phase center correction frequency dependent Relativistic clock correction A Pre processing module e Carrier phase pre alignment e Carrier phase pseudo range consistency check e Relativistic path range correction e Cycle slip detection customizable e onospheric correction parameters Klobuchar Melbourne W bbena Geometry free CP combination L1 C1 difference single e Tropospheric correction Simple and Niell mappings frequency Simple and UNB 3 nominals e Pseudo range smoothing e Differential Code Bias corrections e Decimation capability e Wind up correction e On demand satellite enable disable e Solid tides correction up to 2nd e Elevation mask degree e Frequency selection e Discard eclipsed satellites Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 9 B aC KU Tutorial associated to the GNSS Data Processing book D J Sanz Subirana J M Juan Z
26. smoothed with the precise but ambiguous carrier L measurements This carrier smoothing can be done in real time applying the Hatch filter P k PH et Pun L k L k 1 where n k if k lt N and n N if k gt N The algorithm is initialised with P 1 P 1 The previous algorithm can be interpreted as real time alignment of carrier with code ibiguity P L o Oe Spt E S DT lonospheric combination meters P k PU Pd 0 LG Lk 1 4 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 UT seconds 1997 January 9th L k P L T where n 1l P L P k L k P aa Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 112 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares HW Iono Divergence on Smoothing Time varying ionosphere induces a bias in the single frequency smoothed code when it is averaged in the smoothing filter This effect is analysed as follows Let Where P includes all non dispersive terms geometric range clock P p 1 T offsets troposphere and L represents the frequency dependent terms ionosphere and DCBs D is the carrier ambiguity which is L p 4 t D T6 constant along continuous carrier phase arcs and j 6 account for code and carrier multipath and thermal noise thence N
27. the working terminal Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 58 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex la Full processing gt 1 Compute SPP using files amc23020 030 brdc3030 03n gLAB Version 2 0 0 gLAB Version 2 0 0 2 T Mibi www gagees a esa Preferences About Preferences Positioning Analysis L C Show ANTEX A priori receiver position Output Des Examine guai out Examine Orbit anc Clock Source O Calculate Use RINEX Position Output File Messages Broadcast Precise 1 file Precise 2 files X m Print INFO Messages RINEX Navigation File brdc3030 03n iu Print CS Cycle Slip Messages O Specify Use SINEX File Z m amp Print INPUT Messages ionosphere Source if activated SINEX File Print MEAS Message By d efa u t t h e O u t D U L RINEX Observation File himc23030 030 show Broadcast same as navigation Broadcast specify IDNEX Print MODEL Messages Examine Print EPOCHSAT Messages fi e n a i j e S g LA B B O u t Auxiliary Files Sj Print PREFIT Messages P1 Cl Correction P1 F2 Correction Show C Show Print POSTFIT Messages l 3 Print FILTER Messages amp Print OUTPUT Messages
28. water vapor and electron density among others GPS Signal i2 GPS Satellite FORMOSA COSMIC Satellite Fic Schematic diagram illustrating radio occultation of GPS signals Figure courtesy of NSPO Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 108 R q ck Tutorial associated to the GNSS Data Processing book U D J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares 1 Introduction 2 The gLAB tool suite 3 Examples of GNSS processing using gLAB 4 Laboratory session organization LABORATORY Session e Starting up your laptop e Basic Introductory lab exercises rono amp Posit SF storm TIDs e Medium Laboratory Work Projects LWP1 LWP2 Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 109 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares HW Iono Divergence on Smoothing The target of this HW is to analyze the error induced by the divergence of the ionosphere between code and carrier into the Single Frequency SF carrier smoothed code The Divergence Free Dfree and the Tonosphere Free IFree smoothed codes will be compared with the SF one 60000 65000 70000 75000 time s This effect will be analyzed analytically and tested with single and d
29. 000 30000 40000 50000 60000 70000 80000 90000 SEE 154 120 UT seconds 1997 January 9th Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 34 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Example 2 GPS measurements content Code measurements Carrier measurements a l p I K L p QI B 5 a 1 546 P p LK e Ly P Gol B 6 pil AY p Refers to all non dispersive terms geometric range clocks tropo delay see R 1 lonospheric delay STEC N dl STEC is in TECUs 403 fes he 16 IO STEC 1 is in m of L L delay 1 TECU 10 e m 0 10m of L1 L2 delay Interfrequency bias As the satellite clocks are referred to the ionosphere free combination K K Lkw of codes Po the K cancels in such combination Hitec gt Note TGD K is broadcast in GPS nav Message Carrier ambiguities B AN b N is an integer number b is a real number fractional part of ambiguity l l l l Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 35 B aC KU Tutorial associated to the GNSS Data Processing book D J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 2 Ionospheric delay analysis 1 Read RINEX file with gLAB and generate a measurements
30. 03 Greenland Ly r M qaqa iceland i a Norway United Klnadam 7 T Poland Germany France E Spain Lp Atlantic Murus EF kr wir Atgha anist n Lr Iran OR Ocean Alaeria Egypt 2m Palietad m a Libya Saudi l ko u r Arabla i ara i j Mall Niger Sudan i Id A Chad 1 ndi M Do eg Mere em pis d Colombia Wy E cies gt R m EXT Tanzania D asci Namibia South Botswana Atlantic P amp outh Ocean uh Madagascar Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 73 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 4 Halloween storm P2 P1 analysis Associated with the Solar Flare analysed in the previous exercise a Coronal Mass Ejection occurred which sent a large particle cloud impacting the Earth s magnetosphere about 19 hours later on October 29 Subsequent impacts were still occurring several hours later This material interacted with the Earth s magnetosphere and a Storm Enhancement Density SED appeared in North America and affected later the northern 0 1TECU 21 20UT 08803 140r latitudes in Europe Extra large gradients of TEC associated with this phenomenon were also produced degrading the GPS positioning performance The TEC evolution in October 30 2003 i e Day 303 of year 2003 can
31. 04 x2 y4 s l PRNO4 ELEV a id f PI txt c 1 04 x2 y3 so l PRNO4 P2 P1 xn 0 xx 144 M v meters of L1 L2 delay North Atlantic Ocean Propagation effects channel Ex 5 Halloween storm evolution Zoom at time interval 70 to 78 h graph py f PI txt x2 y3 1 ALL P2 P1 graph py f PI txt x2 y3 1 ALL P2 P1 f PI txt c 1 04 x2 y4 1 04 EL f PI txt c 1 04 x2 y4 1 04 EL f PI txt c 1 04 x2 y3 so 1 04 f PI txt c 1 04 x2 y3 so 1 4 xn O0 xx 144 xn 70 xx 78 IONO Halloween Storm 28Oct 02Nov garl Lat 40 Lon 119 ALL P2 P1 IE PRNO4 ELEV NET cm PRNO4 ELEV e e PRNO4 P2 P1 e e PRNO4 P2 P1 gt 2 amp L Q Q oO o N N ei nd man 5 o Q9 n r Q9 E E 80 Hours from 2003 Oct 28th Oh GPS time Hours from 2003 Oct 28th Oh GPS time Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 81 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 6 Travelling Ionospheric Disturb Travelling Ionospheric Disturbances TIDs are understood as plasma density fluctuations that propagate through the ionosphere at an open range of velocities and frequencies The trend of such fluctuations can be seen from the geometry free
32. 3 14 15 16 gLAB linux input cfg meas cfg input obs UPC33510 080 gawk if 6 03 print 0 upc3 meas b Using previous expression compute the C1 multipath and code noise gawk print 4 11 14 3 09 14 16 21 3 upc3 meas upc3 C1 results are Shifted by 21 3 to remove the carrier ambiguity c Plot the raw unsmoothed measurements for PRNO39 graph py f upc3 C1 s 1 C1 Raw xn 35000 xx 40000 yn 5 yx 5 xl time s yl meters t PRNO3 C1 Raw measurement noise and multipath SSS FE ee NO Sm Y ww ew ee wee ww ewe a wwe ewe we ee e urs i w u a ees 7 w weet ee w Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares HW Iono Divergence on Smoothing 2 Apply the Hatch filter to smooth the code using a filter length of N 100 samples as the measurements are at 1Hz this means 100 seconds smoothing Then as in the previous case depict the multipath and noise of the smoothed code a Smoothing code T 100sec gawk BEGIN Ts 100 if NR gt Ts n Ts else n NR C1s 11 n n 1 n C1s 14 L1p L1p 14 print 4 C1s 14 3 09 14 16 21 3 upc3 meas upc3 C1s100 PRNO3 C1 100s sulci and divergence of ionosphere b Plot results and compare with the raw C1 graph py f upc3 C1 s 1 C1 Raw f upc3 C1s100 s cl r 1 C1 SF smoothed xn 35000 xx 40000 yn 5 yx 5 xl time s yl meters
33. 8 so c 1 OUTPUT 1 Full mod cl b xl East error m yl North error m xn 20 xx 20 yn 20 yx 20 t Horizontal pos error SPP graph py f gLAB out x4 y25 s c 1 MODEL 1 Klobuchar STEC T f gLAB out x4 y 10 9 s c 1 INPUT cl r l ALLPI E x1l time s yl meters o NAT yn 0 yx 40 t Ionospheric Combination rot 0 RRETA Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 3 y vee cm Tutorial associated J Sanz Subirana J Example 1 gLAB processing in command line gLAB Version 2 0 0 mir OOO e The different messages provided LA B A gAGE UPC by gLAB and its content can be Cesa gE napi was pagana found in the OUTPUT section Preferences About Positioning Analysis INPUT messages Input data message It is shown after an epoch is read and By p a ci n g t h e m o u se o n d ES It contains the measurements for each satellite for this g ive n m essa g e n a mM e i a to O ti D Output Destination UCM QR appears describing the different Output File gLAB out e Field 3 Doy fi id e Field 4 Seconds of day e S Messages Field 5 GNSS System GPS GAL GLO or GEO v Print INFO Messages Field 6 PRN satellite identifier Print CS Cycle Slip Mellfages Field 7 Arc length number of undecimated epoch
