master: lecture 6 - upc universitat politècnica de...

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Master of Science in GNSS @ J. Sanz & J.M. Juan

1

Lecture 6

Differential positioning with

Code pseudoranges

Contact: [email protected]

Web site: http://www.gage.upc.edu

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Authorship statement

The authorship of this material and the Intellectual Property Rights are owned by J. Sanz Subirana and J.M. Juan Zornoza.

These slides can be obtained either from the server http://www.gage.upc.edu, or [email protected]. 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.

5 March 2017

http://www.gage.upc.edu/

mailto:[email protected]

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Contents

3

1. Linear model for DGNSS: Single Differences

1.1. Linear model

1.2. Geographic decorrelation of ephemeris errors

1.3. Error mitigation and `short´ baseline concept

1.4. Differential code based positioning

2. Augmentation Systems

2.1. Introduction

2.2. Ground-Based Augmentation system (GBAS)

2.3. Satellite based Augmentation system (SBAS)

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Error mitigation: DGNSS residual error

Error

Short-baselinesLong-baselines

Errors are similar for users separated tens, even hundred of kilometres, and these errors vary ‘slowly’ with time. That is, the errors are correlated on space and time.

The spatial decorrelation depends on the error component (e.g. Clocks not decorrelate, ionosphere ~100km...). Thence, long baselines need a reference stations network.

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P

j j j j j j j j

i i i i i i i iP c t t T I K K M

L

j j j j j j j j j j

i i i i i i i i i iL c t t T I N b b m

Code and carrier measurements

When approximate values of both receiver and satellite APC positions are taken, a linearization around them yields:

0 0 0ˆ ˆ j j j j j

i i i i iρ r ρ r

ir : Receiver coordinates error

jr : Satellite coordinates error

To Earth Centre

ir

jr

j

i0

j

i

0ir

ir

ˆ j

iρ0ρ

j

i

0 j j jr r r

0 i i ir r r

Satellite coordinates deviation

User coordinates deviation

00

0

ˆ

jj oii j

oi

r rρ

r r

Linear model for Differential Positioning

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To Earth Centre

Reference Station

Baseline

ˆ j

uρ ˆ j

rρ

ru u rr r r

rur

ur rr

User receiver

6

Single difference


P

j j j j j

ru ru ru ru ru ru ruP c t T I K

L

j j j j j j j

ru ru ru ru ru ru ru ru ruL c t T I N b

jr( ) ( ) ( ) ( ) j j j j

ru ru u r


P

j j j j j j j

u u u u u u uP c t t T I K K

P

j j j j j j j

r r r r r r rP c t t T I K K

The same for the carrier :

P

j j j j j j j j


L

j j j j j j j j j j


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To Earth Centre

Reference Station

Baseline

ˆ j

uρ ˆ j

rρ

ru u rr r r

rur

ur rr

User receiver

7

Single difference


P

j j j j j


L

j j j j j j j


Single difference cancels:• Satellite clock • Satellite code instrumental delays • Satellite carrier instrumental delays

Single differences mitigate/remove errors due• Satellite Ephemeris• Ionosphere• Troposphere• Wind-upThe residual errors will depend upon the baseline length.

( ) jt( )jK

( )jb

jr

( ) jr

( )j

iI( )j

iT

( ) ( ) ( ) ( ) j j j j

ru ru u r


( )j

i

P

j j j j j j j j


L

j j j j j j j j j j


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1 1( ) sat sat

ru ruL L

PRN06

PRN30

PRN06

PRN30

PLAN-GARR: 15km

1( )L

j j j j j j j

ru ru ru ru ru ru ru ru ruL L c t T I N b

1 1( ) sat sat

ru ruP P

1( )P

j j j j j

ru ru ru ru ru ru ruP P c t T I K

Dif. Tropo. and Iono. :Small variations

Dif. Instrumental delays and carrier ambiguities:constant

Dif. Wind-up: Very small

Dif. Receiver clock:Main variations Common for all satellites

Single-Difference of measurements

(corrected by geometric range!!)

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PRN06

PRN30

PRN06

PRN30

PRN06

PRN30

PLAN-GARR: 15km

IND1-IND2: 7m

PRN06

PRN30

IND1-IND2: 7m

1 1( ) sat sat

ru ruL L 1 1( ) sat sat

ru ruP P

1 1( ) sat sat


ru ruP P



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Dif. Tropo. and Iono. :Small variations

Dif. Instrumental delays and carrier ambiguities:constant

Dif. Wind-up: Very small

Dif. Receiver clock:Main variations Common for all satellites



PRN06

PRN30

IND1-IND2: 7m

PRN06

PRN30

IND1-IND2: 7m

1 1( ) sat sat


ru ruP P

1( )L

j j j j j j j

ru ru ru ru ru ru ru ru ruL L c t T I N b

1( )P

j j j j j

ru ru ru ru ru ru ruP P c t T I K

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P

j j j j j j j

i i i i i i iP c t t T I K K

Single difference

L

j j j j j j j j j

i i i i i i i i iL c t t T I N b b


( ) ( ) ( ) ( ) j j j j

ru ru u r

j j j j j


where:0 0 0

ˆ ˆ j j j j j

i i i i iρ r ρ r

where:

With some algebraic manipulation, it follows:

L

j j j j j j j


0 0 0 ;j j j

ru u r ru u site r r εbeing:


j j j

ru u r

0 0 0 0ˆ ˆ ˆ j j j j j j

ru ru u ru ru site ru ephρ r ρ ε ρ ε

0 u u ru siter r r εFinally:

j j

eph r ε

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Ref.Sta.

