Vincent Fabbro

A duct mapping method using least squares support vector machines

This paper introduces a “refractivity from clutter” (RFC) approach with an inversion method based on a pregenerated database. The RFC method exploits the information contained in the radar sea clutter return to estimate the refractive index profile. Whereas initial efforts are based on algorithms giving a good accuracy involving high computational needs, the present method is based on a learning machine algorithm in order to obtain a real-time system. This paper shows the feasibility of a RFC technique based on the least squares support vector machine inversion method by comparing it to a genetic algorithm on simulated and noise-free data, at 1 and 5 GHz. These data are simulated in the presence of ideal trilinear surface-based ducts. The learning machine is based on a pregenerated database computed using Latin hypercube sampling to improve the efficiency of the learning. The results show that little accuracy is lost compared to a genetic algorithm approach. The computational time of a genetic algorithm is very high, whereas the learning machine approach is real time. The advantage of a real-time RFC system is that it could work on several azimuths in near real time.

Joint French-German radar measurements for the determination of the refractive index in the maritime boundary layer

To predict the performance of coastal and shipborne radars, it is essential to assess the propagation characteristics of electromagnetic waves in the maritime boundary layer. To be independent upon environmental measurements, which are generally not as precise and reliable as they have to be for a proper input to simulation programs, usually based upon parabolic equation models, a method to retrieve the refractive index gradients in the low troposphere is the Refractivity from Clutter (RFC) algorithm. The propagation factor is computed from the received clutter power and is iteratively processed in order to retrieve the refractive index profiles. Under a respective French-German technical agreement a measurement program concerning radar propagation in the maritime boundary layer has been initiated, with contributions from ONERA-CERT, DGA MI / TN, Fraunhofer-FHR and the German Technical Center for Ships and Naval Weapons (WTD 71). The paper gives an overview on the RFC method with examples from the previous campaigns. It describes the experimental set-up and its methodology.

Illuminated height PDF of a random rough surface and its impact on the forward propagation above oceans at grazing angles

When solving electromagnetic rough-scattering problems, the effect of shadowing by the surface roughness often needs to be considered, especially as the illumination angle thetas approaches grazing incidence. Indeed, due to the surface roughness, only a part of the surface is illuminated. This phenomenon is characterized by the statistical illumination function which gives the probability that a point on a rough surface is illuminated. In this paper, we propose to calculate the bistatic statistical illumination function for any one-dimensional random rough surface and to analyse its impact on the forward propagation above rough sea surfaces by considering Gaussian statistics and for grazing angles Phi of the order of one degree.

The GO-SSA Extended model for all-incidence sea clutter modeling

The GO-SSA-Extended model is an extension of the physical GO-SSA model with augmented range of validity. It is obtained through the addition of extra empirical terms. This improved model can predict the backscatter reflectivity from the sea surface for the full range of grazing and azimuthal angles. This model compares favorably with Xband experimental measurements (VV and HH polarization) acquired by the ONERA and DSTO.

Retrieve the evaporation duct height by least-squares support vector machine algorithm

The detection and tracking of naval targets, including low Radar Cross Section (RCS) objects like inflatable boats or sea skimming missiles requires a thorough knowledge of the propagation properties of the maritime boundary layer. Models are in existence, which allow a prediction of the propagation factor using the parabolic equation algorithm. As a necessary input, the refractive index has to be known. This index, however, is strongly influenced by the actual atmospheric conditions, characterized mainly by temperature, humidity and air pressure. An approach is initiated to retrieve the vertical profile of the refractive index from the propagation factor measured on an onboard target. The method is based on the LS-SVM (Least-Squares Support Vector Machines) theory. The inversion method is here used to determine refractive index from data measured during the VAMPIRA campaign (Validation Measurement for Propagation in the Infrared and RAdar) conducted as a multinational approach over a transmission path across the Baltic Sea. As a propagation factor has been measured on two reference reflectors mounted onboard a naval vessel at different heights, the inversion method can be tested on both heights. The paper describes the experimental campaign and validates the LS-SVM inversion method for refractivity from propagation factor on simple measured data.

Low grazing angle propagation above rough surface by the parabolic wave equation

In this communication, shadowing effects from rough surfaces are introduced in forward propagation computed by a parabolic wave equation (pwe) method. The discrete mixed Fourier transform is used, taking into account a surface impedance boundary condition. The surface impedance is computed from a rough surface reflection coefficient including shadowing effect at grazing angle. In the computation, shadowing is introduced through a shadowed distribution of the illuminated surface height.

Scintillation modelling in troposphere using Multiple Phase Screen

Microwaves propagation modelling in clear air troposphere i.e. without rain is investigated. Large scale variations of refractivity are computed from mesoscale meteorological modelling. Small scale variations are deduced from large scale considering that the inertial regime of Kolmogorov spectrum is established. The propagation effects are estimated applying launching ray to take into account large scale refractivity effects and resolution of Parabolic Wave Equation with Multiple Phase Screen technique for small scale. The proposed approach has been evaluated versus earth satellite measurements of log-amplitude scintillation measured at Louvain-la-Neuve.

Refractivity from sea clutter applied on VAMPIRA and Wallops’ 98 data

For coastal and ship-borne survey radars, coverage prediction is a critical question. In sea environment, the spatial variations in temperature conditions involve refractive index gradients and create atmospheric ducts. These events modify the radar coverage in the lower troposphere. A means to retrieve the refractive index gradients in the low troposphere is to use the Refractivity From Clutter (RFC). The principle of RFC is to compute the propagation factor from the radar received power, thus to process it in order to retrieve the refractive index profiles. In this paper, the RFC is applied on data obtained from VAMPIRA and Wallopspsila98 measurement campaigns. Since refractive index quickly varies, fast inversion methods based on a pre-generated database of propagation factors are used.

Parameter-Based Rules for the Definition of Detectable Ducts for an RFC System

Refractivity from clutter (RFC) consists in inferring the lower atmospheric conditions from the clutter measured by a coastal or shipborne radar. A data processing tool based on an inverse or optimisation method is required. However, RFC cannot be used to retrieve all the atmospheric conditions. For some refractivity conditions, the modification of the electromagnetic wave behavior in the low troposphere is not detectable on the radar clutter return. In this paper, analytic conditions are given for trilinear atmospheric ducts to be retrievable by an RFC system. The study is based on a ray approach, and the results are validated through numerical simulations. It is finally extended to any piecewise linear profile. In the context of decision analysis, an RFC system user should know which ducts can be detected.

Radar propagation modeling using the boundary integral equations in a maritime environment with a duct

One popular approach to solve the sea surface scattering and propagation in a ducting environment is the parabolic wave equation (PWE) method. An alternative method is the boundary integral equations (BIE) method. The implementation of the BIE in inhomogeneous media (ducting environments) is not straightforward, however, since the Greens function for such a medium is not usually known. In this paper, a closed-form approximation of the Greens function for a two-dimensional (2-D) ducting environment made up of a duct having a linear-square refractive index profile below a medium of constant refractive index, recently published, is used. This paper demonstrates how the BIE method can model the combined effects of surface roughness and medium inhomogeneity. Furthermore, it illustrates its capability of accurately predicting scattering in all directions including backscattering. Then, the PWE combined with the Split-Step Fourier (SSF) method is compared with this method.