34. Course on Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 October 2012 Authorship statement The authorship of this material and the Intellectual Property Rights are owned by the authors of the GNSS Data Processing book These slides can be obtained either from the server http www gage upc edu Or jaume sanz upc edu Any partial reproduction should be previously authorized by the authors clearly referring to the slides used This authorship statement must be kept intact and unchanged at all times Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 2 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares gt Introduction 1 The gLAB tool suite 2 Examples of GNSS Data Processing using gLAB 3 Laboratory session organization LABORATORY Session e Starting up your laptop Basic Introductory lab exercises Iono amp Posit SF storm TIDs e Medium Laboratory Work Projects LWP1 LWP2 e Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 3 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Introduction This practical lecture is devoted to analysing and assessing different issues associated w
35. ESAC Madrid Spain 15 17 Oct 2012 Slide 71 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 3 Solar Flare October 28 2003 Execute gLAB_linux input gLAB_linux input gLAB_linux input gLAB_linux input graph py f ankr3010 03 meas x4 y 14 16 1 ankr f asc13010 03 meas x4 y 14 16 1 asc1 f kour3010 03 meas x4 y 14 16 1 kour f qaq13010 03 meas x4 y 14 16 1 qaqi xl time s yl meters of L1 L2 xn 38500 xx 40500 yn 20 yx 20 28 Oct 2003 Solar flare t Id YY Doy sec GPS PRN el Az N list C1C L1C C1P L1P C2P L2P 12 3 5 6 7 8 9 10 11 xx 13 14 15 16 cfg meas cfg input obs ankr3010 030 ankr3010 03 meas cfg meas cfg input obs asc13010 030 gt asc13010 03 meas cfg meas cfg input obs kour3010 030 kour3010 03 meas cfg meas cfg input obs qaq13010 030 qaq13010 03 meas Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 72 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares meters of L1 L 2 Ex 3 Solar Flare October 28 28 Oct 2003 Solar flare TENERE pE HU gaint oe pania ennn eeee eee 808 88 sesctoosgtit niin 59 59 EHH ETETE asesseaneancerepesesoe Ei il eeecrressoc eta MM 38500 39000 39500 40000 40500 time s 20
36. J Sanz Improving the Abel inversion by adding ground data LEO to radio occultations in the ionospheric sounding Geophysical Research Letters Vol 27 16 pp 2743 2746 2000 R 6 Hajj GA Kursinsky ER Romans LJ Bertier WI Leroy SS A technical description of atmospheric sounding by GPS occultation JASTP Vol 64 pp 451 469 2002 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 122 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Acknowledgements e The ESA UPC GNSS Lab Tool suite GLAB has been developed under the ESA Education Office contract N P1081434 e The other data files used in this study were acquired as part of NASA s Earth Science Data Systems and archived and distributed by the Crustal Dynamics Data Information System CDDIS To the NSPO UCAR Agency for the FORMOSAT 3 COSMIC data e To Adria Rovira Garcia for his contribution to the editing of this material and gLAB updating and integrating this learning material into the GLUE Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 123 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Course on Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17
37. P Template Run gLAB bhow Output Equivalent command line sentence Propagation effects channel models and related error sources on G gLAB_linux input e cfg gLAB_pc_IFree cfg input obs ramo1250 000 input nav brdc1250 00n J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares uir ee NEU positioning error SPP Full model 1 freq SPS 50 North error time s Propagation effects channel models and related gle frequency vs Dual frequency oe gLAB Version 2 0 0 T Horizontal positioning error SPP Cesa _AB 0 se http www gage es 40 East error UP error Preferences Mf h K l b h Positionine Analysis with Klobuchar 10 sa 5L lorizontal positioning error Zenith Tropospheric Delay lonospheric combinations E f 20 5 Dilution Of Precision Satellite skyplot Carrier phase ambiguities Measur Multipath Noise 5 5 or Model components i t Qq 10 3 5 Global Graphic Parameters P l Ot g LAB 2 e O U t Title NEU positioning error e 0 1oL Sf Automatic Limits X min r ea S U l t S a S aL n i Individual Plot s Configuration p s al ILE previous cases LAB Source File gLAB out gLAB out T 20 Condition oyrpur 1 QUTPUT 0 10000 20000 30000 40000 50000 60000 70000 80000 9000 id diis UN ae in I ME time s mae SHEET X Column Y Column DSTAN Label North error a NEU positioning error 2 freq lono free b Horizontal p
38. RN 13 28 and 29 and 3 The elevation of each satellite 13 28 and 29 graph py f PI txt x2 y3 l ALL f PI txt c 1 28 x2 y3 so l 28 P2 P1 f PI txt c 1 28 x2 y4 1 29 ELEV f PI txt c 1 29 x2 y3 so 1 29 P2 P1 f PI txt c 1 29 x2 y4 1 13 ELEV f PI txt c 1 13 x2 y3 so 1 13 P2 P1 f PI txt c 1 13 x2 y4 1 13 ELEV xn 15 xx 25 yn 0 yx 85 xl time h yl meters of L1 L2 delay Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 4 Halloween storm P2 P1 analysis IONO Halloween storm 2003 10 30 amc 80 m ALL 3 3 3 3 28 P2 P1 70 29 ELEV 29 P2 P1 _ 60 29 ELEV 13 P2 P1 q 50 13 ELEV e E 40 un Q o 30 20 10 A SN S 2003 0 ad Lx x Mexico time h Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 78 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 5 Halloween storm evolution Exercise Analyze the ionospheric delays for 6 consecutive days including the Halloween storm This is a simple exercise aimed to illustrate the ionospheric delays variation during the Halloween storm A period of 6 consecutive days from October 28 to November 2 2003 are analyzed using measurements collected in the garl station in Nor
39. There if you prefer you can jump to slide 86 and choose one from the two LWPs Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 69 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 3 Solar Flare October 28 2003 On October 28 2003 an intense solar eruption a Solar Flare was detected around 11h UT in an active region which had grown one of the largest sunspots ever seen by the SOlar Helioscopic Observatory SOHO It appeared as a bright spike in the SOHO ultraviolet images This sudden enhancement of the solar radiation in the X ray and extreme ultra violet band produced a sudden increase in the ionospheric electron density on the daylight hemisphere see R 3 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 70 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 3 Solar Flare October 28 2003 Exercise Analyze the effect of the Solar Flare on the Slant Total Electron Content STEC measurements of four permanent IGS receivers ankr asc1 kour and qadt covering a wide range of longitude and latitude Data sets ankr3010 030 asc13010 030o kour3010 030 qaq13010 030o Propagation effects channel models and related error sources on GNSS
40. a FIN M e e P2 P1 n P2 L2 5 09 S P1 L1 3 09 P L 20 1 ambiguity2 ol r i y a 1 546 1 y 1 3 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 time s 10000 20000 30000 40000 50000 60000 70000 80000 90000 time s Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 40 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 2 Sky plots gLAB Version 2 0 0 Sesion 1 Ex5a4 Sky plot alrt 2009 11 02 Sesion 1 Ex5b4 Sky plot madr 2009 11 02 H 3 eee Preferences Aboul Positioning Analysis Templates NEU positioning error Horizontal positioning error Zenith Tropospheric Delay lonospheric combinations sie i ayin AE ee Ye T uet 22 v st i HE EUN Dilution Of Precision Satellite skyplot Carrier phase ambiguities Measur Multipath Noise sar E Tw t DX g s Jg P E bt Modcl componcnts Prent residuals Postfit residuals Orbit and Clock comparison e z wes ae ui a i ILI HE S Fy x E EJ ee ee A E s 9 r 4 Global Graphic Parameters E TERN s 1 Title lonospheric combinations X label time s YHabel meters of L1 L2 delay m Clear wee ee E Ei LiT BENE M ucc see x L
41. a Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares FORMOSAT 3 COSMIC mission Constellation Observing System for Meteorology Ionosphere and Climate 6 microsatellites orbit altitude 800km Three instruments GPS receiver 4 antennas 2 for POD 2 for RO TIP Tri band beacon Weather Space Weather data Global observations of Pressure Temperature Humidity Hefractivity lonospheric Electron Density Courtesy of UCAR lonospheric Scintillation Demonstrate quasi operational GPS limb sounding with global coverage in near real time Climate Monitoring Information available at www cosmic ucar edu Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 1 Mitre PCM baitom i LD A e y Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 2 STEC in a Radio Occultation RO Exercise The file RO obs contains the following fields YY DoY HH HH CODE PRN elev r LEO AR LEO DEC LEO r_GPS AR GPS DEC GPS L1 L2 L1 L2 arc deg km Deg Deg km Deg Deg cycles m 6 7 8 9 10 11 12 13 14 15 16 Plot the L1 L2 measurement in function of time to depict the variation of STEC along the occultation gt Select for instance PRN 02 and CODE 1241 that corresponds to LEO 4 and Antenna 1 Selecting CODE 1241 and PRN 02 grep 1241 RO obs gawk if 5 02