ru u rr r r

ur rr

User receiver

siteε

j

ephε

To Earth Centre

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0ˆ ;j

ru site sitej

u

b

ρ ε ε 0

ˆ

j j j

ru eph ephj

u

bρ ε ε

Thence, taking into account the relationships:

and being it follows that for a baseline

1

1000

j

u

b

20000kmj

u 20kmb

The effect of 5 metres error in orbits or in site coordinates is less than 5 mm in range for the estimation of . rur

But, the user position estimate will be shifted by the error in the site coordinates 0u u ru site r r r ε

rub r

0 0 0 0ˆ ˆ ˆ j j j j j j


and where the estimate will be affected in turn by the ephemeris and sitting site errors as:

Range error due toreference station

coordinates uncertainty

Range error due toSat. coordinates uncertainty

rur


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Exercise:

Let be:

where

0 0 0 0ˆ ˆ ˆj j j j j j

ru ru u ru ru r ru ρ r ρ r ρ r

Show that the Single Differences are given by:

j j j

ru u r

0 0 0ˆ ˆj j j j j

i i i i i ρ r ρ r (from Taylor expansion)

0 0 0 ;j j j

ru u r ru u r r r rbeing:

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Ref.Station

Baseline

ˆ j

uρ ˆ j

rρ

ru u rr r r

rur

ur rr

User receiver

ur rr

jr

To Earth Centre

0ˆ j

uρ 0ˆ j

rρ

14

P

j j j j j j j

i i i i i i iP c t t T I K K

Single difference

L

j j j j j j j j j

i i i i i i i i iL c t t T I N b b


( ) ( ) ( ) ( ) j j j j

ru ru u r

j j j j j


where:0 0 0

ˆ ˆ j j j j j

i i i i iρ r ρ r

where:

0 0 0 0 0

0 0 0 0

ˆ ˆ ˆ ˆ

ˆ ˆ ˆ

j j j j j j j j

ru ru u u r r u r

j j j j j

ru u ru ru r ru

ρ r ρ r ρ r ρ r

ρ r ρ r ρ r

L

j j j j j j j


0 0 0 ;j j j

ru u r ru u r r r rbeing:

Hint: Linear model for Differential Positioning

j j j

ru u r

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Let’s assume that:

• The satellite coordinates are known with an uncertainty • The reference station coordinates are known with an

uncertainty

Thence, the user position can be computed from the estimate, with an error , as:

15

0 0 0 0ˆ ˆ ˆ j j j j j j

ru ru u ru ru r ruρ r ρ r ρ r

0 0 0 0ˆ ˆ ˆ j j j j j j


0 u u ru siter r r ε

r site r ε0( . . ) r r sitei e r r ε





siteε rur

rur

Ref.Sta.

ru u rr r r

ur rr

User receiver

siteε

j

ephε

To Earth Centre


ru u r r r rwith

0 0 0u u u u ru r u ru site r r r r r r r r ε

j j

eph r ε

Backup

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Ref.Sta.

ru u rr r r

ur rr

User receiver

siteε

j

ephε

To Earth Centre

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0ˆ ;j

ru site sitej

u

b

ρ ε ε 0

ˆ

j j j

ru eph ephj

u

bρ ε ε

Thence, taking into account the relationships:

and being it follows that for a baseline

1

1000

j

u

b

20000kmj

u 20kmb

The effect of 5 metres error in orbits or in site coordinates is less than 5 mm in range for the estimation of . rur

But, the user position estimate will be shifted by the error in the site coordinates 0u u ru site r r r ε

rub r

0 0 0 0ˆ ˆ ˆ j j j j j j






rur


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Exercise:

Demonstrate the following relationship:

0ˆ

j

ru site site

bρ ε ε

Hint:

0 0 0

0 0

ˆ ˆ ˆj j j

ru site u r site

j j

u rsite site

b

ρ ε ρ ρ ε

ρ ρε ε

To Earth Centre

Reference Station

ˆ j

uρ ˆ j

rρ

ru u rr r r

rur

ur rr

User receiver

jr

Satellite-j

0 00

0

0 0

0 00

0

ˆ

ˆ

j jj r rr j j

rj j

r u j jj u uu j j

u

ρ ρρ

ρ ρρ

Note: the following approaches have been taken:

rub r

u v u v0ru rub r r


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Contents

18


1.1. Linear model





2.1. Introduction



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Master of Science in GNSS @ J. Sanz & J.M. Juan19

True position

Reference Station

Geographic decorrelation of ephemeris errors

Satellite location error

Position from broadcast ephemeris

User

user

user

user

ρε

ref

ref

ρε

user

refuser

user ref

ρρε ε

Differential range error due to satellite obit error

with a baseline 20

20 1

20000 1000

b km

b

A conservative bound:

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True position

Reference Station


Position

from broadcast

ephemeris

User

user

user

user

ρε

ref

ref

ρε

user

refuser

user ref

ρρ

ε ε

user

userρ

ε


Range error from CREU and EBRE

Differential range error from between CREU and EBRE

288 km of baseline

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288 km of baseline

CREUAbsolute positioning

CREU-EBREDifferential positioning

refuser

user ref

ρρ

ε ε

Differential range error from between CREU and EBRE

user

userρ

ε

Range error from CREU and EBRE

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1 1

2 2

eph

eph

1 2 1 2 constant 0

eph

1 2

2

1

Orbit Errors over the hyperboloid will not produce differential range errors.

