Report

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 Received signal: 5 Interference Pattern Technique Received signal after integration : 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 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 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 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. => 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 Received signal (sampled) 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] Received signal 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 Received signal (sampled) 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] Received signal 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 Received signal (sampled) 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] Received signal 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 0 200 200 200 200 200 200 200 200 400 400 400 400 400 400 400 400 600 600 600 600 600 600 600 600 800 800 800 800 800 800 800 800 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1200 1200 1200 1200 1200 1200 1400 1400 1400 1400 1400 1400 1400 1400 1600 1600 1600 1600 1600 1600 1600 1600 1800 1800 1800 1800 1800 1800 1800 1800 2000 2000 2000 2000 2000 2000 2000 2000 Weights (6 satellites) Messages of navigation 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 received signal. 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 Phase [rad] 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. Thank You For Your Attention 26