42. acy m3 over 24h data is achieved ev e s NEU positioning erra J Horizontal positioning error Zenith Topospheric Delay tonospheric combinations 0 15 je S A DE m 777777 gas iei Hh ong 3HM v Dilution Of Precision Satellite skyplot carier phase ambiguities Measur Multipath Noise n D oem Parameters i i Title NEU positioning error X4abel time s Yabel error m Clear 0 Fi Cine hemi E D Feu 0 10000 20000 30000 40000 50000 60000 0000 80000 90000 Individual Plot s Configuration Plot Nr 1 Plot Nr 2 D Plot Nr 3 Plot Nr 4 time 5 Sourc gLAB ou mii Do Condition oureur fis TPU Column sec olumn DSTAN Nort Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 43 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Example 3 Zenith Troposphere Delay estimation gLAB Version 2 0 0 Preferences About Zenith Tropospheric Delay Zenith Tropospheric Delay Estimation fito Hives gag a ses EET 2 54 Positioning Analysis 2 52 Templates NEU positioning error Horizontal positioning error lonospheric combinations 2 50 p Dilution Of Precision Satellite skypl
43. al associated to the GNSS Data Processing book D J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares fe 9 gLAB Version 2 0 0 E glab aage Example 1 gLAB processing in command line 43 Applications Place bloc 2ndorder w WordPad File Edit view Insert Format Help c E amp amp 5 A 1 4 3 45 5 6 7 69 10 11 i 13 14 15 16 17 18 MEAS YY Doy sec GAL PEN el z N list C1B L1B C1C Lic C7Q L7G C80 Leo With the En vin command Hows gawk if 5 GAL amp amp 6 16 print 4 211 1 42 15 211 1241 42 12 2156 56 93 11 212 78 32 215 316 72 35 line enten e i Generate MEAS file p gc n to facilitate gL B linux input cfg meas cfig input obs 15dt1260 090 input nav 15dt1260 09n pre dec 0 grep GPS gt l5dti126 09 meas Note RINEX file UPC53620 080 does not provides P1 code L2 H Nevertheless this is not a problem because gLAE works in writ n E ust EX E EEC ETT lt i g E J SINE TRAIT B Con peor Help press F1 To run a command as administrator user roo use sudo lt command gt See man sudo root for details graph py gien327Pc2LcZ2 dat x1 y3 1 PC2 LCZ 178 gien327PczLe2 dat x1 y2 1 PC LC 17 cl r yn GNSS Formats glabagage fj Console to execute command line search group of Astronomy amp GEomatics University of Catalonia UPC sentences Te 4 gLAE Version 2 0 0 FJ glab gage E Pr
44. ate MEAS file Tg sn GNSS Formats from notepad to console Note RINEX file UPC53620 080 does not provides P1 code H Nevertheless this is not a problem because gL B works in w 477 N 4 glaba gag E IM ie en or Help press F1 To run a command as administrator user roct use sudo lt command gt See man sudo root for details Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 55 g ab gage fj Console search group of Astronomy amp GEomatics niversity of Catalonia UPC 9 gLAB Version 2 0 0 E glab gage Ge E T7 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares 1 Introduction 2 The gLAB tool suite 3 Examples of GNSS processing using gLAB 4 Laboratory session organization LABORATORY Session e Starting up your laptop gt Basic Introductory lab exercises Iono amp Posit SF storm TIDs e Medium Laboratory Work Projects LWP1 LWP2 e Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 56 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares EX 1 Halloween storm October 2003 A severe ionospheric storm was experienced on October 29 31 2003 producing and increase of the electro
45. be seen in the movie TEC 2003oct30 anim gif Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 74 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 4 Halloween storm P2 P1 analysis The measurement files gar13010 030 gar13020 030 gar13030 03o gar13040 030 gar13050 03o gar13060 030 were collected by the permanent receiver garl in Empire Nevada USA o 40 42 deg 119 36 deg from October 28 to November 2 2003 Using these files plot the STEC for all satellites in view and discuss the range of such variations Analyse in particular the satellite PRN 04 and calculate the maximum rate of STEC variation in mm s of L1 delay Add the elevation of satellite PRN 04 in the plot The associated broadcast navigation les are brdc3010 03n brdc3020 03n brdc3030 03n brdc3040 03n brdc3050 03n brdc3060 03n Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 75 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 4 Halloween storm P2 P1 analysis Exercise Depict the ionospheric delays for the different satellites in view from station amc2 This is a simple exercise aimed to illustrate how to use gLAB to easily analyze GNSS measurements and their combinatio
46. c Disturbance MSTID propagation ional 4 us Emeryville aa g Bx TP Mes X Met Nm j Area JUENI NS gu ae exu um r TE s y MS Travelling lonospheric Disturbance MSTID propagation sodb PRN14 mhcb PRN14 monb PRN14 0 06 0 04 y Recreation Ne A aa TE Del Vile State oe 0L os S E Areal E Ko 3 ce cee V fOnone Reporal ee EN ih S Wid derness JAN WE D uS 0 02 NS Palo Alto Palo Alto 0 00 Mad od 244 Y jo Cree Trail 0 02 Detrended STEC meters of L1 L2 delay ie Gatos e d See ay Xl 0 04 55600 55800 56000 56200 56400 56600 56800 57000 E Leu pice ifs VECINA Mu EE A NONU time s J Sanz Subirana d M ian TOTER M Hern ndez Pajares 1 Introduction 2 The gLAB tool suite 3 Examples of GNSS processing using gLAB 4 Laboratory session organization LABORATORY Session e Starting up your laptop e Basic Introductory lab exercises rono amp Posit SF storm TIDs Medium Laboratory Work Projects LWP1 LWP2 e Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 87 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP 1 Electron Density Profile from RO In the previous Exercise 2 the variation of the Integrated Electron zs Content along the ray
47. combinations of RO measurements The output file 1 2 3 4 5 6 7 8 9 10 11 12 13 14 sec CODE PRN p dRho dL1 dL2 dLc d L1 Lc d L2 Lc DDdRho DDdL1 DDdL2 DDLC units m s where Rho is the Euclidean Distance between GPS and LEO e d means differences in time DD means Double Differences between GPS and LEOs satellites Note the GPS PRN13 and LEO I252 are used as reference satellites the rays between these satellites are not in occultation The results are computed for the RO between GPS PRNO2 and LEO I241 the same occultation as in previous cases The aim of this exercise is to analyse the phase excess rate in the different combinations due to the bending of the ray Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 99 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO 1 Run the program RO perl over the file RO obs and generate the combinations of measurements indicated in the previous table Note the results are provided for the occultation associate to PRN 02 and CODE 1241 that corresponds to LEO 4 and Antenna 1 This is hard code in the program but can be changed as well Execute the file RO obs must be available in the directory RO perl gt bending dat 2 Discuss next plots Propagation effects channel model
48. cts channel models and related error sources on GN Equivalent command line sentence gLAB linux input cfg gLAB pi NoIlono cfg input obs ramo1250 000 input nav brdc1250 00n Example 1 NEU Position Error plot from gLAB Version 2 0 0 No Iono correction NEU error SPP No lono corr 4th May 2000 Positioning Analys 3 North error East error UP error NEU positioning error Horizontal positioning error Zenith Tropospheric Delay lonospheric combinations Satellite skyplot Carrier phase ambiguities Measur Multipath Noise Prefit residuals Postfit residuals Orbit and Clock comparison Title NIU positioning error Autofhatic Limits X min error m M X max gt Ymin Ymax Configuratio y O Plot Nr 2 O Plot Nr 3 gLAB out WV Examine Dotted Line v 4h AA C emen ame Dum ev a Equivalent command line sentence graph py f gLAB1 out x4 y18 s c 1 OUTPUT 1 North error f gLAB1 out x4 y19 s c 1 OUTPUT 1 East error N rth t U f gLAB1 out x4 y20 s c 1 OUTPUT 1 UP error O as D yn 20 yx 50 xl time s yl error m t NEU positioning error SPP No Iono Corr IndiviaW Plo Plot Nr 1 Source File Plot Nr 4 60000 70000 80000 90000 Propagation e
49. d os ad 55 n 1 a z 7 1 m 7 Y 9 Core Es DP t w abad E AQ rc se cm Ue non vp hg nn sn cle cera cc gt eee net Sh cece ers re be ches avi en hers fag fn evens te eh me a eMac Coogee PE JEMEN a MEME MEME gibson S pute I a 60000 65000 70000 75000 9 60000 65000 70000 75000 time 5 time s Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 121 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Bibliography R i J Sanz Subirana J M Jaun Zoroza M Hernandez Pajares GNSS Data Processing Volume I and Volume II ESA Publications Division in Press R 2 J Sanz Subirana J M Jaun Zoroza M Hernandez Pajares Tutorial on GNSS Data Processing Laboratory Exercises ESA International Summer School on GNSS 2010 R 3 Hernandez Pajares M J M Juan J Sanz EGNOS Test Bed Ionospheric Corrections Under the October and November 2003 Storms IEEE Transactions on Geoscience and Remote Sensing Vol 43 10 pp 2283 2293 2005 R 4 Hernandez Pajares M J M Juan J Sanz Medium Scale Traveling Disturbances Affecting GPS Measurements Spatial and Temporal Analysis Journal of Geophysical Research Space Physics Vol 111 A07 S11 2006 doi 10 1029 2005JA011471 R 5 Hernandez Pajares M J M Juan
50. del gag out E mu aks E TES aW Up error m North error m 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 Time s 0 East error m pe uic Combination Ionospheric correction broadcast Klobuchar Ionospheric delays are larger at noon due to the higher insulation Klobuchar model is unable to mitigate the large ionospheric errors during the storm Position domain errors reach up to 40 meters with Klobuchar corrections used 0 10000 20000 30000 40000 50000 60000 70000 80000 90001 time s Propayduon elects Channel moues anu reiaceu error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 63 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares error m error m Ex 1 Assessing Iono effects on single freq pos NEU ooa rer p EE ii oe postining error SPP Ionospheric correction 4 freq SPS EE broadcast Klobuchar with Klobuchar p pe 40L s hix TERMS UNSERES ERN Ls T The ionosphere free combination PC of P1 and P2 codes is immune to the ionospheric storm e Although PC is three times noisier than P1 or P2 it provides positioning accurate at the level of a few meters North error m 10000 20000 30000 40000 50000 60000 70000 80000 9000 time s NEU sec error 2 freq lono free North error East error UP error North err
