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IonospherIc correctIon AlgorIthm for gAlIleo sIngle frequency users

̄NAVIGATION

SOLUTIONS

POWERED BY

EUROPE

Document subJect to terms of use AnD DIsclAImers pAge.i european commission, 2016

European GNSS (Galileo) Open Service

- Ionospheric Correction

Algorithm for Galileo Single Frequency Users

i

Ionospher

I c c orrect I on Algor I thm for gA l I leo sI ngle f requency u sers , Issue 1.2, september 2016 terms of use AnD DIsclAImers T his document describes the ionospheric model developed for the G alileo satellite navigation system, which can be used to determine G alileo single-frequency ionospheric corrections. Its content has been prepared and scrutinised by various groups of specialised scientists. T he model has been characterised and thoroughly tested and gives encouraging performance improvements compared to other currently used solutions. T he physical behaviour of the ionosphere is however such that one cannot produce an algorithm that will systematically deliver fully satisfactory compensation of ionospheric error under all conditions. T he European Commission, ESA, the author(s) or contributor(s) therefore do not assume any responsibility whatsoever for its use, and do not make any guarantee, expressed or implied, about the quality, reliability, suitability for any particular use or any other characteristic of the algorithm. U nder no circumstances shall the European Commission, European Union, ESA, the author(s) or contributor(s) be liable for damages resulting directly or indirectly from the use, misuse or inability to use the algorithm.

AcKnoWleDgements

T he NeQuick electron density model was developed by the Abdus S alam International C enter of T heoretical P hysics (I CTP ) and the U niversity of G raz. T he adaptation of NeQuick for the Galileo single-frequency ionospheric correction algorithm (

NeQuick

G ) has been performed by the E uropean S pace Agency ( ES

A) involving the original

authors and other E uropean ionospheric scientists under various ES

A contracts. The step-by-step algorithmic

description of

NeQuick

for G alileo contained in this and the E uropean C ommission, including JRC ii

Document chAnge recorD

REASON FOR CHANGEISSUEREVISIONDATE

First Issue10November 2014

ȓ11June 2015

Inclusion of errata12September 2016

iii

Ionospher

I c c orrect I on Algor I thm for gA l I leo sI ngle f requency u sers , Issue 1.2, september 2016 tAble of contents

SECTION 1:

INTRODUCTION ........................................................................ .......................................1

1.1 DOCUMENT SCOPE ........................................................................

..............1

1.2 BACKGROUND........................................................................

..........................1

SECTION 2:

SINGLE FREQUENCY IONOSPHERIC CORRECTION

2.1 OVERVIEW ........................................................................ ..................................5 ɌɌ .................................................................5

2.3 INPUTS AND OUTPUTS ........................................................................

...6

2.3.1 GALILEO NAVIGATION MESSAGE RELEVANT TO

Ɍ ......................6

2.4 MODIP REGIONS ........................................................................

.....................6

2.5 NEQUICK G IONOSPHERIC ELECTRON DENSITY

MODE ........................................................................

2.5.1 THE EPSTEIN FUNCTION ........................................................................

.........7

2.5.2 CONSTANTS USED ........................................................................

.......................8

2.5.3 COMPLEMENTARY FILES ........................................................................

.........8

2.5.3.1.

MODIP GRID ........................................................................

2.5.3.2.

CCIR FILES ........................................................................

2.5.4 AUXILIARY PARAMETERS........................................................................

........8

2.5.4.1.

LOCAL TIME ........................................................................

2.5.4.2.

READ MODIPNEQG_WRAPPED.ASC VALUES IN

AN ARRAY........................................................................

2.5.4.3.

COMPUTE MODIP ........................................................................ .........................9

2.5.4.4.

EFFECTIVE IONISATION LEVEL AZ .................................................10 12

ɇ ............................10

2.5.4.6. SOLAR DECLINATION ........................................................................

............10

2.5.4.7.

SOLAR ZENITH ANGLE ........................................................................ .........10

2.5.4.8.

