Collaboration FST-ULCO
1
Context and objective of the work
Water level : ECEF Localization of the water surface in order to get a referenced water level.
Soil moisture : Measuring the degree of water saturation to prevent flood and measuring drought indices
- Interference Pattern Technique (Altimetry)- SNR estimation (Soil moisture)
Context : Wetland monitoring
Research topics :
2
Outline
• 1) Application context
• 2) Problem statement
• 3) Non-linear model
• 4) Estimation
• 5) Experimentation
3
Altimetry system:
Interference Pattern Technique
4
5
Interference Pattern Technique
Received signal:
Interference Pattern Technique
Received signal after integration :
6
With :
Interference Pattern Technique
We estimate with the observations of phase the antenna height :
7
Soil moisture estimation
The system is composed of :
• Two antennas with different polarization• A multi-channel GNSS receiver• A mast for ground applications
Estimation :
• Estimation with the SNR of the direct and reflected GPS signals
• Tracking assistance of the nadir signal with the direct signal
Problem : Weak signal to noise ratio for the nadir signal.
8
Values of the coefficient Γ and power variations as a function
of satellite elevation and sand moisture
- Roughness parameter- Fresnel coefficient
(elevation)
- Antenna gain- Path of the signal
Soil moisture estimation
9
Problem Statement
These applications, soil moisture estimation and pattern interference technique, used measurements of the SNR in order to respectively estimate the soil permittivity and the antenna height.
- A GNSS receiver provides measurements of the correlation. You can derive from themean value of the correlation the amplitude of the received signal. The amplitude is not normalized in this case.
- If you want to derive from these measurements the signal to noise ratio C/N0 , you must estimate its mean value and its variance :
-> So we have to derive the statistic of the correlation on a set of observations (to estimate two parameters).
=> In this work we propose to derive a direct relationship between the mean correlation value and the SNR of the received signal. We will define in this case a filter for the direct estimation of the SNR with the observations provided by the correlation.
10
fs fs fs
ci CkriIFrIF(t)r(t)
sin(ωL1 t)
cos(ωsd t+Φs) CA(t-τs)
=> In the next (3 slides) we report the detections “c i” for a period of code (1 ms) and the sum “Ck” (maximum value of correlation) as a function of the Doppler.
Problem Statement
11
• “Ck” is the maximum of correlation because the local code and carrier are supposed to be aligned with the received signal.
• We assume that signals are sampled and quantified on one bit. The sampled signal takes the values 1 or -1.
0 0.5 1
x 10-3
-0.1
-0.05
0
0.05
0.1
t [s]
Sig
nal a
mpl
itude
[V]
Received signal
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]
Sam
ples
Received signal (sampled)
0 0.5 1
x 10-3
0
0.5
1
1.5
2
t [s]
Sam
ples
I i
Signal after demultipleing and demodulation
0 0.5 1
x 10-3
-0.1
-0.05
0
0.05
0.1
t [s]
Sig
nal a
mpl
itude
[V]
Local signal (code*carrier)
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]
Sam
ples
Local signal (sampled)
value of Ik=20000
Doppler=800 Phase=0.7854
false detectiongood detection
Problem Statement
12
• “ci” takes the value one when a sample of the received signal has the same sign than the local signal.• “ci” takes the value minus one there is a difference between the sign of the received and the local signal.
0 0.5 1
x 10-3
-0.2
-0.1
0
0.1
0.2
t [s]
Sig
nal a
mpl
itude
[V]
Received signal
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]S
ampl
es
Received signal (sampled)
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]
Sam
ples
I i
Signal after demultipleing and demodulation
false detectiongood detection
0 0.5 1
x 10-3
-0.1
-0.05
0
0.05
0.1
t [s]
Sig
nal a
mpl
itude
[V]
Local signal (code*carrier)
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]
Sam
ples
Local signal (sampled)
value of Ik=18926
Doppler=3000 Phase=0.7854
Problem Statement
13
0 0.5 1
x 10-3
-0.2
-0.1
0
0.1
0.2
t [s]
Sig
nal a
mpl
itude
[V]
Received signal
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]S
ampl
es
Received signal (sampled)
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]
Sam
ples
I i
Signal after demultipleing and demodulation
false detectiongood detection
0 0.5 1
x 10-3
-0.1
-0.05
0
0.05
0.1
t [s]
Sig
nal a
mpl
itude
[V]
Local signal (code*carrier)
0 0.5 1
x 10-3
-1
-0.5
0
0.5
1
t [s]
Sam
ples
Local signal (sampled)
value of Ik=19344
Doppler=800 Phase=0.7854
Problem Statement
14
• For these examples we use a weak noise (small variance) and we can notice that the number of false detections increases with the Doppler. This effect is dueto the number of zero crossing of the curve. When the noise is strongerthe number of false detections increases also.
• In our work we define the statistic of “ci” and then “Ck” as a function of the amplitude, Doppler, delay of code and phase of the received signals.
• We can then compute the expecting function of correlation in the coherent or non coherent case. For this application only the maximum of the coherent value of correlation is considered.
