GNSS Signals Amplitude estimation

```Collaboration FST-ULCO
1
Context and objective of the work
Context : Wetland monitoring
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
Research topics :
- Interference Pattern Technique (Altimetry)
- SNR estimation (Soil moisture)
2
Outline
• 1) Application context
• 2) Problem statement
• 3) Non-linear model
• 4) Estimation
• 5) Experimentation
3
Interference Pattern Technique
Altimetry system:
4
Interference Pattern Technique
5
Interference Pattern Technique
With :
6
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 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
Soil moisture estimation
- Roughness parameter
- Fresnel coefficient (elevation)
- Antenna gain
- Path of the signal
Values of the coefficient Γ and
power variations as a function
of satellite elevation and
sand moisture
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 the
mean 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
Problem Statement
r(t)
rIF(t)
sin(ωL1 t)
ci
riIF
fs
fs
Ck
fs
cos(ωsd t+Φs) CA(t-τs)
•“Ck” is the maximum of correlation because the local code and carrier are supposed to be
• We assume that signals are sampled and quantified on one bit.
The sampled signal takes the values 1 or -1.
=> In the next (3 slides) we report the detections “ci” for a period of code (1 ms) and the sum
“Ck” (maximum value of correlation) as a function of the Doppler.
11
Problem Statement
0.05
0.5
Signal after demultipleing and demodulation
2
false detection
good detection
1.5
0
-0.05
-0.1
Samples I
i
1
Samples
Signal amplitude [V]
0.1
0
-0.5
0
0.5
t [s]
-1
1
1
0.5
0
-3
x 10
Local signal (code*carrier)
0.5
t [s]
1
-3
x 10
0
0
0.5
t [s]
1
-3
x 10
Local signal (sampled)
0.1
1
0.05
0
-0.05
-0.1
Doppler=800 Phase=0.7854
0.5
Samples
Signal amplitude [V]
value of Ik=20000
0
-0.5
0
0.5
t [s]
1
-3
x 10
-1
0
0.5
t [s]
1
-3
x 10
• “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.
12
Problem Statement
0.1
0.5
Signal after demultipleing and demodulation
1
false detection
good detection
0.5
0
-0.1
-0.2
Samples I
i
1
Samples
Signal amplitude [V]
0.2
0
-0.5
0
0.5
t [s]
-1
1
0
-0.5
0
-3
x 10
Local signal (code*carrier)
0.5
t [s]
1
-3
x 10
-1
0
0.5
t [s]
1
-3
x 10
Local signal (sampled)
0.1
1
0.05
0
-0.05
-0.1
Doppler=3000 Phase=0.7854
0.5
Samples
Signal amplitude [V]
value of Ik=18926
0
-0.5
0
0.5
t [s]
1
-3
x 10
-1
0
0.5
t [s]
1
-3
x 10
13
Problem Statement
0.1
0.5
Signal after demultipleing and demodulation
1
false detection
good detection
0.5
0
-0.1
-0.2
Samples I
i
1
Samples
Signal amplitude [V]
0.2
0
-0.5
0
0.5
t [s]
-1
1
0
-0.5
0
-3
x 10
Local signal (code*carrier)
0.5
t [s]
1
-3
x 10
-1
0
0.5
t [s]
1
-3
x 10
Local signal (sampled)
0.1
1
0.05
0
-0.05
-0.1
Doppler=800 Phase=0.7854
0.5
Samples
Signal amplitude [V]
value of Ik=19344
0
-0.5
0
0.5
t [s]
1
-3
x 10
-1
0
0.5
t [s]
1
-3
x 10
14
Problem Statement
• 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 due
to the number of zero crossing of the curve. When the noise is stronger
the 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.