51. e curvature of the LI temporal dependency It must be pointed out that that this detrending procedure can be used in real time with a single receiver so it is suitable for identifying these ionospheric perturbations in navigation applications Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 83 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares 6 Travelling Tonospheric Disturb An example of MSTID propagation can be depicted as follows using the measurements of three TAN Reve he jer E stations SODB MHCB and 9 Ses Tee e ott oe N H arene ACE MONB which are separated B ox eges by a few tens of kilometres E B The target is to reproduce the figure 10 of the above mentioned paper R4 2006 R4 2006 Hernandez Pajares M Juan M Sanz J 2006 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 84 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 6 Travelling Ionospheric Disturb Exercise Execute in a single line a gLAB linux input cfg meas cfg input obs mhcb2910 010 gt mhcb meas gLAB linux input cfg meas cfg input obs monb2910 010 monb meas gLAB linux input cfg meas cfg input obs sodb2910 010 sodb meas b gawk gawk ga
52. eceiver L i a MJ Lp IE SENSORS Propagation effects channel models and related error sources on GNSS ESAC Madrid Spai RINEX Measurements File 2 OBSERVATION DATA G GPS RINEX VERSION TYPE RGRINEXO V2 4 1 UX AUSLIG 10 JAN 97 10 19 PGM RUN BY DATE Australian Regional GPS Network ARGN COCOS ISLAND COMMENT BIT 2 OF LLI 4 FLAGS DATA COLLECTED UNDER AS CONDITION COMMENT 0 000000000103 HARDWARE CALIBRATION S COMMENT 70 000000054663 CLOCK OFFSET S COMMENT MARKER NAME MARKER mrh auslig OBSERVER AGENCY 126 ROGUE SNR 8100 93 05 25 2 8 33 2 REC TYPE VERS 327 DORNE MARGOLIN T ANT TYPE 741950 3241 6190961 9624 1337769 9813 APPROX POSITION XYZ 0 0040 0 0000 0 0000 ANTENNA DELTA H E N 1 1 WAVELENGTH FACT L1 2 5 C1 L1 L2 P2 P1 TYPES OF OBSERV SNR is mapped to signal strength 0 1 4 9 COMMENT SNR gt 500 gt 100 gt 50 gt 10 5 0 bad n a COMMENT sig 9 8 7 6 5 4 1 0 COMMENT 30 INTERVAL 1997 1 9 0 7 30 0000000 TIME OF FIRST OBS 1997 1 9 23 59 30 0000000 TIME OF LAST OBS END OF HEADER 97 1 9 0 730 0000000 0 125 9 52317 6 22127685 105 14268715 899 8 11118481 28445 22127685 4014 lt 1 22672158 746 11510817 892 7 8969469 30045 22672158 5184 lt s 25 22594902 367 12949753 825 7 10090708 53945 22594903 7304 lt 9 22731128 796 11621184 951 7 9055464 16945 22731130 0000 lt 5 24610920 702 924108 174 6 T20085 67045 24610920 0404 lt
53. ed to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares LWP2 Atmospheric Bending in RO P5 Plot impact parameter p as a function of dL1 dRho and dLi dLc Discuss the results found graph py f bending dat x 6 5 y4 1 dL1 dRho f bending dat x9 y4 1 dL1 dLc xl m L1 s yl p km t COSMIC 4 Antenna 1 PRN 2 n COSMIC 4 Antenna 1 PRNO2 dle Mic Q5 Justify the discrepancy 6700 between the two plots _ 6600 Answer 5 E The large drift in dL1 dRho curve ru is due to the satellites GPS and LEO clock drift These large clock variations do uisi not allow to see the atmospheric bending effect 630070 0 10 20 30 40 50 60 70 80 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 105 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO P6 Plot dL2 dRho and dL2 dLc as a function of time Discuss the results found graph py f bending dat x 7 5 y4 1 dL2 dRho f bending dat x10 y4 1 dL2 dLc xl m L2 s yl p km t COSMIC 4 Antenna 1 PRNO2 COSMIC 4 Antenna 1 PRNO2 6800 Q6 Justify the discrepancy 6700 H VPE ME IEEE ONE NE TM b etween the CWO plots T MM M MM ee E Answer 6 E
54. ez Pajares LWP2 Atmospheric Bending in RO Let L be the carrier measurement at frequency f A procedure to depict the L1 bending is given next L p di B p 2p4T l being 9 the Euclidean distance between GPS and LEO and B a constant bias along continuous phase arc e The bias B cancels taking time differences of L1 Thence from previous equation it follows Ao i AL _ Acdt Refer puni um LEO a are Pda Af mE Ar EVE in NON OCULTATION X Ap occult Ap occult Ms At At Note LEO and GPS orbits are known at the level of few cm 5cm thus the Euclidean range can be calculated accurately and thus the range rate Ao At e And clocks cancel taking Double Differences between pairs of LEO and GPS satellites Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO Next expressions generalize previous results for L1 L2 and Lc measurements L p ctcdt B n iii j 1 2 The differences in time to depict the bending Ap AL _Acdt AL 5 pp pp At At At At At O sat Ap Abe Addi sppe pp ate At At At At 1 tent patei GPS LEO a are And the clock term cancels taking Double taken in NON OCULTATION Differences between LEO and GPS satellites Apu AD AL mu M DD pp2P 0 e At At At At GPSRef GPSRef Af Apia Ale pM ue DD 2o Oizo zo Oira n Ar nm n Exce
55. ffects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 20 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 1 VPE plot from gLAB out gLAB Version 2 0 0 gLAB Version 2 0 0 Vertical positioning error SPP Full model No lono corr Up error m Preferences Positioning Analysis itioning Analysis dJemplates Positioning y T Templates bis NEU positioning error Horizontal positioning error Zenith Tropospher s NEU positioning error Horizonte iospheric combinations Dilution Of Precision Satellite skyplot Carrier phase aml Dilution Of Precision nN j Y 1 lax Measwr Multipath Noise Model components Prefit residuals Postfit residu Model components Prefit residuals EC residuals Orbit and Clack comparison Global Graphic Parameters b Title Vertical positioning error X label Y label en Gigpai Graphic Parameters Wi 0 eee EE TS Ful 40 Title Vertical positioning error X label Y label S Individual Plot s Configuration HL lc Am n EmN X mex 1 Plot Nr 1 O Plot Nr 2 O Plot Nr 3 Individual Plot s Configuration Plot Nr 2 guai out Colum DSTAU v 20 OUTPUT v 1 OUTPUT ENS aaa Preference
56. file in a columnar format the easiest to manipulate and plot content gt Using the configuration file meas cfg READ the RINEX and generate the MEAS file coco0090 970 brdc0090 97n gt gLAB configuration file RINEX RINEX gLAB linux input cfg input obs input nav Measurement Navigation file file OUTPUT measurement file in columnar format Id YY Doy sec GPS PRN el Az N list C1C L1C C1P L1P C2P L2P 12 3 4 5 6 7 8 9 10 11 xx xx 14 15 16 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 36 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Example 1 gLAB processing in command line gLAB_linux input cfg meas cfg input obs coco0090 970 input nav brdc0e 98 97n gt coco meas RINEX RINEX Measurement Navigation ED Z E iter cute file file A priori receiver position RIMEX Observation File cocoo090 97To Examine Calculate Use RIMEX Position gLAB Version 2 0 0 Show AMTEX Orbit and clock source I Broadcast Precise 1 file Precise 2 filesi n put Fi les a FINES Navigation File brdcuos0 9 m coco0090 970 lonasphere Source if activated show Broadcast same as navigation Broadcast specify b rd C 0090 e g 7 n Auxiliary Files P1 CL Correction P1 P2 Correction Show gLAB Version 2 0 0 gLAB Version 2 0 0 oet default M
57. frequency positioning This is done both in the Signal In Space SIS and User Domains b A receiver will be positioned in Standard Point Positioning SPP mode a with full modelling b neglecting the ionospheric correction Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 13 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Solar radio flux F10 7 Example 1 Iono effects on single freq Positioning Data set 24h data collected by the IGS permanent receiver ramo Lon Lat on May 4th 2000 May 4 2000 Source NOAA OOO I ET Ee 1950 1960 1970 1980 1990 2000 2010 si 13 0UT upci00178 Time years O 80 160 240 320 400 480 560 640 720 800 880 960 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 14 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares The input data are code and carrier measurements and satellite orbits and clocks o0000800080808080880888 8880 O e RINEX FILES Pseudoranges C A P1 P2 e phase tracking L1 L2 One or e Navigation data D t multiple antennas e J Kalman filter position estimation DISPLAY correction Man Machine Interface e i e t e Aiding oc integrated c
58. ify IONEX Examine Sha loc 9 ode NEU positioning error SPP Full model Source File North error Auxiliary Files East error P1 Cl Correction P1 P2 Correction a UP error O Show 1 C Show 3 Condition OUTPUT v X Colu SEC mem 4 vie 3 g Save Config Show Config SPP Template PFFF Template RungLAB gMihow Output g LAB e O U t 10000 20000 30000 40000 50000 60000 70000 80000 90000 time s Equivalent command line sentence gLAB linux input cfg gLAB p1 Full cfg input obs ramo1250 000 in 15 17 Oct 2012 Slide 16 z input nav brdc1250 00n Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 1 Iono effects on single freq Positioning gLAB Version 2 0 0 FULL SPP model NEU poo error SPP Full model 50 North error mess v 4 NEU plot template configuration a Fart arr SS SS SSS rere UP error NEU positioning error Horizontal positioning error Zenith Tropospheric Delay lonospheric combinations Diluti pn ot Presion Satellite skyplot Carrier phase ambiguities Measur Multipath Noise Mo Prefit residuals Postfit residuals Orbit and Clock comparison emi Graphic Parameters Autoflhatic Limits X min AV error m L ei Xmax Nd Y min M IA Y max _ Plot Nr 2 Plot Nr 3 Plot N
