gism global ionospheric scintillation modelieea.fr/publications/ieea-2014-kigali-gism.pdfprn8 prn29...

GISMGlobal Ionospheric Scintillation Model

http://www.ieea.fr/en/gism-web-interface.html

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

•Béniguel Y., P. Hamel, “A Global Ionosphere Scintillation Propagation Model for Equatorial Regions”, Journal of Space Weather Space Climate, 1, (2011),doi: 10.1051/swsc/2011004

Y. Béniguel, IEEA

Contents

� Bias

� Scintillations

� Modelling Results vs Measurements

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

� Conclusion

� Scattering Function Calculation (SAR observations)

� Modelling Results vs Measurements

� Positioning errors

Measurement Campaigns

Béniguel Y., J-P Adam, N. Jakowski, T. Noack, V. Wilken, J-J Valette,M. Cueto, A. Bourdillon, P. Lassudrie-Duchesne, B. Arbesser-Rastburg, Analysis of scintillation recorded during the PRISmeasurement campaign, Radio Sci., Vol 44, (2009),doi:10.1029/2008RS004090

PRIS

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Prieto Cerdeira R., Y. Béniguel, "The MONITOR project:architecture, data and products", Ionospheric Effects Symposium,Alexandria VA, May 2011

http://telecom.esa.int/telecom/www/object/index.cfm?fobjectid=29210

MONITOR

MONITOR Extension

On going; start : 30 june 2014

Ionosphere Variability

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

TEC Map S4 map cumulated over 24 hours

Mean Errors(ray technique calculation)

( ) ( ) cos Y X 1 2

sin Y

X 1 2

sin Y 1

X 1 n 2 /1

22

2 222

2

+

−±

−−

−=

ϑϑϑ

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

ωi

2i k c

td

xd =i

P P i

x

td

k d

∂∂−= ω

ωω

Haselgrove equations (Simplified)

2

2 P X

ωω=

ωω b Y =

Bias

Range error

Faraday rotation

Te

2

N 2

r L

πλ

=∆ ds N N e

z

0T ∫= f

N 3.40 L

2T=∆

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Faraday rotation

Inputs : Ne ; B at any point inside ionosphere

s d cos B N m c 2

e

z

0 e220

3

ϑωε ∫=Ψ

Example of results / Solar Flux 150

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

HF Ground to Ground Propagation(Sky Wave)

120

140

160

Ray Paths vs Elevation Angles5° to 45°

0,4

0,5

0,6

0,7

0,8

0

30

60

330

ωi

2i k c

td

xd =

i

ppi

x

td

k d

∂∂

−=ω

ωω

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

20

40

60

80

100

0 200 400 600 800 1000 1200 1400al

titud

e (k

m)

distance from source (km)

0

0,1

0,2

0,3

0,4

90

120

150

180

210

240

|Eth

eta|

(V)

HF Antenna Pattern as an input

Turbulent Ionosphere(scintillation)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

(scintillation)

