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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
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