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1 1

2 2

eph

eph

1 2 1 2 constant 0

eph

1 2

2

1

eph

Orbit Errors over the hyperboloid will not produce differential range errors.

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• Errors over the hyperboloid (i.e. ) will not produce

differential range errors.• The highest error is given by

the vector , orthogonal to the hyperboloid and over the plain containing the baseline vector and the LoS vector .Note:

Being the baseline b much smaller than the distance to the satellite, we can assume that the LoS vectors from A and B receives are essentially identical to .That is,

u

ρb

uB A ctt

( ) / 2 : hyperboloid semiaxis

/ 2 : focal length

1cos

2

B Aa

b

where a b

B A

( ) 2

2 2 sin

1sin

B A a

a ab

b

ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ

ˆ ˆ ˆˆ ˆ ˆ ˆ

T T

T T

u ρ b ρ b ρ ρ -ρ ρ b

Ib ρ ρ b I ρ ρ b

ε

sinˆ ˆsin

ˆ ˆ

T T

T T

b bε u ε u

bε I ρ ρ

Differential range error produced by anorbit error parallel to vector

Let

Thence:

Note: ε ρ

ˆNote: being a vector orthogonal

ˆ ˆ to the LoS , thence, T

u

ρ ε u

u

ˆWhere:

is the baseline vector

bb = b

ˆNote: sin u u

Note: in this 3D problem is NOT the elevation of ray.

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ORBIT TEST : Broadcast orbits Along-track Error (PRN17)

PRN17: Doy=077, Transm. time: 64818 sec

17 10 3 18 20 0 0.0 1.379540190101E-04 2.842170943040E-12 0.000000000000E+007.800000000000E+01-5.059375000000E+01 4.506973447820E-09-2.983492318682E+00

-9.257976353169E-05 5.277505260892E-03 8.186325430870E-06 5.153578153610E+034.176000000000E+05-5.401670932770E-08-4.040348681654E-01-7.636845111847E-089.603630515702E-01 2.215312500000E+02-2.547856603060E+00-7.964974630307E-09

-3.771585673111E-10 1.000000000000E+00 1.575000000000E+03 0.000000000000E+002.000000000000E+00 0.000000000000E+00-1.024454832077E-08 7.800000000000E+014.104180000000E+05 4.000000000000E+00

diff EPH.dat.org EPHcuc_x0.dat --------------------------------------------------< -2.579763531685E-06 5.277505260892E-03 8.186325430870E-06 5.153578153610E+03> -9.257976353169E-05 5.277505260892E-03 8.186325430870E-06 5.153578153610E+03---------------------------------------------------------------------------------

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ˆ ˆ

T T bε I ρ ρ

εOrbit error Range error

Differential range errorBaseline: b=31.3km

rov3

rov1

rov2

11 km

31.3 km

19.7 km

15.2 km

39.3 km

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Exercise:

Justify that clock errors completely cancel in differential positioning.

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Contents

28


1.1. Linear model





2.1. Introduction


2.3. Satellite based Augmentation System (SBAS)

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If the distance between the user and the reference station is "short enough", so that the residual error ionospheric, tropospheric and ephemeris are small compared to the typical errors due to receiver noise and multipath, it can be assumed:

Error mitigation and short baseline concept

0ˆ0 ; 0j j j j

ru ru ru ephT I ρ ε

Note that the previous definition of “shortness” is quite fussy

Working with smoothed code, a residual error of about 0.5 metres could be tolerable, but for carrier based positioning it should be less than 1 cm to allow the carrier ambiguity fixing.

• The differential ephemeris error is at the level of few centimetres for baselines up to 100 km (i.e. 5 cm assuming a large bound of ).

• The typical spatial gradient of the ionosphere (STEC) is 1-2 mm/km (i.e. 0.1-0.2 m in 100km), but it can be more than one order of magnitude higher when the ionosphere is active.

10 m j

eph

29

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Note that the previous definition of “shortness” is quite fussy

• The correlation radio of the troposphere is lower than for the ionosphere. At 10km of separation the residual error can be up to 0.1-0.2 m. Nevertheless, 90% of the tropospheric delay can be modelled and the remaining 10% can be estimated together with the coordinates (for high precision applications). For distances beyond a ten of kilometres or significant altitude difference it would be preferable to correct for the tropospheric delay at the reference station and user receiver.

Carrier-smoothed code:Pseudorange code measurement errors due to receiver noise and multipath can be reduced smoothing the code with carrier measurements. Smoothed codes of 0.5m (RMS) can be obtained with 100 seconds smoothing. On the other hand, the ionospheric error is substantially eliminated in differential mode and the filter can be allowed for lager time smoothing windows.