Satellite signal

Drift

Physical Mechanism

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Receiver level

Drift velocity

Medium Radar Observations

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

The vertical extent may reach hundreds of kilometers

Observations at Kwajalen IslandsCourtesy K. Groves, AFRL

Observations in BrazilCourtesy E. de Paula, INPE

Scintillation on Galileo SatellitesL1 vs E5a

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Field Propagation Equation

( ){ } dz' )z' (k t j exp ) , z , ( U t), , z , ( E ∫−= ωωρωρ

The field amplitude value U is a solution of the the parabolic equation

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0 ) U()( k ) U( z

) U(k j 2 1

22t =+∇+

∂∂ ρρερρ

Method of solution : phase screen technique

Field Propagation Equation

0 r) ( U)r ( k r) ( U r) ( U z

k j 2 22t =+∇+

∂∂ ε

Solution of the parabolic equation

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0 r) ( U 0) (A 4

k j r) ( U r) ( U

z k j 2

32t =+∇+

∂∂

( ) dz z, B ) (A ∫= ρρ( ) ) ( ) ( , z B 21 ρερερ =

Using the phase index autocorrelation function

Phase Screen Technique

Propagation

Propagation

Scattering

Scattering

Transmitter

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Propagation

Scattering

Receiver

Propagation : 1st & 3rd terms ; scattering : 2nd & 3rd terms

Medium CharacterizationIndex Spectral Density

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Index Spectral Density

Medium’s Phase Spectrum

0.01

0.1

1

10

100

1 .103 Power densities

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

( )( ) ( )

q

C

q

C L r )(

2 /p 20

2

P2 /p 2

02

2NeS

2e

+Κ=

+Κ=ΚΦ

σλγ

3 parameters : p ; q ; 0Neσ

1 .103

0.01 0.1 1 10 1001 .10

6

1 .105

1 .104

1 .103

PhaseAmplitude

frequency (Hz)

Sample characteristics : S4 = 0.51, sigma phi = 0.11

One Sample : Intensity

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Sample characteristics : S4 = 0.51, sigma phi = 0.11

One Sample : Phase

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Spectrum Parameters

5 days RINEX files considered in the analysis

S4 > 0.2 & sigma phi < 2 (filter convergence)

2 parameters to define the spectrum : T (1 Hz value) & p

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

3

4

5

slope Power spectrum

3

4

5slope phase spectrum

Slope spectrum vs time after sunset

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

1

2

3

0 2 4 6 8 10 12 14

p

Time after sunset

0

1

2

3

0 2 4 6 8 10 12 14p

Time after sunset

Phase varianceTime domain vs frequency domain

Slope set to 2.8

1) p (if )1(

2

12 2 )( 2

1

12 >

−=

+−=== −

∞+−∞−

∞

∫∫ p

fc

p

fc

p

fc fcp

T

p

fTdffTdffPSDphiσ

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Slope set to 2.8

Medium Characterization(Correlation Function)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Isotropic

1D

Anisotropic

2D Analysis : Isotropic Medium

LOS

C∫∫

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

( ) d ) . j ( exp ) (

2

C )( B

2P ∫∫ ΚΚ−Κ= ΦΦ ργ

πρ

( ) L L r (0) B 2Ne0

2e

2 σλσ == ΦΦ

[ ] ( ) ( ) ( )0 ) 2 / 2) (p ( ) 2 / 2) (p (

02 / 4) (p

2

iso q K q 2 / 2) (p 2

)( B ρρσρ −−

−Φ

Φ −Γ=

1D AnalysisIsotropic Medium

LOS

∫ −= dk ) k j ( exp k) ( C

)( B P ργρ

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

∫ −= ΦΦ dk ) k j ( exp k) ( 2

C )( B P ργ

πρ

[ ] ( ) ( ) ( )0 2 /1) p (2 /1) p (

0p 1

02 /3) p (P

1D q K q q 2 / p 2

2

C )( B ρρπ

πρ −

−−−Φ Γ

=

1D vs Isotropic

p � p - 1

Slope

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Multiplicative factor

( )( )( )

2 / p

2 / 1 p 2

Γ−Γ

π

Anisotropic vs Isotropic

( )( ) q K C q K B KA

C b a )(

2 /p 20

22y y x

2x

P

+++=Κ

⊥⊥⊥⊥

Φγ

( )( )

q q

b a C L r )(

2 /p 20

2

2NeS

2e

+=ΚΦ

σλγLOS

B field

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Additional geometric factor with respect to the 2D case ( ) 2 / 1 2 4/B CA

b a G

−=

a, b ellipses axes

A, B, C trigonometric terms resulting from rotations related to variable changes

Phase Synthesis(1D)

( ) )k ( * )u ( FFT FFT )( 1 Φ

−=Φ γρ

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

u random number with a uniform spectral density

Done at each successive layer

Frequencyband

Medium parameters(1)