Problem Statement
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Non-linear model
Probabilistic model:
Card{V} satellites case:
=>
16
Non linear filtering :
State equations (alpha beta filter):
Measurement equations (Observations of Ck):
Tracking process :- Each millisecond the tracking loop provides an estimation of phase, Doppler, and code delay for all the satellites in view- These estimate and the predicted state are used to construct predictedmeasurements-These measurements are compared in the filter with the observations of correlation provided by the tracking loops
Measurements equation of the correlation are highly non linear an EKF can not be used, the proposed solution is a particle filter
Estimation
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Particle Filter :
Initialization
Prediction
Update
Estimation
Multinomial Resampling
Particles : xi1,k xi
2,k Weights pi1,K i=1….N
Amplitude
Amplitude velocity
Initialization (inversion of the carrier less case)
Covariance of state and measure : tuning parameters
N(0,Q)
Estimation
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0 200 400 600 800 1000 1200 1400 1600 1800 2000-5000
05000
0 200 400 600 800 1000 1200 1400 1600 1800 2000-5000
05000
0 200 400 600 800 1000 1200 1400 1600 1800 2000-5000
05000
0 200 400 600 800 1000 1200 1400 1600 1800 2000-5000
05000
0 200 400 600 800 1000 1200 1400 1600 1800 2000-5000
05000
0 200 400 600 800 1000 1200 1400 1600 1800 2000-101
x 104
0 200 400 600 800 1000 1200 1400 1600 1800 2000-2000
02000
0 200 400 600 800 1000 1200 1400 1600 1800 2000-2000
02000
=>Each ms the estimate Doppler, phase and code delay are used as input in the filter,to construct with the predicted state of Av,k a predicted observation compared to Ck.
0 0.1 0.22
3
4
5
6
7
8x 10
-3
0 0.1 0.23
4
5
6
7x 10
-3
0 0.05 0.12
3
4
5
6
7
8x 10
-3
0 0.05 0.13
3.5
4
4.5
5
5.5
6x 10
-3
0.05 0.1 0.15 0.22
3
4
5
6
7x 10
-3
-0.1 0 0.12
4
6
8
10x 10
-3
=>The filter runs a set of particles for each satellite in view. The estimation is processed with the particles which act as the sampled distribution of the states.
Mes
sage
s of
nav
igat
ion
t [ms]
Wei
ghts
(6 s
atel
lites
)
Particles
Estimation
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Experimentation
We show with the proposed model :- Inter-correlation effect due to the satellites codes.- Inter-correlation effect due to the carrier
On the estimate value of the correlation
- The sampling period is 1 [ms].- The number of visible satellites is 6.- The amplitudes of the GNSS signals is 0.21 (50 [dBHz])
For these amplitudes the noise variance is 1 on the received signal.
Configuration of the experimentation:
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SATELLITE SKYPLOTNORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
3 6 16
18
2127
Experimentation
Random evolution due to :
• the code inter-correlation
• The carrier evolution
21
SATELLITE SKYPLOTNORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
3 6 16
18
2127
3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196
x 105
1100
1200
1300
1400
1500
1600
1700
1800
time [ms]
Ck
Evolution of Ck for the visible satellites : Code intercorrelation noise
3 616182127
3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196
x 105
800
1000
1200
1400
1600
1800
2000
time [ms]
Ck
Evolution of Ck for the visible satellites : Carrier noise
3 616182127
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ExperimentationSATELLITE SKYPLOT
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
NORTH
SOUTH
36
16
18
21
27
3 3.02 3.04 3.06 3.08 3.1 3.12 3.14
x 105
-500
0
500
1000
1500
2000
2500
3000
time [ms]
Ck
Evolution of Ck for the visible satellites
3 616182127
3 3.02 3.04 3.06 3.08 3.1 3.12 3.14
x 105
-10
0
10
20
30
40
50
60
70
80
90
time [ms]
Ele
vatio
n [d
eg]
Evolution of the elevation of the visible satellites
3 616182127
3 3.02 3.04 3.06 3.08 3.1 3.12 3.14
x 105
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
time [ms]
frequ
ency
[Hz]
Doppler frequency of the visible satellites
3 616182127
23
• Assessment on synthetic data
• The two satellites case• Static case and dynamic case
Model of simulation :
Goal of the experimentation :
Doppler frequency :Satellite s1 : 1000 HzSatellite s2 : 3000 Hz
Jitter noise model :phase : random walk σ=0.01 frequency : random walk σ=0.1
Code delay :linear evolution
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
2
4
6
8
time [s]
Pha
se [r
ad]
Sat s1Sat s2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-8
-6
-4
-2
0
2
4
time [s]
Dop
pler
var
iatio
ns [H
z]
Experimentation
24
Experimentation
SNR [dBHz] Satellite 1 Satellite 2Theoretical (Real) 37.6 48
Proposed estimate 38 47.9Classical estimate (2s) 33.5 44.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-400
-200
0
200
400
600
800
time [s]
Cor
rela
tion
I k
ObservationEstimationTheoretical
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.01
0.02
0.03
0.04
0.05
time [s]
Am
plitu
de A
s,k
Estimate C/N0 :
Estimate parameters (Sat 1):
Experimentation
25
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
time [s]
Am
plitu
de A
s,k
Estimate A1,k
Estimate A2,k
Theoretical value of A1,k
Theoretical value of A2,k
Error (Mean/Std) Satellite 1 Satellite 2Proposed estimate (0.7/1) (0.7/1)
Classical estimate (20 ms) (3.7/1.6) (3.6/1.7)
Error of estimation of C/N0 :
Estimate Amplitude :
Conclusion
26
*We state the problem of defining a link between the SNR and the amplitude of the GNSS signals.
*We propose a direct model of the maximum of correlation as a function of amplitude, Doppler, code delay and phase of the received signal.
*We propose to use a particle filter to inverse the non linear model.
*We access the model on synthetic data.
Thank You For Your Attention