59. in the GPS navigation message 1996 1998 2000 2002 2004 2006 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 28 B aC KU Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 1 Iono effects on single freq Positioning Annex gLAB processing in command line Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 29 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 1 gLAB processing in command line NEU positioning error SPP Full model North error East error UP error Execute in a single line gnuplot can also be used graph py f gLAB out x4 y18 s c 1 OUTPUT 1 North error f gLAB out x4 y19 s c 1 OUTPUT 1 East error f gLAB out x4 y20 s c 1 OUTPUT 1 UP error yn 20 yx 50 xl time s yl error m t NEU positioning error SPP Full model graph py f gLAB out x4 y20 s c 1 OUTPUT 1 Full model f gLAB1 out x4 y20 s c 1 OUTPUT 1 No Iono cl r yn 20 yx 50 xl Time s yl Up error m t Vertical positioning error SPP graph py f gLAB1 out x19 y18 so c 1 OUTPUT 1 No Iono cl r f gLAB out x19 y1
60. ith GNSS signal propagation effects in the atmosphere The laboratory exercises will be developed with actual GPS measurements and processed with the ESA UPC GNSS Lab Tool suite gLAB which is an interactive software package for GNSS data processing and analysis All software tools including gLAB and associated files for the laboratory session are included in the USB stick delivered to those who attend the lecture The laboratory session will consist of a set of exercises organized in three different levels of difficulty Basic Medium and Advanced A set of introductory examples range from a first glance assessment of the ionosphere effects on single frequency positioning and Zenith Tropospheric Delays estimate to showing different perturbation effects in the ionosphere Solar Flair Halloween storm TIDs Electron density profiles Ne retrieval bending effects analysis phase excess rate depicture are analysed in detail in two Laboratory Work Projects Finally the code carrier ionosphere divergence on single frequency smoothed codes is proposed as homework The target is to provide the participants with a wide range of selected exercises to choose from according their interests and their level of knowledge of these topics Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 4 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M
61. ither a guided or a self learning GNSS course 1 GNSS Book Complete book with theory practical examples and with a Laboratory course on GNSS Data Processing amp Analysis R 1 2 gLAB tool suite Source code and binary software files plus configuration files allowing processing GNSS data from standard formats The options are fully configurable through a GUI 3 gAGE GLUE Bootable USB stick with a full environment ready to use based on LINUX Ubuntu OS Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 11 Tutorial associated to j J Sanz Subirana J M uuaiT Zuii IUZQ IVI ICI IIa Iucz I ajai cS 1 Introduction 2 The gLAB tool suite gt Examples of GNSS processing using gLAB 4 Laboratory session organization LABORATORY Session e Starting up your laptop Basic Introductory lab exercises Iono amp Posit SF storm T IDs e Medium Laboratory Work Projects LWP1 LWP2 e Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 12 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Examples of GNSS Data Processing using gLAB Example 1 Ionospheric effects on single frequency positioning a This exercise is devoted to analysing the effect of the ionospheric error in single
62. ization LABORATORY Session e Starting up your laptop e Basic Introductory lab exercises rono amp Posit SF storm TIDs e Medium Laboratory Work Projects LWP1 LWP2 e Advanced Homework Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 46 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Laboratory session organization The laboratory session is organized as an assisted activity where a set of exercises must be developed individually or in groups of two As they are conceived as self learning work a detailed guide is provided in the slides pdf file to carry out the exercises A notepad file with the command line instructions is also provided to help the sentence writing doing copy amp paste A set of questions is presented and the answers are also included in the slides e Teachers will attend individual or collective questions that could arise during exercise resolution Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 47 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Laboratory session organization The exercises are organized at three different levels of difficulty The student can choose the level of exercises to do although at leas
63. l associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 2 Ionospheric delay analysis 3 Plot results with qraph py you can use the gnuplot as well gt From obs txt file PRN sec P2 P1 P2 L2 5 09 P1 L1 3 09 L1 L2 Elev 10 5 Show in the same plot the following ionopheric delays for satellite PRNO1 P2 P1 P2 L2 5 09 P1 L1 3 09 L1 L2 Elev 10 lonospheric Refraction code and carrier phase e P2 P1 P2 L2 5 09 P1 L1 3 09 L1 L2 Elev 10 Condition Fields to plot Select PRNO1 2 x axis from 1 st field versus 3 y axis File to plot meters of L1 L2 delay f aoe C een X2 bh 1 reg L1 3 09 f obs txt c 1 01 x2 y6 1 L1 L2 f obs txt c 1 01 x2 y7 l Elev 10 yn 10 yx 15 xl time s yl meters of L1 L2 delay 10000 20000 30000 40000 50000 60000 70000 80000 90000 time s Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 39 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares meters of L1 L2 delay 10 Example 2 Ionospheric delay analysis lonospheric Refraction code and carrier phase 15 P2 P1 P2 L2 5 09 P1 L1 3 09 f fj 154 120 10 L1 L2 Elev 10 E code and carrier phase FE L 201 ambiguity 5 CAE
64. n Zornoza M Hernandez Pajares Starting up your laptop 43 Applications Places System gt Tue Jun 21 8 48AM glab Esp F E QGLAB Version 2 0 0 gt ae http www gage es Prererences About Now the system 2 is ready to start File Edil View Terminal Help To run a command as administrator user root usc sudo lt command gt alc wd for details WO rki nN Q Console to execute T E command line isearch group of Astronomy amp GEomatics sentences University of Catalonia UPC gLAE Version 2 0 0 2 glabggage Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 54 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Starting up your laptop bloc Zndorder w WordPad File Edit View Insert Format Help 43 Applications Places EE Computer a 4 5 6 7 88 10 ll i 13 14 15 16 17 18 H MEAS YY Doy sec GAL PRN el z N list C1B L15 C1C Lic C a L7G CEQ Leg a glab s Home iij Flot results E gawk if 5 GAL es 6 16 print 4 11 1 432 15 11 1 1241 42 12 16 1 6 33 11 212 78 32 15 16 472 35 1 aste th e Terminal graph py gien327Pc2Lc2 dat x1 y3 1 PCZ LCZ 178 f gien327PcZLce2 dat x1 y2 1 PC LC 17 cl r yn sentences i Gener
65. n density which led to large ionospheric refraction values on the GPS signals Such conditions were beyond the capability of the GPS Klobuchar model broadcast for single frequency users producing large errors in the SPS see details in R 3 Dual frequency users navigating with ee ee aon mtm the ionospheric free combination of i i ey GPS signals were not affected by such ionospheric errors as the ionospheric refraction can be removed up to 99 9 using dual frequency signals Up error rn Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 57 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 1 Assessing Iono effects on single freq pos Exercise Repeat the previous study of Example 1 to analyze the single frequency solution but for the Halloween storm The following steps are recommended 1 Using files amc23020 030o brdc3030 03n compute with gLAB the following solutions a Solution with full SPS modeling Name output file as gLAB out b Solution with the ionospheric corrections disabled gLAB1 out C Solution with the 2 freq Ionosphere free code PC gt gLAB2 out 2 Plot results Note The gLAB GUI or the command line sentences can also be used A notepad with the command line sentence is provided to facilitate the sentence writing just copy and paste from notepad to
66. ns gLAB will be used to read the RINEX measurements file and to generate a text with the measurements D ESL ed in a columnar format more suitable to make plots Using such text file the STEC pattern for the different satellites in view during the storm is depicted from the geometry free combination of codes P2 P1 Note P P I K Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 76 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 4 Halloween storm P2 P1 analysis The next commands read a RINEX file and generate a text file in columnar format that allows to easily plot the measurements and their combinations 1 Using the configuration file meas cfg READ the RINEX and generate the MEAS message with me format Tid YY Doy sec GPS PRN el Az N list C1C L1C C1P L1P C2P L2P Execute 123 4 5 67 8 9 10 11 xx 13 14 15 16 gLAB linux input cfg meas cfg input obs amc23030 030 input nav brdc3030 03n gt amc23030 03 meas 2 From meas txt file Compute the ionospheric combination of codes PI P2 P1 Generate the file PI txt with the following content PRN hour PI elevation gawk print 6 4 3600 15 13 7 amc23030 03 meas gt PI txt 3 From PI txt file Plot the PI P2 P1 for time interval 15 to 24 hours Show in the same graph 1 ALL satellites 2 P
67. nts e The input data is p n L1 L2 n with pin km and L1 L2 in meters of L1 L2 delay where the impact parameter must be sorted from larger to lower value gt Only measurements with negative elevation must be given i e occultation The output data is n p n L1 L2 n Ne n where Ne is given in e m Tangent point Note the Impact parameters can be tgo elev lt 0 Gmpact parameter computed from the LEO elevation Va to GPS elev and its distance to Earth s i a Ho centre r zo by see figure o p p T zo cos elev o RN Geocenter Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 91 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP 1 Electron Density Profile from RO Exercise The file HO obs contains the following fields see Ex 5 YY DoY HH HH CODE PRN elev r_LEO AR LEO DEC LEO r GPS AR GPS DEC GPS L1 L2 L1 L2 arc cycles m deg km Deg Deg km Deg Deg 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 Using the file RO obs select the measurements with negative elevations for GPS satellite PRNO2 the LEO 4 and antenna 1 and generate the input file p n L1 L2 n for program abel perl Selecting CODE 1241 and PRN 2 and negative elevations ocult grep 1241 RO obs gawk if 5 02 amp amp 6 0 print 0 gt ro tmp