EFFECTIVE SOLAR ZENITH ANGLE .................................................11

2.5.5 MODEL PARAMETERS ........................................................................

.............11

2.5.5.1.

foE AND NmE ........................................................................ ..................................11

2.5.5.2. foF1 AND NmF1 ........................................................................

............................12

2.5.5.3.

foF2 AND NmɆɇ ...............................................................12

2.5.5.4. hME ........................................................................

2.5.5.5. hMF1 ........................................................................

2.5.5.6. hMF2 ........................................................................

2.5.5.7.

B2BOT, B1TOP, B1BOT, BETOP, BEBOT ......................................16

2.5.5.8. A1 ........................................................................

2.5.5.9. A2 AND A3 ........................................................................

2.5.5.10.

SHAPE PARAMETER k ........................................................................ ..............................17

2.5.5.11.

H 0 ..........18

2.5.6 ELECTRON DENSITY COMPUTATION ..................................................18

2.5.6.1.

THE BOTTOMSIDE ELECTRON DENSITY ..................................18

2.5.6.2.

THE TOPSIDE ELECTRON DENSITY ...............................................19

2.5.7 AUXILIARY ROUTINES ........................................................................

............20

2.5.7.1. THIRD ORDER INTERPOLATION FUNCTION

Z X 1 , Z 2 , Z 3 , Z 4 .....................20

2.5.8 TEC CALCULATION ........................................................................

....................21

2.5.8.1.

VERTICAL TEC CALCULATION ..............................................................21

2.5.8.2. SLANT TEC CALCULATION ......................................................................22

2.5.8.3. ALTERNATIVE COMPUTATIONAL EFFICIENT TEC

INT EGRATION METHOD ........................................................................ ......28

2.5.9 CLARIFICATION ON COORDINATES USED IN NeQuick ...............28

2.6 DIFFERENCES BETWEEN NeQuick G AND

NeQuick 1 AND NeQuick 2 ...................................................................28

2.6.1 SUMMARY OF DIFFERENCES wITH NeQuick 1 .............................29

2.6.2 SUMMARY OF DIFFERENCES WITH NeQuick 2 ............................29

SECTION 3:

IMPLEMENTATION GUIDELINES FOR USER RECEIVERS ...............30 EFFECTIVE IONISATION LEVEL ........................................................31

3.2 APPLICABILITY AND COHERENCE OF

BROADCAST COEFFICIENTS ..............................................................31

3.3 EFFECTIVE IONISATION LEVEL BOUNDARIES .....................31

3.4 INTEGRATION OF NEQUICK G INTO HIGHER

LEVEL SOFTWARE ........................................................................ .............32

3.5 COMPUTATION RATE OF IONOSPHERIC

CO RRECTIONS ........................................................................ ......................32 iv

AnneX A:

ApplIcAble AnD reference Documents .......................................34 A.1. ApplIcAble Documents .................................................................35 A.2. reference Documents ...................................................................35

AnneX b:

Acronyms AnD DefInItIons ........................................................................ .36 b.1. Acronyms ........................................................................ ..............................37 b.2. DefInItIons ........................................................................ ..........................37

AnneX c:

Ɋɋ ........................................40

AnneX D:

nequIcK g performAnce results .........................................................42

AnneX e:

Input/output VerIfIcAtIon DAtA ...........................................................48 e.1. AzɊɋ ............................49 e.2.

AzɊɋ ...................50

e.3.