Phase variance(2) Aliasing(3) Propagation

P450 MHz

RMS = 20 %( )

( ) 2Ne0

2e

2 L z r σλσ ∆=Φ2 L

z L

0

Φ>σλ

λ x L 2

z ∆<∆

1.41 2 =Φσ

1.19 =Φσ

m. 822 L> km 52 z <∆

m. 3.3 x =∆

m. 2500 L =m. 500 L0 =

312 e m / el 10 N = 1 ;3.10 5 == Φσz

Numerical Constraints

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

L1.5 GHz

RMS = 20 %( )

S2.5 GHz

RMS = 20 %( )

m. 500 L0 =312

e m / el 10 N =1 ;3.10 5 == Φσz

m. 2500 L =

m. 500 L0 =312

e m / el 10 N =0.12 2 =Φσ

0.36 =Φσ

m. 58 L>

1 ;3.10 5 == Φσz

km 221 z <∆

pts) 1024 : (FFT

m. 4.88 x =∆

0.05 2 =Φσ

0.22 =Φσ

m. 15 L> km 032 z <∆

m. 2500 L =

pts) 1024 : (FFT

m. 4.88 x =∆

Sub Models(1 / 2)

Seasonal Dependency

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

(Low Latitude Scintillations)

Seasonal Dependency

Scintillation EventsHistograms

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

1

1.2

1.4

1.6

S4 vs Day of year 2012 Lima

Scintillation Events / Lima 2012

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350

S4

Doy

Measurements in Malindi, Kenya

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

600

800

1000

Koudougou (Burkina Fasso)Geographic Latitude : 12°15 / Magnetic Latitude : - 1°14

weakstrong

Num

ber

of E

vent

s

Measurements in Burkina Fasso

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

200

400

600

2011 2011 2011 2012 2012 2013

medium

Num

ber

of E

vent

s

year

Sub Models(2 / 2)

Local Time Dependency

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

(Low Latitude Scintillations)

Local Time Dependency

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Intensity standard deviation (S4)all satellites: week 10/11/2006 to 15/11/2006

S4

0

0.2

0.4

0.6

0.8

1

S4 all satellites days 314 to 319 / year 2006

PRN2PRN13PRN10PRN4PRN24PRN28PRN17PRN12PRN8PRN29PRN26PRN9PRN6PRN23

One week of measurements in Guiana

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0.2

0 4 8 12 16 20 24

Local Time (hours)

0

-40 -20 0 20 40 60 80 100

GPS Week Time (hours)

Local time : post sunset hours (CLS measurements, PRIS Campaign)

Checking Results

� Indices

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

� Probability of intensity

� Fades distribution

� Loss of Lock

� Inter frequency correlation

Medium Characterisation

Mean Effects (Sub Models)

NeQuick, Terrestrial Magnetic Field (NOAA)

Geophysical Parameters

SSN, Medium Drift Velocity

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Scintillations (Fluctuating medium)

SSN, Medium Drift Velocity

Spectrum slope (p), BubblesRMS, OuterScale (L0)

Anisotropy ratio

LT & Seasonal dependency

Numerical Implementation

Inputs

Medium Characterisation

Geophysical Parameters

Scenario

The model includes an orbit generator (GPS, Glonass, Galileo, …)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Outputs

Scintillation indices

Correlation Distances (Time & Space)

Scenario

Intermediate calculation : LOS, Ionisation along the LOS

Scattering function

Signal at receiver level

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0.2

0.4

0.6

0.8

1

S4 all satellitesCayenne days 314 to 319 : year 2006

PRN2PRN13PRN10PRN4PRN24PRN28PRN17PRN12PRN8PRN29PRN26PRN9

S4

Modelling vs Measurements(Intensity)