68. o Carrier phase ambiquities Measur Multipath Noise Model components Prefit pAiduals Postfit residuals Orbit and Clock comparison ui DER SS D cttm a 2 48 a p Global Graphic Parameters Title zenith Tropospheric Delay label time s Y label Itroposphere m Clear j 2 2 46 Automatic Limits X fi X max Y min Ymax The aborum iS estimated Individual Plot s Confgefiration Plot Nr 1 O Plot Nr 3 O Plot Nr 4 2 44 d D a Ra ndom Wa k FOCeSS in pev m LL Source File home jaume edunav LECTURES TUTORIAL2 TUT2 roap igs trp Examine Lines th e Ka m a n Fi Itei p A p ro cess T i a 2 12 AS oe EN tem V aL E MENS T TP Condition o d dx areen He se cm S rt h A a S X Column CHUTE Aa EXE ts 20 ee n take n A 0 10000 20000 30000 40000 50000 600000 70000 80000 90000 1 2 time s Plot ftp cddis gsfc nasa gov pub gps products troposphere new 2009 181 roap1810 09zpd gz The ZTD in this file is given in mm of delay Thus it is converted to m to compare with gLAB results grep ROAP roap1810 09zpd gawk F print 3 gawk print 1 2 1000 gt roap igs trp Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 44 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example
69. on Smoothing 4 Generate the ionosphere free combinations of code and carrier measurements to compute the lonosphere Free IFree smoothed code _p_VE F yh Lb TY Cee f L zh 5 r Free 60 y 1 y l gawk BEGIN g 77 60 2 pc g 13 15 g 1 lc g 14 16 g 1 print 4 pc 1c 3 5 upc3 meas gt upc3 PC a Apply the Hatch filter to compute the Free smoothed code gawk BEGIN g 77 60 2 pc g 13 15 g 1 1c g 14 16 g 1 if NR gt 10 n 100 else n NR XE ps 1 n pc n 1 n pstlc lcp lcp 1c Vi i print 4 ps 1c 3 5 upc3 meas gt upc3 PCs100 m ii Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares b Plot results and compare with the unsmoothed graph py f upc3 PC s 1 IFree raw cl yellow f upc3 PCs100 s cl black 1 Ifree 100s xn 35000 xx 40000 yn 5 yx 5 xl time s yl meters SS i Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 119 HW Iono Divergence on Smoothing 5 Repeat previous plots but using N 360 N 3600 and compare results Plot also the ionospheric delay from L1 L2 see more details in R 1 T 360s T 3600s PRNO3 C1 100s smoothing and divergence of ionosphere PRNO3 C1 360s smoothing and divergence of ionosphere PRNO3 C1 3600s smoothing and divergence of ionosphe
70. opagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 32 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 2 Ionospheric delay analysis Example 2 Depict the ionospheric delays for the different satellites in view from station amc2 e This is a simple exercise aimed to illustrate how to use gLAB to easily analyze GNSS measurements and their combinations gLAB will be used to read the RINEX measurements file and to generate a text with the measurements provided in a columnar format more suitable to make plots From text file compute and plot the Ionospheric delay for a given satellite by using code and carrier measurements at f1 f2 P L 2 amp I t ambiguityl P L 2G ambiguity2 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 33 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 2 Ionospheric delay analysis c The target is to generate this plot to depict the ionospheric delay from code amp carrier data ID P h F I Kk L L L I Ambiguity P L 2 1 ambiguity lonospheric combination meters 2 P L 2 amp I ambiguity2 I a 1 546 a 14 4 f217 l QO 10000 20
71. or m 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 4050 30 20 10 0 10 20 30 40 WC time s East error m Mexico Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 64 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Ex 2 STEC in a Radio Occultation RO Radio Occultation RO commonly refers to a sounding technique in which a radio signal from a transmitting satellite e g GPS passes through a planetary atmosphere before arriving at a receiver on board a Low Earth ET Orbiter LEO satellite rz Along the ray path the phase of the This is a simple exercise where the STEC radio signal is perturbed in a variation along a radio occultation will be manner related to the refractivity amp ePlcted using GPS L1 L2 measurements from a receiver on board a LEO of RO measurements can reveal the COSMIC constellation refractivity from which one can then derive atmospheric quantities such In the LWP1 Electron Density Profiles will as Pressure Temperature and the be retrieved from this data using an gt partial pressure of water vapor and 2 gorithm equivalent to the Abel Transform electron density among others Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 65 Tutorial associated to the GNSS Dat
72. ornoza M Hern ndez Pajares The gLAB Tool suite Filtering module Output module e Cartesian NEU coordinates e Able to chose different e Configurable message output measurements to process 1 or more with different weights This design could be useful in Other functionalities future Galileo ape sei where e Computation of satellite processing with different coordinates and clocks from RINEX measurements may be desired and SP3 files e Satellite coordinates comparison mode For instance RINEX navigation vs SP3 or SP3 vs SP3 e Fixed or elevation dependent weights per observation Troposphere estimation on off Coarse e Carrier Phase or Pseudo range e Show input mode No processing positioning only parsing RINEX observation e Static Kinematic positioning full files Q Phi PO customization e Current version allows full GPS data e Able to do a forward backward processing and partial handling of processing Galileo and GLONASS data e Able to compute trajectories no e Future updates may include full need for a priori position GNSS data processing Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 10 B aC KU Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares GNSS learning material package Includes three different parts allowing participants to follow e
73. ositioning error 2 freq lono free North error e East error 40 2 freq TL UP error lono free zn E 20 E L X p z o Or 5 10 B i o Z 5 i mS ail lea d ndi EROS vest edt banal altho an ico MI B gLAB2 0out 15F g OU 0 10000 20000 30000 40000 50000 60000 70000 80000 9000 20 15 10 Z5 0 5 10 20 15 East error m error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 27 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ionospheric delay The ionosphere extends from about 60 km over the Earth s surface until more than 2000 km with a sharp electron density maximum at around 350 km The ionospheric refraction depends among other things on the location local time and solar cycle 11 years Example 1 Iono effects on single freq Positioning First order 99 9 ionospheric delay 1 depends on the inverse of squared frequency l 40 3 STEC amp where STEC is the number of electrons per area unit a along ray path STEC Slant Total Electron Content STEC N ds i Two frequency receivers can remove this error source up to 99 996 using ionosphere free combination c fP fp of pseudo ranges PC or carriers LC fg Single frequency users can remove about a 50 70 of the ionospheric delay using the Klobuchar model whose parameters are broadcast
74. ospheric correction UNB 3 Nominal Simple Mapping Pl P2 correction RINEX Nav File Flexible O Wind up correction Carrier phase only P1 Cl correction Solid tides correction O Relativistic path range correction Save Config Show Config SPP Template PPP Template Run gLAB Show Output he different model terms can be analyzed with gLAB eUsing the previous data file the impact of neglecting the ionospheric correction is evaluated in the Range and Position domains e his is a baseline example of this analysis procedure The same scheme must be applied for all model terms troposphere relativistic correction A full analysis of the different model components can be found in R 2 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 18 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Example 1 Model component analysis Ionosphere The procedure Cesa gGLAB e SAGE URC explained here is n applicable for all model Modelli 3 Modelling Options Sst STN terms IONO tropo v Satellite clock offset correction V Consider satellite movement during signal flight t i Consider satellite movement during signal flight osse Spit On dS ignal flight time D f It Disable b gt J Satellite mass center to antenna phase center
75. ote the carrier noise is neglected against code noise PB L 2Il B e amp 2 Code carrier divergence Substituting P L in previous equation P k L k P L o PUK 1 k B Q1 B k p k 1 k 2 f 400 dd i hl aun Ml where U is the noise term after smoothing bias where being the ambiguity term 5 a constant bias thence B B and cancels in the previous expression Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 113 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares HW Iono Divergence on Smoothing Raw assessment of the induced bias on P smoothed code by ionosphere e Let assume a simple model where the STEC vary linearly with time f I t bias where T is the Hatch filter smoothing time constant i e 7 N in previous eq Exercise Proof the previous statement Solution Let be f t amp I t and y t i le The averaging in the Hatch filter can be implemented as vtr yO E peur STI t fit AT y y SO Thence L 1 t gt 1 h 0 th l e bias 2 1 10 221 t Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 114 Tutorial associated to the GNSS Data Processing book J Sanz Subi