AzɊɋ ............................51

AnneX f:

nequick g DetAIleD processIng moDel ............................................52 f.1. eXternAl InterfAces ........................................................................ 53
f.1.1 IntroDuctIon ........................................................................ ...........................53 F.1.1.1. INPUTS ........................................................................ F.1.1.2. OUTPUTS ........................................................................ F.1.1.3. INPUT/OUTPUT ........................................................................ ...........................53 f.2. moDules ........................................................................ ................................54 f.2.1 IntroDuctIon ........................................................................ ...........................54 f.2.2 functIon oVerVIeW ........................................................................ ...........54 f.2.3 nequick.c moDule ........................................................................ ...................55 F.2.3.1. FUNCTION "NeQuickɆɇ................................55

F.2.3.2. NeQuick INTERNAL FUNCTION

"NEQCHECKINPUTS" ........................................................................ ..............56

F.2.3.3. NeQuick INTERNAL FUNCTION

"DOTECINTEGRATION" ........................................................................ .........56 f.2.4 neqcAlcmoDIpAz.c moDule ................................................................58

F.2.4.1. NeQuick INTERNAL FUNCTION

"NEQCALCMODIP" ........................................................................ ....................58F.2.4.2. NeQuick INTERNAL FUNCTION "NEQINTERPOLATE" ........................................................................ ................59 F .2.4.3. NeQuick INTERNAL FUNCTION "NEQMODIPTOAz" ........................................................................ .....................60 f.2.5 neqgetrAypropertIes.c moDule .................................................61

F.2.5.1. NeQuick INTERNAL FUNCTION

"NEQGETRAYPROPERTIES" .....................................................................61

F.2.5.2. NeQuick INTERNAL FUNCTION

F.2.5.3. NeQuick INTERNAL FUNCTION

"NEQCALCRAYPROPERTIES2" ..............................................................63 f.2.6 neqIntegrAte.c moDule ........................................................................ 64
F.2.6.1. NeQuick INTERNAL FUNCTION "NEQINTEGRATE" .......64 f.2.7 neqgetneonVertrAy.c moDule .....................................................66

F.2.7.1. NeQuick INTERNAL FUNCTION

"NEQGETNEONVERTICALRAY" ............................................................66 f.2.8 neqgetneonslAntrAy.c moDule .................................................67

F.2.8.1. NeQuick INTERNAL FUNCTION

"NEQGETNEONSLANTRAY" ....................................................................67

F.2.8.2. NeQuick INTERNAL FUNCTION

"NEQCALCLLHONRAY" ........................................................................ ........68 f.2.9 neqcAlcepstpArAms.c moDule .....................................................69

F.2.9.1. NeQuick INTERNAL FUNCTION

"NEQCALCEPSTPARAMS" ........................................................................ ..69

F.2.9.2. NeQuick INTERNAL FUNCTION

"NEQCALCSPHLEGCOEFFS" ...................................................................72 F .2.9.3. NeQuick INTERNAL FUNCTION "NE QGETF2FREQFROMCCIR" ...............................................................73 F .2.9.4. NeQuick INTERNAL FUNCTION "NE QCRITICALFREQTONE" ......................................................................74

F.2.9.5. NeQuick INTERNAL FUNCTION

"NEQCALCF2PEAKHEIGHT" ....................................................................75 F.2.9.6. NeQuick INTERNAL FUNCTION "NEQEPSTEIN"................76 f.2.10 neqcAlctopsIDe.c moDule .................................................................76

F.2.10.1. NeQuick INTERNAL FUNCTION

"NEQCALCTOPSIDENE" ........................................................................ .......76 f.2.11 neqcAlcbottomsIDene.c moDule ..............................................77

F.2.11.1. NeQuick INTERNAL FUNCTION

"NEQCALCBOTTOMSIDENE" ..................................................................77 f.2.12 nequtIls.c moDule ........................................................................ .............79 F.2.12.1. NeQuick INTERNAL FUNCTION "NEQJOIN" ..........................79 F.2.12.2. NeQuick INTERNAL FUNCTION "NEQCLIPEXP" ................79 F.2.12.3. NeQuick INTERNAL FUNCTION "NEQSQUARED" ...........80 f.3. nequick functIon DAtA structures .................................80 v

Ionospher

I c c orrect I on Algor I thm for gA l I leo sI ngle f requency u sers , Issue 1.2, september 2016 lIst of fIgures OBTAINED WITH NEQUICK ............................................3