30

Error mitigation and short baseline concept

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Contents

31


1.1. Linear model





2.1. Introduction



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0 0ˆj j j

ru ru u u ρ r

P

j j j j j


Differential code based positioning

0 0 0 , 0ˆ ˆ ˆj j j j j j

ru ru u ru ru site r ru eph ρ r ρ ε ρ εP

j j j

ru ru ru ru ruP c t K

Thence,

If the reference station coordinates are known at the centimetre level and the distance between reference station and user are “not too large”, we can assume 0

0 ; 0

ˆ 0

0

j j

ru ru

j j

ru eph

site ru u

T I

ρ ε

ε r r

Or, what is the same:

0 0ˆ

P

j j j j

ru ru u u ru ru ruP c t K ρ r

The left hand side of previous equation can be spitted in two terms: one associated to the reference station and the other to the user:

0 0 0

j j j j j j

ru ru u u r rP P P

Note : for baselines up to 100 km

the range error of broadcast orbits is less than 10 cm

(assuming ).10 mj

eph

ru u r u site r r r r ε

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0

j j j

r rPRC P

0 0ˆ

P

j j j j j

u u u u ru ruP PRC c t ρ r

• The term is the error in range measured by the reference station, which can be broadcasted to the user as a differential correction:

0j j

r rP

• The user applies this differential correction to remove/mitigate common errors:

Where the receiver’s instrumental delay term is included in the differential clock ruc t

ruK

For distances beyond a ten of kilometres, or significant altitude difference, it would be preferable to correct for the tropospheric delay at the reference station and user receiver. 33

0 0ˆ

P

j j j j

ru ru u u ru ru ruP c t K ρ r

The left hand side of previous equation can be spitted in two terms: one associated to the reference station and the other to the user:

0 0 0

j j j j j j

ru ru u u r rP P P

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– The reference station with known coordinates, computes pseudorange

and range-rate corrections: PRC= ref, –Pref , RRC= PRC/t .

– The user receiver applies the PRC and RRC to correct its own measurements, Puser + (PRC + RRC (t-t0)), removing SIS errors and

improving the positioning accuracy.

Reference station(known Location)

Actual SV Position

Broadcast SV Position

Differential Message Broadcast

PRC, RRC

Measured Pseudoranges

Range Differential Correction Calculation

Calculated Range ref

Pref

Puser

User

DGNSS with code ranges: users within a hundred of kilometres can obtain one-meter-level positioning accuracy using such pseudorange corrections.

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35

0

0

0

1

1

2 2

ˆ 1Pref

ˆPref 1

Prefˆ 1

T

u

T

uu

ru

nT

n

u

c t

ρ

rρ

ρ

0 0ˆ

P

j j j j j

u u u u ru ruP PRC c t ρ r

The user applies this differential correction to remove/mitigate common errors:

where the receiver’s instrumental delay term is included in the differential clock ruc t

ruK

0Pref j j j j

u uP PRC

The previous system for navigation equations is written in matrix notation as:

where


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Time synchronization issues:

For simplicity we have dropped any reference to measurement epochs, but real-time implementations entail delays in data transmission and the time update interval can be limited by bandwidth restrictions.

• Differential corrections vary slowly and its useful life can be up to several minutes with S/A=off.

• To reduce bandwidth, the reference station computes Pseudorange Corrections (PRC) and Range-Rate Correction (RRC) for each satellite in view, which are broadcast to every several seconds, up to a minute interval with S/A=off.

• The user computes the PRC at the measurement epoch as:

36

0 0( ) ( ) ( ) j j jPRC t PRC t RRC t t


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Note: we have considered here only code measurements. The carrier based positioning will be treated next, using double differences of measurements and targeting the ambiguity fixing.

Data handling:

Reference station and user have to coordinate how the

measurements are to be processed:

• Corrections must be identified with an Issue of Data (IOD) and

time-out must be considered.

• Both receivers must use the same ephemeris orbits (which are

identified by the IODE).

• If reference station uses a tropospheric model the same model

must be applied by the user.

• If reference station uses the broadcast ionospheric model, the user

must do the same.


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– The reference station with known coordinates, computes pseudorange and

range-rate corrections: PRC= ref – Pref, RRC= PRC/t .

– The user receiver applies the PRC and RRC to correct its own measurements, Puser + (PRC(t0) + RRC(t-t0)), removing SIS errors and

improving the positioning accuracy.

Reference station(known Location)

Actual SV Position

Broadcast SV Position

Differential Message Broadcast

PRC, RRC

Measured Pseudoranges

Range Differential Correction Calculation

Calculated Range ref

PrefPuser

User

DGNSS with code ranges : users within a hundred of kilometres can obtain one-meter-level positioning accuracy using such pseudorange corrections.

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Master of Science in GNSS @ J. Sanz & J.M. Juan39

ftp://cddis.gsfc.nasa.gov/highrate/2013/

1130752.3120 -4831349.1180 3994098.9450 gods1130760.8760 -4831298.6880 3994155.1860 godn1112162.1400 -4842853.6280 3985496.0840 usn3

GODN

76 mUSN3

GODS

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GPS Standalone GPS Standalone

DGPS

GODN

USN3

GODS

GODN

USN3GODS: reference

station

GODN

USN3

GODS

DGPS

GODN

USN3GODS: reference

station

S/A=off

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PRC

RRC

DGPS

GODS: referencestation

GODS: referencestation

GODN

USN3GODS: reference

station

DGPS

GODN

USN3GODS: reference

station

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Contents

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1.1. Linear model





2.1. Introduction



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Introduction: What Augmentation is?

• To enhance the performance of the current GNSS with additional information to:– Improve INTEGRITY via real-time monitoring

– Improve ACCURACY via differential corrections

– Improve AVAILABILITY and CONTINUITY

• Satellite Based Augmentation Systems (SBAS)

– E.g., WAAS, EGNOS, MSAS

• Ground Based Augmentation Systems (GBAS)

– E.g., LAAS

• Aircraft Based Augmentation (ABAS)

– E.g., RAIM, Inertials, Baro Altimeter

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Why Augmentation Systems?

