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:

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 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

fsfs fsfs fsfs cici CkCk r i IF r IF (t)r(t) sin(ω L1 t) cos(ω s d t+Φ s ) CA(t-τ s ) => In the next (3 slides) we report the detections “c i ” for a period of code (1 ms) and the sum “C k ” (maximum value of correlation) as a function of the Doppler. Problem Statement 11 “C k ” 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.

Problem Statement 12 “c i ” takes the value one when a sample of the received signal has the same sign than the local signal. “c i ” takes the value minus one there is a difference between the sign of the received and the local signal.

Problem Statement 13

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 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 “c i ” and then “C k ” 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 15

Non-linear model Probabilistic model: Card{V} satellites case: => 16

Non linear filtering : State equations (alpha beta filter): Measurement equations (Observations of C k ): 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 Measurements equation of the correlation are highly non linear an EKF can not be used, the proposed solution is a particle filter Estimation 17

Particle Filter :  Initialization  Prediction  Update  Estimation  Multinomial Resampling Particles : x i 1,k x i 2,k Weights p i 1,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 18

=>Each ms the estimate Doppler, phase and code delay are used as input in the filter, to construct with the predicted state of A v,k a predicted observation compared to C k. =>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. Messages of navigation t [ms] Weights (6 satellites) Particles Estimation 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 -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: 20

Experimentation Random evolution due to : the code inter-correlation The carrier evolution 21

22 Experimentation

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 Hz Satellite s2 : 3000 Hz Jitter noise model : phase : random walk σ=0.01 frequency : random walk σ=0.1 Code delay : linear evolution Experimentation

24 Experimentation SNR [dBHz]Satellite 1Satellite 2 Theoretical (Real) Proposed estimate Classical estimate (2s) Estimate C/N 0 : Estimate parameters (Sat 1):

Experimentation 25 Error (Mean/Std)Satellite 1Satellite 2 Proposed estimate(0.7/1) Classical estimate (20 ms)(3.7/1.6)(3.6/1.7) Error of estimation of C/N 0 : 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