Theoretical Simulations of GNSS Reflections from Bare and Vegetated Soils R. Giusto 1, L. Guerriero, S. Paloscia 3, N. Pierdicca 1, A. Egido 4, N. Floury 5 1 DIET - Sapienza Univ. of Rome, Rome DISP - University of Tor Vergata, Rome 3 CNR/IFAC, Sesto Fiorentino 4 Starlab, Barcelona 5 CNR/IFAC, Rome URSI Comm. F 010 Florence, October 5-8, 010 1
Content Introduction: the Leimon project Simulator description General formulation SW Structure Models and algorithms Simulator output examples Simulator validation during Leimon GNSS-R 010 Barcelona, October 1-, 010
Leimon Project ESA funded the LEIMON project aiming at evaluating the potential of GNSS signals for remote sensing of land bio-geophysical parameters, through a ground based experimental campaign (see previous presentation) developing a simulator to theoretically explain experimental data and predict the capability of airborne and spaceborne GNSS-R systems for moisture and vegetation monitoring GNSS-R 010 Barcelona, October 1-, 010 3
The Bistatic Radar Equation The mean power of received signal vs. delay τ and frequency f is modeled by integral Bistatic Radar Equation which includes time delay domain response Λ (τ τ) and Doppler domain response S (f -f ) of the system (Zavorotny and Voronovich, 000). T P G G S f f Y f i Tλ T RΛ ( τ ' τ ) ( ' ) 0 ( ˆ, τ ˆ) = σ da 3 (4π ) R R Y Processed signal power at the receiver vs. delay τ and frequency f. P T The transmitted power of the GPS satellite. G T, G R The antenna gains of the transmitting and the receiving instrument. R R, R T The distance from target on the surface to receiving and transmitting antennas. T i The coherent integration time used in signal processing. σ Bistatic scattering coefficient Λ The GPS correlation (triangle) function S The attenuation sinc function due to Doppler misalignment da Differential area within scattering surface area A (the glistening zone). GNSS-R 010 Barcelona, October 1-, 010 4 R T
The BRE integration function of point scattering delay Ti PT GT GR S f f 0 Y f λ Λ ( τ ' τ ) ( ' ( ˆ, τ ˆ) = ) σ da 3 (4π ) R R function of incidence direction function of point scattering Doppler function of point looking direction wrt boresight In order to solve the integral we have to introduce the equations relating all those variables to the coordinates over the surface. R T Integrand variables are the coordinates defined on the surface function of point bistatic angle (zenith function of point and azimuth) wrt RX and TX position GNSS-R 010 Barcelona, October 1-, 010 5
Local vs global frames RX z z θ s =θ i θ i y TX Earth ellipsoide Earth surface y λ SP=[x s,y s,z s ] ECEFF Elliptic Earth approximation x y z local frame centered in the specular point z axes along the geodetic vertical x z plane coincident with the bistatic scattering plane x x Given RX and TX trajectory/velocity & epoch, integral is computed in the local frame, where soil/vegetation parms are defined GNSS-R 010 Barcelona, October 1-, 010 6
Simulator structure Bistatic σ of each point combined by Receiver BRE on a regular GPS orbit grid position database Time of delay and Doppler shift Receiver polarization accounted for by polarization synthesis using real antenna polarization Geometry Receiver antenna gain described as function of the point Module looking angle assuming a cosinusoidal pattern Target type Range of target parameters C/A Code ID Spacecraft position/ velocity Specular Point position Range of target parameters Vegetated target model Identification of the point of specular reflection from epoch and PRN code. Delay-Doppler map Scattering Peak coefficient Simulator Computation of positions and velocities of transmitter and receiver in a local frame x'y' above the surface Computation of scattering direction, ranges from receiver to point, and Doppler shift for each Delay-Doppler point x'y' maps Peak amplitude of the local frame within antenna FOV. Bare soil target model Scattering coefficient GNSS-R 010 Barcelona, October 1-, 010 7