76. ouble frequency GPS measurements under large ionospheric gradients Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 110 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares HW Iono Divergence on Smoothing The noisy code can be smoothed with the precise but ambiguous carrier measurements This carrier smoothing can be done in real time applying the Hatch filter The smoothing depends on the time smoothing constant or filter length The more the filter length is used the more smoothed the code is but with single frequency measurements a higher code carrier divergence error is induced by the ionosphere This is because the ionospheric refraction has opposite sign on code and carrier being its effect twice on the difference of code and carrier This double ionospheric refraction is propagated forward through the filter producing a bias The error induced by the code carrier divergence of the ionosphere on the single frequency smoothed codes is assessed in this exercise for different filter lengths Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 111 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares HW Iono Divergence on Smoothing The noisy code P can be
77. r 4 gLAB out A Examine Dotted Line v emm um J f Df fate lv E S E E E ME xcolumn sc Iv s e fe aber 0 10000 20000 30000 40000 E 60000 70000 80000 90000 Equivalent command line sentence graph py f gLAB out x4 y18 s c 1 OUTPUT 1 North error f gLAB out x4 y19 s c 1 OUTPUT 1 East error East U f gLAB out x4 y20 s c 1 OUTPUT 1 UP error D yn 20 yx 50 xl time s yl error m t NEU positioning error SPP Full model Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 17 Jodivichl plar s Configuratigg Source File Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 1 gLAB Modeling panel gLAB Version 2 0 0 ER q i gt d OAUDI P Preferences p sn Positioning Analysis Modelling Options Satellite clock offset correction Consider satellite movement during signal flight time Consider Earth rotation during signal flight time O Satellite mass center to antenna phase center correction options set in this panel are applied by default to the SPP solution Receiver antenna phase center correction O Receiver antenna reference point correction Relativistic clock correction orbit excentricity lonospheric correction Klobuchar Trop
78. rana J M Juan Zornoza M Hern ndez Pajares HW Iono Divergence on Smoothing Divergence Free smoothing DFree With 2 frequency measurements the ionosphere can be removed from a combination of two carriers 8 130 L Bta gt Azp gt DFree smoothed code is not affected by iono temporal gradients being the ionospheric delay the same as in the original code FE Ionosphere Free smoothing IFree Using both code and carrier 2 frequency measurements it is possible to remove the frequency dependent effects using the ionosphere free combination Le gt fo pPtV IFree smoothed code is not affected by either spatial or temporal gradients but is 3 times noisier than the DFree or the Single Freq smoothed code Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 115 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares HW Iono Divergence on Smoothing 1 Multipath and measurement noise assessment on raw code measurements The C1 code multipath and receiver noise can be depicted using the following combination that removes all frequency dependent and not dependent terms C L OE s ei PEREAT M CG L 20 L L a gA 1 545 y u 2 Id YY Doy sec GPS PRN el Az N list C1C L1C C1P L1P C2P L2P a Generate the meas file for PRNO3 123 4 5 67 89 10 11 12 1
79. re STEC PRNO3 shifted Gm Cl Raw 1 Raw zu ope C1 SF smoothed 100s 4 i r C1 SF smoothed 360 C1 SF smoothed 3600 t C1 DFree smoothed 100s C1 DFree smoothed 360 C1 DFree smoothed 3600 eo h eee T E nad E EE RE amm Arann mannan Note that the y range in bottom row plots is 3 times larger than in top plots meters 209 a 48000 Sum m 38000 39000 400 35000 T 37000 NE 39000 40000 ime s time s ime s Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 120 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares HW Iono Divergence on Smoothing Repeat the previous exercise using the RINEX file amc23030 030 1Hz collected for the station amc2 during the Halloween storm Take N 100 i e filter smoothing time constant 72100 sec PRN13 C1 100s smoothing and divergence of ionosphere 120 STEC PRN13 shifted 1 546 L1 L2 Cl Raw C1 SF smoothed l00L TORTE SEE Renee re pi DO H UE Uu E WIUITIHVMWIWWEMIPUEEP EUCH a0 rc cS ee mec eH eaten vps ce genet ses coe rp sms gt en cess vse eb ccs see btn ete sense alec ean ca heen age np events tee a as ep ace orange seca ta Cor M onm 8 Baa
80. rection Carrier phase only Solid tides correction Relativistic path range correction Save Config Show Config SPP Template PPP Template RungLAB Show Output Equivalent command line sentence gLAB linux input cfg gLAB p1 IFree cfg input obs amc3030 030 input nav brdc3030 03n Positioning Analysis Parameters Save Config Show Config AC Madrid Spain 15 gLAB Version 2 0 0 gLAB Preferences About Measurements Troposhere Selection C Estimate Troposphere Pseudorange Pseudorange Smoothing epochs O Pseudorange Carrier phase Available Frequencies Measurement configuration and noise IPC Fixed StdDev m 1 amp Dual Frequency Elevation StdDev m Receiver Kinematics Static Kinematic gLAB Version 2 0 0 Coordinates Cesa Receiver Clock Preferences About Positioning Analysis a Output D Output FEM gaBajout Message Print INFO Messages Examine Bj Print Cs Cycle Slip Messages C h ad n g e O u t p u t I Print INPUT Messages file name to gLAB2 out C Print MEAS Message Print MODEL Messages Print EPOCHSAT Messages Print PREFIT Messages Print POSTFIT Messages Print FILTER Messages Print OUTPUT Messages Save Config Show Config SPP Template PPP Template Run gLAB Silv Output
81. s channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 89 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP 1 Electron Density Profile from RO from GPS to LEO Thence starting from the outer ray P lico for a given ray i where 1 with impact 7h parameter p its STEC can be CA vL written in a discrete SO CA representation as 4 X4 ARN Wz j i l j i STEC p 2 N p l zs N p lj i where p stands for the impact parameter the closest where is the fraction of ith ray within point to the Earth centre along the optical ray path Il PA SPRETEN REEC TUE QI EG As measurements we use L1 L2 carrier phases that are related with the STEC by The previous equation defines a triangular linear equations system L L STEC b that can be solved recursively for the electron density Ne p differences to a reference in the arch data where the bias term b is eliminated making Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 90 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP 1 Electron Density Profile from RO The program abel perl implements the previous algorithm to estimate the Ne p profile from GPS L1 L2 carrier measureme
82. s after the last cycle slip Z Print INPUT Messages ee ra I 0 RR Field 8 C1 C1C 6 glab gag _ Print MEAS Message i d e Field 9 P1 C19 E rcnt ME In console mode execute SEN B File Edit View Termir Print MODEL Messages Field 10 P2 C2P i To run a command as administrator user root use sudo command Print EPOCHSAT Messages Field 11 L1 L1P prealigned in meters T caus See sinless E E Field 12 L2 L2P prealigned in meters l ae L Print PREFIT Messages e For Galileo GAL J Pri Field 8 C1A glab gage Jj _ Print POSTFIT Messages e Field 9 C1B e Field 10 C1C Print OUTPUT Messages Field 11 C7Q Field 12 C8Q Print FILTER Messages gLAB linux messages Field 13 L1A prealigned in meters Field 14 L1B prealigned in meters Save Config Field 15 L1C prealigned in meters Run gLAB Show Output Field 16 L7Q prealigned in meters Field 17 L8Q prealigned in meters For GLONASS GLO e Field 8 C1 C1C e Field 9 C2 C2C Field 10 L1 L1P prealigned in meters Field 11 L2 L2P prealigned in meters For GEO Propagation efi Fiala NU CI CIC ies on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 31 Sample INPUT 2006 200 0 00 GPS 19 1 23119003 9020 23119002 6110 23119004 0750 23119002 7507 23119004 0925 5 ac KU Tutori
83. s and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 100 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares p km 6800 LWP2 Atmospheric Bending in RO P1 Plot the impact parameter p as a function of DDdL1 DDdRho and DDdL2 DDdRho Discuss the results found graph py f bending dat x 12 11 y4 1 DDdL1 DDdRho f bending dat x 13 11 y4 1 DDdL2 DDdRho xn 0 4 xx 4 COSMIC 4 Antenna 1 PRNO2 Q1 Justify the discrepancy between the two plots 6700 L M T EPEETAN E Sewer 1 3 3 e The curves in the plot show 6600 L ES nm PME MEE S MEME CR pee MEE TESTER D hase excess rate due the effect of both ionosphere and 6500 6400 6300 QM eras ener a nen TEM MM troposphere 3 e As the bending in the ionosphere is a frequency dependent effect the contribution is different for each signal L1 and L2 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 101 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO P2 Plot the impact parameter p as a function of DDdLc DDdRho Discuss the results found graph py f bending dat x 14 11 y4 xn 0 1 xx 0 3 xl