Measurements

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

0.2

-40 -20 0 20 40 60 80 100

PRN9PRN6PRN23

LT

0

0.2

0.4

0.6

0.8

1

18 19 20 21 22 23 24 25

Cayenne day 314 / 2006GISM

132327817284102429226596

S4

LT

Modelling

0.2

0.4

0.6

0.8

1

Sigma Phi all satellitesCayenne, days 314 to 319 / year 2006

PRN2PRN13PRN10PRN4PRN24PRN28PRN17PRN12PRN8PRN29PRN26PRN9

Sig

ma

Phi

(ra

dian

)Modelling vs Measurements

(Phase)

Measurements

The phase RMS value is slightly lower than the S4 value

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

0.2

0.4

0.6

0.8

1

18 19 20 21 22 23 24 25

Cayenne day 314 / 2006G ISM

132327817284102429226596

Sig

ma

phi

LT

0-40 -20 0 20 40 60 80 100

PRN9PRN6PRN23

LT

Modelling

Some samples exhibit high values (both measurements and modelling) due to the phase jumps

Scintillation Modelling vs Measurements

0.6

0.7

0.8

0.9

1

S4 Measurement in CayenneLatitude 4°8 Longitude 37°6 year 2011

0.6

0.8

1

S4 Calculated (GISM) in CayenneLatitude 4°8 Longitude 37°6 year 2011

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Measurements Modelling

0.2

0.3

0.4

0.5

0 50 100 150 200 250 300

Doy

0.2

0.4

0 50 100 150 200 250 300Doy

Scintillation Index Dependency on Frequency

0.6

0.7

0.8

0.9

1

Inter Frequency Correlation L1 vs L2(Modelling --> GISM)

S4

(L2)0.8

1

1.2

1.4

Galileo satellites

S4

(E5a

)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0.2

0.3

0.4

0.5

0.6

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S4

(L2)

S4 (L1)

using Yuma files

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1

S4

(E5a

)

S4 (L1)

Global Maps

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

TEC Map Modelling Scintillation Map Modelling

Inter Frequency Correlation

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Inter Frequency Correlation

0

5

10

15

Tahiti Galileo N° 12 doy 85 / 2013S4(L1) = 0.59 ; S4(E5a) = 1.36

L1E5a

dB

-2

0

2

4

Tahiti Galileo N° 12 doy 85 / 2013S4 (L1) = 0.21 ; S4 (E5a) = 0.36

L1E5a

dB

Weak scintillations vs strong scintillations

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

-15

-10

-5

2340 2350 2360 2370 2380 2390 2400

Time (s.)

-6

-4

-2

420 430 440 450 460 470 480

Time (s.)

Inter Frequency Correlation TimeUsing 1 week of measurements in Tahiti

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

-5

0

5

10

Frequency correlation predicted by GISM

dB

0

1

2

3

Inter Frequency Correlation

S4 (L1) = 0.18S4 (L2) = 0.22

Frequency Correlation(Modelling)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

-20

-15

-10

-5

0 20 40 60 80 100 120

S4(L1) = 0.7S4(L2) = 0.8

dB

Time (s.)

-4

-3

-2

-1

0

0 50 100 150 200 250 300

dB

Time (s.)

Weak scintillations Strong scintillations

Loss of Lock

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

2.5

3

3.5

probability of intensityTheoretical (Nakagami distribution) vs Measurements

S4 = 0.2S4 = 0.3S4 = 0.4S4 = 0.5

+=Φ

I )n / (c 2

1 1

I )n / (c

B n 2

T ησ

The phase noise is related to the Intensity of the received signal

Loss of Lock when σφ > threshold value

Probability of Loss of Lock

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

0.5

1

1.5

2

2.5

-10 -5 0 5

S4 = 0.5S4 = 0.2S4 = 0.3S4 = 0.4S4 = 0.5

dB

+=Φ I )n / (c 2

1 I )n / (c

00

T ησ

p(I) Nakagami distributed

p(σφ) > threshold valueProbability of Loss of Lock is

Loss of Lock(Measurements in Tahiti)

0

5

10

Loss of Locks L2 / strong scintillations

L1

L2

Inte

nsity

(dB

)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

-20

-15

-10

-5

2400 2500 2600 2700 2800 2900 3000

Inte

nsity

(dB

)

Time (s.)