• Current GPS/GLONASS Navigation Systems cannot met the Requirements for All Phases of Flight:– Accuracy– Integrity– Continuity

– Availability

• Marine and land users also require some sort of augmentation for improving the GPS/ GLONASS performances.

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WHY GNSS NEEDS AN AUGMENTATION ?

PERFORMANCECATEGORY I

Requirements

ACCURACY (95%)

INTEGRITY

AVAILABILITY

H. 13 m V. 22m V 4.0 mH 16.0 m

99% to 99.990%

2.10-7/ approach

Time to alarm 6 s

99% (RAIM)

GPS OnlyCivil Aviation

CONTINUITY OF SERVICE 10-5 / approach

(10-6 / 15 s)

?

?

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GPS Before and After S/A was switched off

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10

Time of Day (Hours UTC)

Ins

tan

tan

eo

us

Err

or

(me

ters

)

Horizontal Error (meters)

Vertical Error (meters)

2 May 2000Colorado Springs, Colorado

ANALYSIS NOTES

- Data taken from Overlook PAN Monitor Station,

equipped with Trimble SVeeSix Receiver

- Single Frequency Civil Receiver

- Four Satellite Position Solution at Surveyed Benchmark

- Data presented is raw, no smoothing or editing

Accuracy: Difference between the measured position at any given

time to the actual or true position.

Even with S/A off a Vertical Accuracy < 4m 95% of time

cannot be guaranteed with the standalone GPS.

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Standalone GPS and GLONAS Integrity is Not Guaranteed

Integrity: Ability of a system to provide timely warnings to users or

to shut itself down when it should not be used for navigation.

GPS/GLONASS Satellites:Time to alarm is from minutes to hoursNo indication of quality of service

Health Messages:

GPS up to 2 hours late

GLONASS up to 16 hours late

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Availability and Continuity Must meet requirements

Availability: Ability of a system to perform its function at initiation of

intended operation. System availability is the percentage of time

that accuracy, integrity and continuity requirements are met.

Continuity: Ability of a system to perform its function without

(unpredicted) interruptions during the intended operation.

Continuity:Less than 10-5 Chance of Aborting

a Procedure Once it is Initiated.

Availability:>99% for every phase of flight (SARPS).

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INTEGRITY

NSE

Confidence bound

Alert LimitLess than 10-7 probability of true error larger than confidence bound.Time to alarm 6 s

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SBAS and GBAS Navigation Modes

SBAS

GBAS

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Aviation Accuracy

(H) 95%

Accuracy

(V) 95%

Alert

Limit (H)

Alert

Limit (V)

Integrity Time

to alert

Continuity Avail-

ability

ENR 3.7 Km

(2.0 NM)

N/A 7400 m

3700 m

1850 m

N/A 1-10-7/h 5 min. 1-10-4/h

to

1-10-8/h

0.99

to

0.99999

TMA 0.74 Km

(0.4 NM)

N/A 1850 m N/A 1-10-7/h 15 s 1-10-4/h

to

1-10-8/h

0.999

to

0.99999

NPA 220 m

(720 ft)

N/A

600 m

N/A 1-10-7/h 10 s

1-10-4/h

to

1-10-8/h

0.99

to

0.99999

APV-I 220 m

(720 ft)

20 m

(66 ft)

600 m 50 m 1-2x10-7 per

approach

10 s

1-8x10-6 in

any 15 s

0.99

to

0.99999

APV-II 16.0 m

(52 ft)

8.0 m

(26 ft)

40 m 20 m 1-2x10-7 per

approach

6 s

1-8x10-6 in

any 15 s

0.99

to

0.99999

CAT-I 16.0 m

(52 ft)

6.0 - 4.0 m

(20 to 13 ft)

40 m 15 -10 m 1-2x10-7 per

approach

6 s 1-8x10-6 in

any 15 s

0.99

to

0.99999

Civil Aviation Signal-in-Space Performance Requirements

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1.1. Linear model





2.1. Introduction



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Most of the measurement errors are common: clock, ephemeris, ionosphere and troposphere.

A common correction valid for any receiver within the LADGPS area is generated and broadcast.

The accuracy is limited by the spatial decorrelation of those error sources (1m at 100Km).

GBAS Concept

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GBAS Concept

• It is also responsible of detecting and alarming space-segment and ground-segment failures.

• The GS must insure that all ranging sources for which GBAS corrections are broadcast are safe to use. If a failure occurs that threatens user safety, the GS must detect and alert users (by not broadcasting corrections for the affected ranging source) within a certain time-to-alert.

The Ground Station (GS) responsible for generating and broadcasting carrier-smoothed code differential corrections and approach-path information to user aircrafts.This system is used to support aircraft operations during approach and landing.

This is from [RD-5]

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GBAS Components

• The GS tracks, decodes, and monitors GPS satellite information and generates differential corrections.

• It also performs integrity checks on the generated corrections. • The correction message, along with suitable integrity parameters

and approach path information, is then broadcast to airborne users on a VHF channel, up to about 40km.

The GBAS station involves redundant Reference Receivers and antennas, redundant High Frequency Data Broadcast equipment linked to a single antenna.