Electromagnetic modelling Absent or homogeneous vegetation cover. Attenuation and multiple scattering by a discrete medium (Tor Vergata model) Indefinite mean surface plane with roughness at wavelength scale. Bistatic scattering of locally incident plane waves by AIEM COHERENT component INCOHERENT component Scattering of spherical wave by Kirchoff approxi. (Eom & Fung, 1988) GNSS-R 010 Barcelona, October 1-, 010 8
Simulator output examples Intermediate product: Scattering zenith angles isodoppler and isorange lines on the surface RX antenna footprint Scattering azimuth angles H RX =10 km V RX =180 m/s Head RX =0 HPBW=10 GNSS-R 010 Barcelona, October 1-, 010 9
AIEM vs scattering direction θ s,ϕ s θ i =31 m v =0 % σ z =1.5 cm l=5 cm H RX =10 km HPBW=10 Incoherent component RR & LR more spread Coherent component RR & LR focused around specular θ s =31 150 100 50 0 150 100 50 0 0.004 0.003 0.0015 Sigma RR inco ( PH s TH s plane ) 0.00 Sigma RR cohe ( PH s TH s plane ) 0.00 0.001 0.005 0.006 0.0005 0.001 0.008 0.009 0.01 0.005 0.003 0.0035 0.007 0.0015 0.00 0.003 0.00 0.004 0.0035 0.003 0.005 0.00 0.001 0.004 0 40 60 80 0.0035 0.00450.005 0 40 60 80 0.003 0.004 GNSS-R 010 Barcelona, October 1-, 010 10 0 5 150 100 50 0 150 100 50 0 0.4 0. Sigma LR inco ( PH s TH s plane ) Sigma LR cohe ( PH s TH s plane ) 0. 0.15 0.35 0.8 0.3 0.4 1 0.5 0.6 0. 0 40 60 80 0.4 0. 0 40 60 80 0.1 0.05
θ i =31 m v =0 % σ z =1.5 cm l=5 cm H RX =10 km HPBW=10 Bistatic scattering in local frame Incoherent component RR & LR more spread Coherent component RR & LR focused around specular 0,0 1.5 x 104 1 0.5 0-0.5-1 1.5 x 104 1 0.5 0-0.5-1 0.003 0.00 0.001 0.005 0.005 0.00 0.003 0.004 0.005 0.006 0.007 0.008 0.008 0.007 RR cohe ( XY local plane ) 0.009 0.01 RR inco ( XY local plane ) 0.011 0.006 0.005 0.0015 0.0035 0.003 0.005 0.00 0.004 0.003 0.00 0.001 0.00 0.0005 0.001 0.005 0.001 0.0015 0.00 0.005-1.5-1 0 1 X axis [meters] x 10 4-1.5-1 0 1 X axis [meters] x 10 4 GNSS-R 010 Barcelona, October 1-, 010 11 Y axis [meters] Y axis [meters] 1.5 x 104 1 0.5 0-0.5-1 1.5 x 104 1 0.5 0-0.5-1 0.8 0.6 1 0.4 0. 0.5 LR inco ( XY local plane ) 0. 0.5 LR cohe ( XY local plane ) 0.8 1. 0.15 0. 0.15 0.6 0.3 0.35 0.4 0.4 0.1-1.5-1 0 1 X axis [meters] x 10 4 0. 0.1-1.5-1 0 1 X axis [meters] x 10 4
DDM output example DDM s (delay on the horizontal axes, frequency on the vertical axes) for incoherent (top) and coherent (bottom) component at RHCP (left) and LHCP (right) airbone incoherent Spaceborne incoherent GNSS-R 010 Barcelona, October 1-, 010 1
Peak power output example m v =0 % σ z =1.5 cm l=5 cm H RX =10 km V RX =180 m/s Head RX =45 HPBW=10 Coherent and incoherent RR & LR peak power as the satellite moves along the orbit RR inco [db] RR cohe [db] RR inco [db] Scattered Power Vs. Angle [degs] -8-30 -3-34 -36-38 -40 0 0 40 60 80 Angle of incidence [degs] RR cohe [db] Scattered Power Vs. Angle [degs] -15-0 -5-30 -35-40 -45 0 0 40 60 80 Angle of incidence [degs] LR inco [db] LR cohe [db] LR inco [db] Scattered Power Vs. Angle [degs] -1-14 -16-18 -0 - -4-6 0 0 40 60 80 Angle of incidence [degs] LR cohe [db] Scattered Power Vs. Angle [degs] -11-1 -13-14 -15-16 -17 0 0 40 60 80 Angle of incidence [degs] GNSS-R 010 Barcelona, October 1-, 010 13