S4 (L1) = 0.44S4 (L2) = 0.69

S4 (L1) = 0.52S4 (L2) = 1.26

S4 (L1) = 0.68S4 (L2) = 0.68

S4 (L1) = 0.49S4 (L2) = 0.87

S4 (L1) = 0.55S4 (L2) = 0.76

S4 (L1) = 0.55S4 (L2) = 0.76

1 2 3 4 5 6

Loss of LockMeasurements vs Modelling

8

10

12

Number of Loss of Lock on L2(Measurements)

0 .2

0 .2 5

0 .3

P ro b a b ility o f lo s s o f lo c k

C / N = 4 2 d B C / N = 3 7 d B C / N = 3 2 d B C / N = 2 8 d B

Modeling

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

2

4

6

0 0.5 1 1.5S4 (L2)

0

0 .0 5

0 .1

0 .1 5

0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1

s 4

3 days of analysis in Tahiti

Geographical Extent

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Simultaneous Scintillation

5

6

7

8Lima 2012

weakmediumstrong

Num

ber

of

Sat

ellit

es

6

8

10Lima 2012

weakmediumstrong

Num

ber

of s

atel

lites

Number of Satellites SimultaneouslyCorrupted by Scintillation

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

1

2

3

4

5

0 20 40 60 80 100 120

Num

ber

of

Sat

ellit

es

Day number

0

2

4

6

200 250 300 350

Num

ber

of s

atel

lites

Day number

Probability of intensity / Modelling

intensity fluctuationss4 = 0.73

-10

0

10

0 100 200 300 400 500

dB

probability of intensity fluctuationss4 = 0.73

0,1000

1,0000

10,0000

-30 -20 -10 0 10

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

-40

-30

-20

s.

dB

Nakagami law ) A m - ( exp ) m (

A m 2 A) ( p 2

1 - m 2m

Γ=

24S / 1 m =with

0,0001

0,0010

0,0100

dB

numerical

Nakagami

GISM output

1.Real

data

Fades Statistics

Example of equatorial scintillation in Ascension Island, in solarmax conditions (2001)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

data

2.GISM

simulation0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

10

20

30

40

50

experimentaltheoretical

fading duration histogram

mc95mc

0 10 20 30 40

10

20

30

40

50experimentaltheoretical

fading times histogram

mi

Probability of intensity / Modelling

Nakagami vs measurements

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Radar Observations

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Mutual Coherence Function

Correlation distance vs LSAR

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Le Synthetic Aperture Length � 10 km

Ionosphere Effects

L ∆

SAR

Free Space Resolution y x ∆∆

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

'y ∆

x'∆

L ∆

y ∆

x∆

Ionosphere Effects

'y ∆ Turbulence Effect

' x ∆ Pulse broadening (dispersion)

L ∆ Group Delay

Two Points - Two FrequenciesCoherence Function

) , k , z ( U) , k , z ( U ) , , k , k , z ( 22*21112121 ρρρρ =Γ

0 ) , z , k ( ) ( D ) 0 ( A k

k

k 8

k

k

k

2

j

z d2

2d

2

4p2

d2d =Γ

++∇−

∂∂ ρρξξ

Using the parabolic equation

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

kk 8k2z 20

20

20

∂

Same process than previously : propagation 1st & 3rd terms ;Diffraction : 2nd & 3rd terms

[ ] ) ( B ) 0 ( B 2 ) , z ( D ρρ ΦΦΦ −=The structure function is quadraticwith respect to the distance

Two Points - Two FrequenciesCoherence Function

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

) , k , z ( U) , k , z ( U ) , , k , k , z ( 22*21112121 ρρρρ =Γ

Solution (one single screen)