15
Non-linear model
Probabilistic model:
Card{V} satellites case:
=>
16
Estimation
Non linear filtering :
Measurements equation of the correlation are highly non linear
an EKF can not be used, the proposed solution is a particle filter
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 predicted
measurements
-These measurements are compared in the filter with the observations of
correlation provided by the tracking loops
17
Estimation
Amplitude
Amplitude velocity
Particle Filter :
Particles : xi1,k xi2,k Weights pi1,K i=1….N
Initialization
Initialization (inversion of the carrier less case)
Prediction
N(0,Q)
Covariance of state and
measure : tuning parameters
Update
Estimation
Multinomial Resampling
18
Estimation
-3
5000
0
-5000
5000
0
-5000
5000
0
-5000
5000
0
-5000
5000
0
-5000
1
0
-1
2000
0
-2000
2000
0
-2000
0
0
0
0
4
0
x 10
0
0
0
200
200
200
200
200
200
200
200
400
400
400
400
400
400
400
400
600
600
600
600
600
600
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600
800
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800
1000
1000
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1000
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1000
1000
1000
1200
1200
1200
1200
1200
1200
1200
1200
1400
1400
1400
1400
1400
1400
1400
1400
1600
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1600
1600
1600
1600
1600
1800
1800
1800
1800
1800
1800
1800
1800
2000
2000
2000
2000
2000
2000
2000
2000
Weights (6 satellites)
8
-3
x 10
7
-3
x 10
8
7
x 10
7
6
6
6
5
5
5
4
4
4
3
2
3
0
0.1
0.2
3
-3
6
0
0.1
0.2
2
-3
x 10
7
5.5
0
0.05
0.1
0
0.1
-3
x 10
10
6
x 10
8
5
5
4.5
6
4
4
3
4
3
3.5
0
0.05
t [ms]
0.1
2
0.05
0.1
0.15
0.2
2
-0.1
Particles
=>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.
=>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.
19
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
SATELLITE SKYPLOT
NORTH
Configuration of the experimentation:
3
-
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
27 6
16
21
18
SOUTH
20
Experimentation
SATELLITE SKYPLOT
NORTH
Random evolution due to :
• the code inter-correlation
3
27 6
16
• The carrier evolution
18
SOUTH
Evolution of Ck for the visible satellites : Code intercorrelation noise
Evolution of Ck for the visible satellites : Carrier noise
1800
1700
1600
21
2000
3
6
16
18
21
27
1800
1600
3
6
16
18
21
27
C
k
C
k
1500
1400
1400
1300
1200
1200
1000
1100
3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196
5
time [ms]
x 10
800
3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196 3.0196
21
5
time [ms]
x 10
Experimentation
Evolution of Ck for the visible satellites
SATELLITE SKYPLOT
NORTH
3000
3
6
16
18
21
27
2500
2000
18
21
C
k
1500
1000
3 27
6
500
16
0
SOUTH
-500
3
3.02
Evolution of the elevation of the visible satellites
3.06
3.08
time [ms]
3.1
3.12
3.14
5
x 10
Doppler frequency of the visible satellites
90
4000
3
6
16
18
21
27
80
70
3
6
16
18
21
27
3000
2000
frequency [Hz]
60
Elevation [deg]
3.04
50
40
30
1000
0
-1000
20
-2000
10
-3000
0
-10
3
3.02
3.04
3.06
3.08
time [ms]
3.1
3.12
3.14
5
x 10
-4000
3
3.02
3.04
3.06
3.08
time [ms]
3.1
3.12
3.14
5
x 10
22
Experimentation
Model of simulation :
8
Doppler frequency :
Satellite s1 : 1000 Hz
Satellite s2 : 3000 Hz
4
2
0
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
4
Doppler variations [Hz]
Jitter noise model :
phase : random walk σ=0.01
frequency : random walk σ=0.1
Code delay :
linear evolution
Sat s1
Sat s2
6
2
0
-2
-4
-6
-8
Goal of the experimentation :
•
Assessment on synthetic data
• The two satellites case
• Static case and dynamic case
23
Experimentation
Estimate parameters (Sat 1):
800
Observation
Estimation
Theoretical
Correlation I
k
600
400
200
0
-200
-400
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
Amplitude A
s,k
0.05
0.04
0.03
0.02
0.01
Estimate C/N0 :
SNR [dBHz]
Satellite 1
Satellite 2
Theoretical (Real)
37.6
48
Proposed estimate
38
47.9
Classical estimate (2s)
33.5
44.2
24
Experimentation
Estimate Amplitude :
0.16
Estimate A 1,k
Estimate A 2,k
0.14
Theoretical value of A 1,k
Theoretical value of A 2,k
0.12
Amplitude A
s,k
0.1
0.08
0.06
0.04
0.02
0
0
0.2
0.4
0.6
Error of estimation of C/N0 :
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
Error (Mean/Std)
Satellite 1
Satellite 2
Proposed estimate
(0.7/1)
(0.7/1)
Classical estimate (20 ms)
(3.7/1.6)
(3.6/1.7)
25
Conclusion
*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.