This is from [RD-5]

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Ground System Functional Flow Diagram

A variety of integrity monitor algorithms that are grouped into:

• Signal Quality Monitoring (SQM) • Data Quality Monitoring (DQM) • Measur. Quality Monitoring (MQM)

• Multiple Reference Consist Check (MRCC)

sm-monitor

• Message Field Range Test (MFRT)

This is from [RD-5]

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SQM: Targets satellite signals anomalies and local interference. Implements tests for Correlation Peak Symmetry, Receiver Signal Power and Code-Carrier Divergence.

DQM: Checks the validity of the GPS ephemeris and clock data for each satellite that rises in view of the LGF and at each time new navigation data messages are broadcast.

MQM: Confirms the consistency of the pseudorange and carrier-phase measurements over the last few epochs to detect sudden step and any other rapid errors.

MRCC: Examines the consistency of corrections for each satellite across all reference receivers.

sm-monitor: Helps ensure a Gaussian distribution for the correction error

with zero mean and that the broadcast spr _ gnd overbounds the actual errors in the broadcast differential corrections.

MFRT: Verifies that the computed averaged pseudorange corrections and correction rates fit within the message field bounds.

Executive Monitors (EXM-I and EXM-II) coordinate all previous monitors and combine failure flags.

This is from [RD-5]

• Signal Quality Monitoring (SQM) • Data Quality Monitoring (DQM) • Measur. Quality Monitoring (MQM)

• Multiple Reference Consist Check (MRCC)

sm-monitor

• Message Field Range Test (MFRT) 57

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1.1. Linear model





2.1. Introduction



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The pseurorange error is split in its components.• Clock error• Ephemeris error• Ionospheric error• Local errors (troposphere, multipath, receiver noise)

Uses a network of receivers to cover broad geographic area

SBAS Concept

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Error Mitigation

Error component

GBAS SBAS

Satellite clock Estimation and

Removal each error

component

Ephemeris Common Mode

Ionosphere Differencing

Troposphere Fixed Model

Multipath and Receiver Noise

Carrier Smoothing by user

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Three existing SBAS Systems

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• EGNOS is the European component of a Satellite Based Augmentation to GPS.

• EGNOS is being developed under the responsibility of a tripartite group:

– The European Space Agency (ESA)

– The European Organization for the Safety of Air Navigation (EUROCONTROL)

– The Commission of the European Union.

The European Geoestationary Navigation Overlay SERVICE (EGNOS)

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-40 -30 -20 -10 0 10 20 30 4020

30

40

50

60

70

Longitude (°)

La

titu

de

(°)

AOR-EIOR

Artemis

ECAC Area(ECAC: European Civil Aviation Conference)

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EGNOS Architecture

GPS

GEO (x3)

NLES

(x 6)

RIMS(x 37)

EWAN

MCC 1 MCC 2 MCC 3 MCC 4 PACF ASQF

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EGNOS ground segment is composed of the following

stations/centres which are mainly distributed in Europe and are interconnected between themselves through a land network.

• 37 RIMS (Ranging and Integrity Monitoring Stations) + seven being deployed: receive the satellite signals and send this information to the MCC centres.

• 4 MCC (Master Control Centres) receive the information from the RIMS stations and generate correction messages to improve satellite signal accuracy and information messages on the status of the satellites (integrity). The MCC acts as the EGNOS system 'brain'.

• 6 NLES (Navigation Land Earth Stations): they receive the correction messages from the CPFs for the upload of the data stream to the geostationary satellites and the generation of the GPS-like signal. This data is then transmitted to the European users via the geostationary Satellite

http://egnos-user-support.essp-sas.eu/egnos_ops/egnos_system/system_description/current_architecture

http://egnos-user-support.essp-sas.eu/egnos_ops/egnos_system/system_description/current_architecture

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Master Control Center (MCC)

MCC is Subdivided into– CCF (Central Control Facility)

Monitoring and control EGNOS G/SMission Monitoring and archiveATC I/F

– CPF (Central Processing Facility)Provides EGNOS WAD correctionsEnsures the Integrity of the EGNOS usersUtilises independent RIMS channels for checking of correctionsReal time software system developed to high software standards

4 MCCs are implemented in EGNOS

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SBAS Differential Corrections and Integrity:

The RTCA/MOPS-DO 229C

Do-229A, B, C, D

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Message Format

• 250 bits

• One Message per second

• All messages have identical format

24-BITSPARITY

8-BIT PREAMBLE OF 24 BITS TOTAL IN 3 CONTIGUOUS BLOCKS

6-BIT MESSAGE TYPE IDENTIFIER (= 2, 3, 4 & 5)

250 BITS - 1 SECOND

IODF (2 BITS)

13 12-BIT FAST CORRECTIONS

DIRECTION OF DATA FLOW FROM SATELLITE; MOST SIGNIFICANT BIT (MSB) TRANSMITTED FIRST

IODP (2 BITS)

PRCf

UDREIREPEAT FOR 12 MORE SATELLITESREPEAT FOR 12MORE SATELLITES

13 4-BIT UDREIs

212-BIT DATA FIELD

The corrections, even for individual satellites are distributed across several individual messages.

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MSG 0 Don't use this SBAS signal for anything (for SBAS testing)

MSG 1 PRN Mask assignments, set up to 51 of 210 bits

MSG 2 to 5 Fast corrections

MSG 6 Integrity information

MSG 7 Fast correction degradation factor

MSG 8 Reserved for future messages

MSG 9 GEO navigation message (X, Y, Z, time, etc.)