Scattering � 2 constants

2

2

2 B

ωσ Φ=

( )20

i021

2

L 6

) / L ( Log S

lLΦ= σ

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

* Nickisch, RS 92, Knepp & Nickisch, RS, 2010

Propagation � 1 constant

0L 6

−

+=

1212 L

1

LL

1

k c 2

1 P

One Single Screen

K xτ K and x

Analytical solution

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

( )

B 4

P K z exp

S 4

K z exp

S B 2

z ) z , K , (

2 2x

22x

2

x

+−

−=Γ ττ

Spreading Extent

A P S 4 KMax K 2 =→= τ

B A 2 0 K 1 =→= τ

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

K = 0

τ

K

Spread factor

B

P S A 2 Q

1

2 ==ττ

Spreading Extent

10 MHz

Very large value of Q

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

100 MHz

435 MHz

Large value of Q

Q around 1

Rogers, N., P. Cannon, and K. Groves, Measurements and simulations of ionospheric scattering on VHF and UHF radar signals: Channel scattering function, Radio Sci., 44, RS0A33, DOI: 10.1029/2008RS004033, 2009.

Analytic vs Numerical

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Several ScreensRefined Analysis

� The algorithm can easily be generalized

� Different statistical properties may be assigned to the different layers

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

� Different statistical properties may be assigned to the different layers

� Numerical FFT (1D) shall be performed to get the coherence function

Ambiguity Function

dt ) r t,( f ) r t,(g ) r r, ( n 0*nn

nn0 ∑ ∫=χ

( ) ( )( ) ωωωωωχ d j exp ) j ( exp 1

) r , r ( 2

∫ Φ−−Φ−−Φ=

ng is the received signal and fn is the matched filter

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

( )( ) ( )( ) ωωωωω

πχ d j exp ) j ( exp

r 4

1 ) r , r ( 2

201002

n

n 0nn ∫ Φ−−Φ−−Φ=

( )( )

( )( )

( ) r / L k cin r 4

exp d

r 2 r k j 2 exp

r 4

exp ) r ,r ( 0e02

0

22 /Le

2 /Le 0

2

0020

2

0 ρπ

σρρπ

σχ sΦ−

Φ −=

+

−= ∫

An attenuation factor on the coherent component is included

Value of Coherent field received

Coherent Length

It is given by function ( )( ) r / D B exp S

D )r , , ( 2

02dd ρωρω −−=Γ

50

60

8000

1 104

Phase Standard Deviation and related Coherent Lengthin the case of strong fluctuations (red lines) & very stro ng fluctuations (blue lines)

Sigma Phi

Sigma Phi

Coh Length (m.)

Coh Length (m.)

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

10

20

30

40

0

2000

4000

6000

0 0,5 1 1,5 2 2,5

Sig

ma

Phi

(ra

dian

s) Coh Length (m

.)

f (GHz)

Positioning Errors

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

Positioning Errors

Modelling

S4 measured for each tracked satellite

στ

is calculated taking the thermal noise as the main contribution

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

GPS constellation simulated with a yuma file

Range error calculated assuming a gaussian distribution

GPS Positioning Errors

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

0,2

0,4

0,6

0,8

1

1,2

1,4

22 23 24 25 26 27 28

s4Moy s4Max

4

6

8

10

12

nbSatPositioning errors from Measurements in

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

0

2

4

22 23 24 25 26 27 28

-0,0006

-0,0004

-0,0002

0

0,0002

0,0004

0,0006

22 23 24 25 26 27 28

utc (hour)

degr

ees

Longitude error Latitude error

Measurements in Brazil in 2001

Conclusion

� Reasonable agreement between modelling (GISM) and measurements

� Positioning errors due to scintillations may reach values up to 50 meters

African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014

� All results will be updated taking measurements campaign data into account

� The azimuthal resolution of a SAR may be significantly decreased