GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29...
Transcript of GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29...
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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
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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
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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
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Ionosphere Variability
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
TEC Map S4 map cumulated over 24 hours
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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 =
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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
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Example of results / Solar Flux 150
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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Turbulent Ionosphere(scintillation)
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
(scintillation)
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Satellite signal
Drift
Physical Mechanism
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Receiver level
Drift velocity
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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
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Scintillation on Galileo SatellitesL1 vs E5a
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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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
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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
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Medium CharacterizationIndex Spectral Density
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Index Spectral Density
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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)
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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
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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
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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
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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
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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
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Medium Characterization(Correlation Function)
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Isotropic
1D
Anisotropic
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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=
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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
=
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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
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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
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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
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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 =∆
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Sub Models(1 / 2)
Seasonal Dependency
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
(Low Latitude Scintillations)
Seasonal Dependency
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Scintillation EventsHistograms
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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Measurements in Malindi, Kenya
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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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
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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)
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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
![Page 38: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/38.jpg)
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
![Page 39: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/39.jpg)
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
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Signal at receiver level
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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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
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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
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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)
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Global Maps
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
TEC Map Modelling Scintillation Map Modelling
![Page 46: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/46.jpg)
Inter Frequency Correlation
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Inter Frequency Correlation
![Page 47: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/47.jpg)
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.)
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Inter Frequency Correlation TimeUsing 1 week of measurements in Tahiti
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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-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
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Loss of Lock
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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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
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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
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Geographical Extent
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Simultaneous Scintillation
![Page 55: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/55.jpg)
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
![Page 56: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/56.jpg)
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
![Page 57: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/57.jpg)
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
![Page 58: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/58.jpg)
Probability of intensity / Modelling
Nakagami vs measurements
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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Radar Observations
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Mutual Coherence Function
![Page 60: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/60.jpg)
Correlation distance vs LSAR
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Le Synthetic Aperture Length � 10 km
![Page 61: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/61.jpg)
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
![Page 62: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/62.jpg)
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
![Page 63: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/63.jpg)
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
![Page 64: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/64.jpg)
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
![Page 65: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/65.jpg)
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
![Page 66: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/66.jpg)
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
![Page 67: GISM Global Ionospheric Scintillation Modelieea.fr/publications/ieea-2014-Kigali-GISM.pdfPRN8 PRN29 PRN26 PRN9 PRN6 PRN23 One week of measurements in Guiana African School on Space](https://reader030.fdocuments.net/reader030/viewer/2022040920/5e98060420084c5658550786/html5/thumbnails/67.jpg)
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.
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Analytic vs Numerical
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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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
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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)
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Positioning Errors
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
Positioning Errors
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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
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GPS Positioning Errors
African School on Space Science – Kigali, Rwanda – 30 june 2014 – 11 july 2014
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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
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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