MSG 10 Degradation Parameters

MSG 11 Reserved for future messages

MSG 12 SBAS Network Time/UTC offset parameters

MSG 13 to 16 Reserved for future messages

MSG 17 GEO satellite almanacs

MSG 18 Ionospheric grid point masks


MSG 24 Mixed fast corrections/long term satellite error corrections

MSG 25 Long term satellite error corrections

MSG 26 Ionospheric delay corrections

MSG 27 SBAS outside service volume degradation


MSG 62 Internal Test Message

MSG 63 Null Message

SBAS Broadcast Messages (ICAO SARPS)

Many Message Types Coordinated Through

Issues Data (IOD)

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GPS

Ephemeris

GPS

Clock

PRN

Mask

(1)

Long-term

Corrections

(25)

Fast

Corrections

(2 - 5, 24)

Integrity

Information

(6)

IODE k

IODC k

IOD k

IODP

No IOD: repeat msg,

small changes

IODF j

IODP

Service

Message

(27)

Ionospheric

Mask

(18)

Ionospheric

Corrections

(26)

IODS

IODI

IODP

Acceleration

Information

(7)

GLONASS DATA

IODG k

Issues of Data (IOD)

IODI

IODF

IODE

IODP

IODP

IODP

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Message Time-Outs:Users can operate even when missing Messages

• Prevents Use of Very Old Data

• Confidence Degrades When Data is Lost

• IODF: Detect Missing Fast Corrections

1 second

Last bit of message:tof+1sec

tof: Time of applicability(1st bit of message)

The Correction is estimated by the master station

Correction time-Out

System Latency

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DataAssociated

Message

Types

Maximum

Update Interval

(seconds)

En Route,

Terminal, NPA

Timeout (seconds)

Precision

Approach

Timeout (seconds)

WAAS in Test Mode 0 6 N/A N/A

PRN Mask 1 60 None None

UDREI 2-6, 24 6 18 12

Fast Corrections 2-5, 24 60 (*) (*)

Long Term

Corrections

24, 25 120 360 240

GEO Nav. Data 9 120 360 240

Fast Correction

Degradation

7 120 360 240

Weighting Factors 8 120 240 240

Degradation

Parameters

10 120 360 240

Ionospheric Grid

Mask

18 300 None None

Ionospheric

Corrections

26 300 600 600

UTC Timing Data 12 300 None None

Almanac Data 17 300 None None

(*) Fast Correction Time-Out intervals are given in MT7 [between 12 to 120 sec]

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PRN MASK (MT01)

PRN

Slot

Assignment

1-37 GPS/GPS Reserved

38-61 GLONASS

62-119 Future GNSS

120-138 GEO/SBAS

139-210 Future GNSS/GEO/SBAS/Pseudolites

Bit No 1 2 3 4 5 6 . 38 . 120 . 210

Value 0 1 0 1 1 0 1 1 0

PRN GPS

PRN 2

GPS

PRN 4

GPS

PRN 5

GLONASS

Slot 1

AORE

PRN 120

PRN mask

Number

1 2 3 21 29

Up to 51 satellites in 210 slots.

Note: Each Correction set in MT 2-5,5,6,7,24,25 its characterized by its PRN-Masknumber, between 1 to 51.

Each MT01 contains its associated IODP

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Example of message: Fast Corrections

(MT2-5,24)

• Primarily Removed SA

– Common to ALL users

– Up to 13 Satellites Per Message

– Pseudorange Correction /confidence Bound

– Range Rate Formed by Differencing

– UDRE degrades Over Time

• Acceleration Term in MT 7

• Reset when new Message Received

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24-BITSPARITY

8-BIT PREAMBLE OF 24 BITS TOTAL IN 3 CONTIGUOUS BLOCKS

6-BIT MESSAGE TYPE IDENTIFIER (= 2, 3, 4 & 5)

250 BITS - 1 SECOND

IODF (2 BITS)

13 12-BIT FAST CORRECTIONS

DIRECTION OF DATA FLOW FROM SATELLITE; MOST SIGNIFICANT BIT (MSB) TRANSMITTED FIRST

IODP (2 BITS)

PRCf

UDREIREPEAT FOR 12 MORE SATELLITESREPEAT FOR 12MORE SATELLITES

13 4-BIT UDREIs

2 2 2 2 2 2,i flt UDRE fc rrc ltc ers s

on

onn

nnn

tt

PRCPRCRRC

ttRRCPRCtPRC

)()( )(tPRC

)100( MTRSSUDRE

*1 sat satY C PRC t dt

TGD IONO TROP

PRC

Example of message: Fast Corrections

(MT2-5,24)

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Example of message: Ionospheric Corrections

(MT26)

• Only Requiered for Precission Approach

– Grid of Vertical Ionospheric Corrections

– Users Select 3 o 4 IGPs that Surrounding IPP

• 5ºx5º or 10ºx10º for 55º<Lat<55º

• Only 10ºx10º for 55º<|Lat|<85º

• Circular regions for |Lat|>85º

– Vertical Correction and UIVE Interpoled to IPP

– Both Converted to Slant by Obliquity Factor

IGP: Ionospheric Grid PointIPP: Ionospheric Pierce Point

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Global IGP Grid

N75

N65

N55

0

0W180

N85

W100 E100W140 W60 W20 E20 E60 E140

N50

S75

S65

S55

S85

S500 1 2 3 4 5 6 7 8

Predefined Global IGP Grid

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Ephemeris+

Clocks

IONO

Fast Corrections+

Long Term Corrections+

UDRE +

Degradation Param.

