G P SIonospheric

E r r o r

Student:Tatiana Quercia

Space Environment and Instrumentation, Prof. L. Iess, Sept. 2014

Agenda

● GPS● Ionospheric error● Computation example● Single frequency users' correction

GPSGlobal Positioning System (USA, 1978)

32 satellites in 6 different orbital planes

Correlation between TX and RX signals based on a code

Globally available since 1994

TT

T

RXisatisatisati

RXTXRX

TXTXRXRX

GGGX

XG

xxx

tczzyyxx

tcttc

ttttc

1

RX

j

iij

i

i2

,2

,2

,

:onminimizatiroot square Using

)tz,y,(x,X and X̂

fG being

:orderfirst the tillseries sTaylor'by f expanding and

ˆ :relationssuch gConsiderin

least)at 1,...,4(i f̂)ˆ()ˆ()ˆ(ˆ

)(

)( Pseudorange (observable); δtTX

<< ΔtRX

^: estimation

Δ: correction

Ionospheric errorIonosphere: From about 85 km to 600 km altitude (upper atmosphere)

Ionization of neutrals/molecules by UV rays, X rays or cosmic rays

Plasma state with diurnal variation of density

Plasma produces refraction of electromagnetic wavesIonospheric refraction model: vertical layers

density electrons theN(h) being

medium dispersive a is Ionosphere [km] 0 )(6.80

1

0 1

)(

index refractive :

2

hf

hN

h

hn

v

cn

222

2

22

2

2

3.401

3.402

3.401

3.402

3.401

3.401

:

f

N

c

N

c

Nn

c

N

d

dn

c

N

f

Nn

d

dnnn

g

g

For Quasi Longitudinal approximation:

1 16.80

12

2 XXf

Nn

Expanding to the first term of Taylor's series:

2

3.401

21

f

NXn

Information does not travel at phase velocity v as plane monochromatic electromagnetic waves. Information is made of impulses and it travels at group velocity v

g, so it is

possible to define:

group refractive index

Then the range difference due to ionospheric delay can be computed in two ways:

Content Electron Total :TEC

]/m[electrons[N]

signal) (modulated vofdown slow TEC3.40

)1(

ave)(carrier w vofon acceleratiTEC3.403.40

)1(

3

g2

22

RX

Sat

ggroupiono

RX

Sat

RX

Sat

phaseiono

fdrnR

fNdr

fdrnR

If the propagation is not along the zenith, then the factor of obliquity 1/sinΦ must be pre-multiplied.

[1]

The associated phase variation is:

onanticipati phaserad 1044.82 7

f

TECR group

iono

Using two measurements at two different frequencies, the relative range difference can be computed as:

22

21

22

21

21 3.40sin

1)()(

ff

ffTECfRfRR group

ionogroupiono

groupiono

Then the time delay error due to ionosphere is:

)(

))((1

1 fv

Rft

g

groupiono

iono

The same relationship can be used with f=f2.

Computation example

example 45

sfrequencieion transmissGPS 1227

1575

22

11

MHzLf

MHzLf

312 /10)layer F2( melectronsN

[3]

216 /1020TECu 20) UT55:17 ,08/19/2014 ,( melectronsEuropeTEC

[2]

ns 10))t(L(

m 3)(

1 group

ionoR

1000032.0

00002.1)( 1

X

Lng

Single Frequency Users' Correction

Empirical approach [Klobuchar, 1987]

Reduction of about the 50% RMS ionospheric range error worldwide

Assumption: electron content is concentrated in a thin layer at 350 kilometres in height

Model:● constant value at night time● half-cosine function in daytime● amplitude and period given as function of eight parameters● parameters broadcast in the GPS navigation message

[4]

[4]

Bibliography[1] Iess, L. - Class notes - www.radioscience.dima.uniroma1.it[2] NASA JPL – Real-Time Ionospheric Maps - www.iono.jpl.nasa.gov[3] INGV- Ionosphere - www.roma2.rm.ingv.it[4] ESA – Klobuchar Ionospheric Model – www.navipedia.net