FIGURE 2. MODIP REGIONS ASSOCIATED TO

DIFFERENT IONOSPHERIC

CH A RACTERISTICS ...............................................................7

FIGURE 3. GEOMETRY OF ZENITH ANGLE

COMPUTATION .....................................................................23

FIGURE 4. GEOMETRY OF RAY PERIGEE

COMPUTATION .....................................................................24 .............43

FIGURE 6. PERFORMANCE OF THE GALILEO

SI NGLE

FREQUENCY IONOSPHERIC

CORRECTION ........................................................................ .44

FIGURE 7. GLOBAL DAILY RMS IONOSPHERIC

L 1

CORRECTION WITH GALILEO NEQUICK G

AND GPS ICA FROM APRIL 2013 TO

MARCH 2014. ........................................................................ .45 OF

GALILEO NEQUICK G AND GPS ICA

CORRECTION MODELS FOR DAY 127,

2013 AND DAY 80, 2014 ............................................46

ERROR CONTRIBUTION TO UERE AFTER

L 1

̇ ..........................47

NEQUICK FUNCTION

HI ERARCHY ........................................................................ ......54 lIst of tAbles TABLE 1. INPUT PARAMETERS ..........................................................6 TABLE 2. DEFINITION OF CONSTANTS .......................................8 TABLE 3. NEQUICK FUNCTION INPUT DATA ........................53 TABLE 4. NEQUICK FUNCTION OUTPUT DATA ...................53 TABLE 5. NEQUICK FUNCTION OUTPUT DATA ...................53

TABLE 6. NEQCHECKINPUTS FUNCTION INPUT

DATA ........................................................................ ......................56

TABLE 7. DOTECINTEGRATION FUNCTION INPUT

DATA ........................................................................ ......................57 TABLE 8. NEQUICK FUNCTION OUTPUT DATA ...................57

TABLE 9. NEQCALCMODIP FUNCTION INPUT

DATA ........................................................................ ......................58

TABLE 10. NEQINTERPOLATE FUNCTION INPUT

DATA ........................................................................ ......................59

TABLE 11. NEQCALCMODIP FUNCTION INPUT

DATA ........................................................................ ......................60

TABLE 12. NEQGETRAYPROPERTIES FUNCTION

INPUT/OUTPUT DATA ......................................................61

TABLE 13. NEQGETRAYPROPERTIES FUNCTION

OUTPUT DATA .......................................................................61

TABLE 14. NEQCALCRAYPROPERTIES1 FUNCTION

INPUT/OUTPUT DATA ......................................................62

TABLE 15. NEQCALCRAYPROPERTIES1 FUNCTION

OUTPUT DATA .......................................................................62

TABLE 16. NEQCALCRAYPROPERTIES2 FUNCTION

INPUT DATA ........................................................................ .....63

TABLE 17. NEQCALCRAYPROPERTIES2 FUNCTION

INPUT/OUTPUT DATA ......................................................63

TABLE 18. NEQCALCRAYPROPERTIES2 FUNCTION

OUTPUT DATA .......................................................................63

TABLE 19. NEQINTEGRATE FUNCTION INPUT

DATA ........................................................................ ......................64

TABLE 20. NEQINTEGRATE FUNCTION OUTPUT

DATA ........................................................................ ......................64

TABLE 21. NEQINTEGRATE FUNCTION INPUT/

OUTPUT DATA .......................................................................65 INPUT DATA ........................................................................ .....66 INPUT/OUTPUT DATA ......................................................67

TABLE 24. NEQGETNEONSLANTRAY FUNCTION

INPUT DATA ........................................................................ .....67

TABLE 25. NEQGETNEONSLANTRAY FUNCTION

OUTPUT DATA .......................................................................67 vi tAble 26. neqgetneonslAntrAy functIon Input/output DAtA ......................................................67 tAble 27. neqcAlcllhonrAy functIon Input DAtA ........................................................................ ......................68 tAble 28. neqcAlcllhonrAy functIon output DAtA .......................................................................68 tAble 29. neqcAlcepstpArAms functIonquotesdbs_dbs9.pdfusesText_15