IONO Corrections+

GIVE +

Degradation Param.

MT1, MT2,5,24, MT6, MT25, MT7, MT12, MT9

MT18MT26

MT10

22222

tropoairUIREflt sssss

*1 sat saty C PRC t dt TGD IONO TROP sattPRC * IONO

2

flts 2

UIREs

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2

21

2

2

N

E

V

T

NE NV NT

NE EV ET

NV EV VT

NT ET VT

d d d d

d d d d

d d d d

d d d d

T

x G WGP

1

y

W P

2

1

2

0

0 N

s

s

yP

22 2 2 2

26.002 2

N NE E

NE

d d d dHPL d

5.33 VVPL d

2 2 2 2 2

, , , ,i i flt i UIRE i air i tropos s s s s

Navigation System Errorand Protection levels

, , ,N E U cdt x

y = G x

ˆ-1

T Tx = G WG G W y

Ks-Ks -s s

7

~ (0,1)

( 5.33) 10

Z N

P Z

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Fast and Long-Term Correction Degradation

, 0 , 0, 0

ltc v ltc vltc v

t tltc

IC floor

mod 2

mod 2

( )

( )4

0 , 1

, 1

current previous

current previous

fc rrc

of

rrc a I B

IODF IODF

IODF IODFt

t t

2

2

u lat

fc

t t ta

_ _ 1

_ 1 _ 0 _ 0

_ _

, , ,

, , ,

, ,

, ,

,

rrc ltc lsb ltc v

ltc v ltc v ltc v

er UDRE

iono ramp iono step

iono iono

B C C

I C I

C RSS

C C

I RSS

MT10

ia,fc iI latt

MT7

2

2

2 2 2 2 2

,

, 0 ( 10)

, 1 ( 10)

UDRE

UDRE

rrc erUDRE fc ltci flt

UDRE fc rrc ltc er

if RSS MT

if RSS MT

s s

s

0 1,ltct v or v

MT25

0 0 _ 1

_ 1 0 0 _ 1

, 1

_

0 ,

max 0, , ,

ltc v

ltc v ltc v

ltc v

lts lsb

if t t t I

C C t t t t I otherwise

MT2-6,24, iIODF UDRE

u oft t

, 3current previous

IODF IODF

0

er

erC

Neither fast nor long term correctionshave time out for precision approach

Otherwise

, 3current previous

IODF IODF

)3( IODFwhen

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_ _ 1

_ 1 _ 0 _ 0

_ _

, , ,

, , ,

, ,

, ,

,

rrc ltc lsb ltc v

ltc v ltc v ltc v

er UDRE

iono ramp iono step

iono iono

B C C

I C I

C RSS

C C

I RSS

MT10

,iono it GIVE

MT26 _ _ ionoiono iono step iono rampiono

t tionoI

C floor C t t

2 2 2

UIRE pp UIVEFs s

12 2

cos1 e

pp

e I

R EF

R h

2 2

,

1

, , 4 3N

UIVE n pp pp n ionogrid

n

W x y N ors s

2

2

2 2

, 0 ( 10)

, 1 ( 10)

GIVE iono

GIVE iono

ionoionogrid

iono

if RSS MT

if RSS MT

s s

s

Degradation of Ionospheric Corrections

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Users know the receiver-satellites geometry and can compute bounds on the horizontal and vertical position errors.These bounds are called Protection Levels (HPL and VPL). They providegood confidence (10-7/hour probability) that the true position is within abubble around the computed position.

P(VPE>VPL) < 10-7 /sample

N

i

iVV isKVPL

1

22 s

GEOMETRY

Tail area Probability

Protection

Level

True

Error

Ks-Ks-s s

2 2 2 2 2

, , , ,i i flt i UIRE i air i tropos s s s s

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EGNOS

DGNSS implementations: WADGNSS (SBAS)

Availability

Integrity

Accuracy

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EGNOSAvailability

Continuity

Integrity

Accuracy

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References

[RD-1] J. Sanz Subirana, J.M. Juan Zornoza, M. Hernández-Pajares, GNSS Data processing. Volume 1: Fundamentals and Algorithms. ESA TM-23/1. ESA Communications, 2013.

[RD-2] J. Sanz Subirana, J.M. Juan Zornoza, M. Hernández-Pajares, GNSS Data processing. Volume 2: Laboratory Exercises. ESA TM-23/2. ESA Communications, 2013.

[RD-3] Pratap Misra, Per Enge. Global Positioning System. Signals, Measurements, and Performance. Ganga-Jamuna Press, 2004.

[RD-4] B. Hofmann-Wellenhof et al. GPS, Theory and Practice. Springer-Verlag. Wien, New York, 1994.

[RD-5] Gang Xie, Optimal on-airport monitoring of the integrity of GPS-based landing systems, PhD Dissertation, 2004.

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12 GPS Standard Positioning Service Performance Standard [RD-3].13 This is the typical range of ionospheric residual errors after application of the baseline Klobuchar

model broadcast by GPS for mid-latitude regions.

EGNOS Safety of Life Service Definition Document (Ref : EGN-SDD SoL, V1.0). European Comission.

http://www.essp-sas.eu/downloads/vubjj/egnos_sol_sdd_in_force.pdf

SREW: Satellite Residual Error for the Worst user location.UIVD: User Ionospheric Vertical Delay.UERE: User Equivalent Range Error

master: lecture 6 - upc universitat politècnica de...

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