An Efficient Algorithm to the Simulation of Delay–Doppler Maps of Reflected Global Navigation Satellite System Signals

Simulating GNSS-R Delay-Doppler Map of Oil Slicked Sea Surfaces Under General Scenarios

“…It should be noted that the scattering coefficient of the oil slick, compared with that of the clean ocean surfaces, decreases more rapidly when the scattering point moves away from the SP, because the diffuse reflection becomes stronger and occurs more frequently on clean surfaces than oil contaminated areas. Although the glistening zone could be more than 400 km in diameter [14], the area of oil slick detection should be determined by the region where the scattering coefficients of oil slick are distinguishable. Fig.…”

“…Therefore, rather than conducting the convolution of WAF and Σ, multiplication of the Fourier transformations could be used to save time [14]. Then, by conducting the inverse Fourier transformation, DDM |Y (∆τ, ∆f )| 2 will be acquired.…”

A Generic Level 1 Simulator for Spaceborne GNSS-R Missions and Application to GEROS-ISS Ocean Reflectometry

“…Certainly, this approach becomes too much time and resource consuming for spaceborne mission simulations because the size of the observed surface (glistening zone) extends over hundreds of kilometers. In [30], an efficient computation was proposed, which uses two dimensional convolution in the delay-Doppler (τ, f d ) domain instead of the double integrals in the spatial (x, y) domain. For the convolution approach, the basic DDM model equation has been re-formulated as…”

“…) denotes the product of scattering coefficient and its Jacobian determinant as described in [30]. Similarly, receiver effects are included in the fringe-washing function denoted byr eq (τ ) [32], and a noise term N (τ, f d ) is added.…”

“…To meet the requirements, the Remote Sensing Laboratory at the Universitat Politècnica de Catalunya (UPC) had developed a specific software tool called the PAU/PARIS End-to-End Performance Simulator (P 2 EPS) [28], built on the experience of the SMOS End-to-end Performance Simulator (SEPS) for ESA [29]. 2 The simulator has the following capabilities: 1) GNSS transmitting and receiving satellites orbit simulation, 2) Location of the specular reflection point and glistening zone (area where scattered power is collected), 3) Instrument modeling including instrument imperfections (antenna arrays, receivers, and correlator), 4) Sea surface scattering coefficient generation based on a global database of geophysical parameters, 5) Observables simulation: full Delay Doppler Maps (DDM) and waveforms (cut of DDM at a fixed Doppler shift) including observation geometry, obtained based on novel algorithm described in [30] highly optimized for computation time, 6) Graphical input/output user interface (GUI). With these capabilities, a complete generic GNSS-R space mission can be accurately simulated in a efficient and convenient manner.…”