84. se orbits amp clocks Select the PPP Template Upload data files Measurement Positioning Analysis novos Input Files roap1810 090 ANTEX igs05 1525 atx A priori receiver position m qmd SERE 08 clocks PE ad Clock SOUCCES i EX 1gs15382 Ssp3 Broadcast Precise 1 file Precise 2 files xm spa Hie 1 SINEX igs09P1538 snx 3 RUN gLAB 1 Ionosphere Source if activated SINEX File C Show home gLAB igs09P1538 snx Auxiliary Files P1 Cl Correction CO Show P1 P2 Correction O Show SPP Templat PPP Template Default output file gLAB out Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 42 Save Config Show Config Run gLAB how Output Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Example 3 Zenith Troposphere Delay estimation NEU positioning error Static PPP Plotting Results e Coordinates are taken as E 31 1721 3 ee Et constants in nav filter vol ds e Dual frequency Code and Carrier measurements NEUES uM MN NUN MEN MU MU UE B e Precise orbits and clocks 5 O00 i aa AE aera TES e Measurements modelling e eee at the centimetre Cen C Gentimetrelevelaccur
85. ss Rate Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 97 Bending is assumed only for the GPS LEO ray in occultation Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO Another possibility to remove the clock term could be to subtract the LC combination from L1 or L2 The result will provide the discrepancy between L1 or L2 and LC excess ray path That is Ap un AL j Acdlt Ux a OI Ax Ap AL At At At P occult u Ju Ab AL j Api AL Acdt At At At Ato 0 At At At Notice that the Euclidian range rate is not needed to subtract as in the previous case because it is cancelled when taking the difference between L1 or L2 and Lc Other delays can also be cancelled In the following exercises we will plot the previous combinations and discuss the different contribution of the ionosphere and troposphere to the phase excess rate Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 98 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO Exercise The program RO per1 uses the RO obs as input data and computes the following
86. t PRNe3 C1 100s smoothing and iono div Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 117 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares HW Iono Divergence on Smoothing 3 Remove the ionospheric refraction of C1 code and L1 carrier measurements using the following expressions to compute the Divergence Free smoothed code Core O AL L 2 i 1DFree L p ve l 24 545 rs L prre L OL L E i c y 1 60 a Apply the Hatch filter to compute the DFree smoothed code gawk BEGIN Ts 100 if NR gt Ts n Ts else n NR C1f 11 1 55 14 16 L1f 1441 55 14 16 C1fs C1f n n 1 n C1fs Lif Lip L1p L1f PRNO3 C1 1005 smoothing and divergence of ionosphere print 4 C1fs L1f 21 3 upc3 meas gt upc3 C1DFs100 C1DFree smoothed 100s b Plot results and compare with the raw C1 code graph py f upc3 C1 s 1 C1 Raw f upc3 C1s100 s cl r 1 C1 SF smoothed 100s f upc3 C1DFs100 s cl g 1 C1 DFree smooth 100s xn 35000 xx 40000 yn 5 yx 5 xl time s yl meters Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 118 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares HW Iono Divergence
87. t one introductory exercise is recommended to learn basic gLAB usage 1 Basic Introductory exercises They consist of simple exercises to 1 Study the Ionosphere effects on single frequency positioning 2 To depict the STEC on a Radio occultation 3 Solar Flare effect on TEC 4 5 TEC evolution during the Halloween Storm 6 To depict a TID propagaction IONO Halloween Storm 2003 10 30 amc2 PRN28 ELEV e e PRN28 P2 P1 PRN29 ELEV e e PRN29 P2 P1 PRN13 ELEV e e PRN13 P2 P1 n Ab EK 000 65000 70000 75000 80000 85000 90000 950 PRMRPAITETEERP time s Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 48 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hernandez Pajares Laboratory session organization 2 Medium Laboratory Work Projects LWP Two different LWP are proposed to choose from LWP1 To show a simple numerical method to estimate electron density profiles Ne h from RO data e LWP2 To analyse the phase excess rate from GPS to Actual measurements LEO due to atmospheric iono amp tropo bending OPA OSA SooS io COSMIC 4 Antenna 1 PRNO2 DDdL1 DDdRho DDdL2 DDdRho A minimum knowledge of UNIX e g awk would be desirable Propagation effects channel models and related error sources on GNSS
88. th America e The STEC variations are depicted from the geometry free combination of codes P2 P1 Note E ITK Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 79 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 5 Halloween storm evolution Id YY Doy sec GPS PRN el Az N list C1C L1C C1P L1P C2P L2P 1 Read RINEX file 1 2 3 5 6 7 8 9 10 11 xx 13 14 415 16 gLAB linux input cfg meas cfg input obs gar13010 030 input nav brdc3010 03n gt garl13010 03 meas gLAB linux input cfg meas cfg input obs gar13020 030 input nav brdc3020 03n gt gar13020 03 meas gLAB linux input cfg meas cfg input obs gar13030 030 input nav brdc3030 03n gt gar13030 03 meas gLAB linux input cfg meas cfg input obs gar13040 030 input nav brdc3040 03n gt garl13040 03 meas gLAB linux input cfg meas cfg input obs gar13050 030 input nav brdc3050 03n gt garl13050 03 meas gLAB linux input cfg meas cfg input obs gar13060 030 input nav brdc3060 03n gt garl13060 03 meas 2 Merge files and refer all the data to Oh of October 28th Doy0301 cat gar130 0 03 meas gawk d 3 301 86400 4 4 d print 6 4 3600 11 13 7 gt PI txt 3 m Plot res u Its IONO Halloween Storm 28Oct 02Nov garl Lat 40 Lon 119 graph py f PI txt x2 y3 1 ALL P2 P1 3 3 3 3 ALL P2 P1 f PI txt c 1
89. to account the relationship between the electron density Ne and the critical frequency f i e minimum frequency for a signal not being reflected R 1 f 8 98 N N ine m f in Hz p M e Compute the minimum frequency of a signal to cross through the ionosphere Answer From previous plot the N of the maximum is 3 7E 11 e m Thence DUE f 2898 3710 5 46MHz 2 Calculate the height where a signal with frequency f 4 MHz will be reflected according to the previous plot of N profile Answer N f 898 4 10 8 98 21 98 10 150 km Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 94 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares LWP2 Atmospheric Bending in RO LWP 2 Target This LWP is focused in depicting and analysing the effect of the atmospheric bending in Radio Occultation measurements A simple procedure will be given to depict the phase excess rate due to the troposphere and ionosphere over L1 L2 and LC measurements Note LC is the Ionosphere Free combination of 271 279 carriers L1 and L2 is given by tout h 2 2 K Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 95 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern nd
90. ver antenna reter ce point correction Relativistic clack correct on orbit excentriciry O Discard satellites under eclipse condition Print PREFIT Messages gi Discard unhealthy satellites Rroadcast onl Print POSTFIT Messages Cycle slip Detection O Geometric free CP Combination F1 F2 onfigure C Print FILTER Messages D IS ab e Print OUTPUT Messages model satphasecenter Save Config Show Config SPP Template PPP Template 3 Output nodel recphasecenter model satclocks C Mclboume Wibbena F1 F2 onfigure _ L1 C1 difference F1 onfigure DLAB Show Output Save config E Run gLAB Show Output Disable cycle slip detectors pre cs li pre cs bw dels and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 37 B aC KU Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Example 2 Ionospheric delay analysis 2 Manipulate the file with the easy and powerful awk or gawk programming language to compute the combinations of measurements P1 L1 P2 12 gt From coco meas file Id YY Doy sec GPS PRN el Az N list C1C L1C C1P L1P C2P L2P 10 11 xx xx 14 15 16 Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 38 Tutoria
91. warning messages Templates for pre configured processing 2 Professionals Experts a Powerful tool with High Accuracy Positioning capability b Fast to configure and use Templates and carefully chosen defaults c Can be executed in command line and included in batch processing 11111 SAJAAJAJAALO P l File Edit View Terminal Help q4 workspace edunav gt gLAB linux input obs test madr2000 060 input sp3 test igs13843 sp 3 input ant test igs05 atx Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 7 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares The gLAB Tool suite 1 In order to widen the tool availability gLAB Software has been designed to work in both Windows and Linux environments a Aw 2 The package contains e Windows binaries with an installable file Linux tgz file e Source code to compile it in both Linux and Windows OS under an Apache 2 0 license Example data files e Software User Manual HTML files describing the standard formats Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 8 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares The gLAB Tool suite Read files capability Modelling
92. wk c gawk gawk gawk Reading RINEX files Selecting satellite PRN14 if 6 14 print 0 mhcb meas gt mhcb 14 meas if 6 14 print 0 monb meas gt monb 14 meas if 6 14 print 0 sodb meas gt sodb 14 meas Detrending on the geometry free combination L1 L2 for 1 0 1 lt 21 i t i t it 1 51 i 1 i 1 t 21 4 1 21 14 16 if NR gt 21 tt t 0 t 10 t 20 if tt 0 print t 10 1 10 1 0 1 20 2 mhcb 14 meas gt mhcb dLi meas for 1 0 1 lt 21 i t i t i s1 1 i 1 is1 t 21 2 4 1 21 2 14 16 if NR 21 tt t o t 10 t 20 if tt z0 print t 10 1 10 1 0 1 20 2 monb 14 meas gt monb dLi meas for 1 0 1 lt 21 i t i t is1 1 i 1 i41 t 21 2 4 1 21 2 14 16 if NR 21 tt t 0 t 10 t 20 if tt 0 print t 10 1 10 1 0 1 20 2 sodb 14 meas gt sodb dLi meas Propagation effects channel models and related error sources on GNSS ESAC Madrid Spain 15 17 Oct 2012 Slide 85 Tutorial associated to the GNSS Data Processing book J Sanz Subirana J M Juan Zornoza M Hern ndez Pajares Ex 6 Travelling Ionospheric Disturb Plotting results Execute in a single line graph py f sodb dLi meas s 1 sodb PRN14 f mhcb dLi meas s 1 mhcb PRN14 f monb dLi meas s 1 monb PRN14 xn 55500 xx 57000 yn 0 05 yx 0 07 xl time s yl Detrended STEC meters of L1 L2 delay t MS Travelling Ionospheri

Analysis of propagation effects from GNSS - gAGE

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