Collaboration FST-ULCO

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


Received signal:


Received signal after integration :

6

With :


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


0 0.5 1

x 10-3

-1

-0.5

0

0.5

1

t [s]

Sam

ples

I i



0 0.5 1

x 10-3

-0.1

-0.05

0

0.05

0.1

t [s]

Sig

nal a

mpl

itude

[V]


0 0.5 1

x 10-3

-1

-0.5

0

0.5

1

t [s]

Sam

ples


value of Ik=18926


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


0 0.5 1

x 10-3

-1

-0.5

0

0.5

1

t [s]

Sam

ples

I i



0 0.5 1

x 10-3

-0.1

-0.05

0

0.05

0.1

t [s]

Sig

nal a

mpl

itude

[V]


0 0.5 1

x 10-3

-1

-0.5

0

0.5

1

t [s]

Sam

ples


value of Ik=19344


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:

=>

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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

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SOUTH

3 6 16

18

2127

Experimentation

Random evolution due to :

• the code inter-correlation

• The carrier evolution

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SATELLITE SKYPLOTNORTH

SOUTH

NORTH

SOUTH

NORTH

SOUTH

NORTH

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NORTH

SOUTH

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NORTH

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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

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NORTH

SOUTH

NORTH

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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

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• 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

http://www.ppt-vorlagen.de/

Documents

Collaboration FST-ULCO