Simulator vs Leimon data In the Leimon experiment the instrument records the complex direct and reflected waveforms and temporal series of the waveform peaks. In the following the mean reflected power normalized to the mean direct power at LR signal will be studied vs. the incidence angle Different soil parameters and different vegetation conditions are investigated W 5 1 3 4 E 6 GNSS-R 010 Barcelona, October 1-, 010 14
Validation: angular trend April 8th SMC=30% East field σ Z =3cm West field σ Z =1.75cm August 6th SMC=10% East σ Z =0.6 cm West σ Z =1cm Simulator reproduces quite well LR signal at incidence angles 45. GNSS-R 010 Barcelona, October 1-, 010 15
Coherent vs. incoherent: soil April 8th SMC=30% East σ Z =3cm August 6th SMC=10% East σ Z =0.6 cm Theoretical simulations show that incoherent component contributes mainly to total signal when soil is rough. GNSS-R 010 Barcelona, October 1-, 010 16
Overall comparison Bare Soils 10%<SMC<30% 0.6<σ z <3cm RMS 1 db disregarding observations at 55 GNSS-R 010 Barcelona, October 1-, 010 17
SMC sensitivity Power difference between soils at different SMC s Rough soil April 8th SMC=30% May 8th SMC=17% Smooth soil July 10th SMC=% August 6th SMC=10% db for a 13% SMC difference GNSS-R 010 Barcelona, October 1-, 010 18
Vegetation Sensitivity Blue=Leimon experimental data Magenta= Simulator data 35 The model trend reproduces the measured one and it falls within the experimental error bars The sensitivity to vegetation is quite low: about db for the whole PWC range GNSS-R 010 Barcelona, October 1-, 010 19
Coherent vs Incoherent: vegetation At 35, the coherent component is attenuated by about 1 db each 1kg/m. This trend is in agreement with works reported in the literature for attenuation at L-band for corn plants (Ulaby et al., 1983; Jackson et al., 198; O Neill, 1983) The Simulator predicts a quite large incoherent component which explains the saturation effect with PWC in the data. The model trend reproduces the measured one although the model is not able to reach the experimental values GNSS-R 010 Barcelona, October 1-, 010 0
Conclusions A simulator has been developed which provides DDM s or waveforms of a GNSS-R system looking at bare or vegetated soils (LHCP and RHCP real antenna polarization) It takes in input for a given range of epochs, arbitrary receiver position/velocity, in view GPS satellite PRN code, surface properties (soil moisture, roughness, vegetation parameters). It singles out coherent and incoherent signal components coming from land with variable soil moisture, roughness, vegetation parameters. Simulator results and experimental data show a fair agreement at LR polarization and angles <45 (the antenna beamwidth) The incoherent component may be high in the ground based Leimon configuration Sensitivity to SMC is significant and well reproduced Sensitivity to Vegetation is reproduced and it is quite low because of the coherent and incoherent combination. GNSS-R 010 Barcelona, October 1-, 010 1
Real antenna polarization Scattering cross section for an arbitrary combination of transmitted (incidence) and received (scattered) polarizations is provided by polarization synthesis = 4 r πr P r BSA t BSA svv s rec vh σ rt = 4π p S p S = t P inc shv shh Nominal polarization unit vector are p RHCP =(θ 0 -jφ 0 )/ and p LHCP =(θ 0 +jφ 0 )/ cos θ0 jφ RHCP 0 Real antenna polariz. unit vector p = 1+ cos θ SCS of real antennas σ σ RR LR 4π = 1+ cos 4π = 1+ cos θ θ cosθ cos θ S j j cosθ cos θ S + j j GNSS-R 010 Barcelona, October 1-, 010 z P=r,θ,ϕ orthogonal dipoles π/ phase shifted x y