In recent years, wake vortex monitoring in real time has emerged as one of the key challenges in air trac control at landing or taking-o. In clear air, several experimental tests have demonstrated that Lidar is an eective sensor for wake vortex monitoring. In rainy weather, Lidar becomes blind and Radar is a candidate sensor to detect the motion of raindrops in wake vortices. Thus, investigation on radar monitoring of wake vortices in rainy weather is of both scientic and practical interests. This topic has been tackled through three successive steps during thisthesis. Firstly, the motion of raindrops in wake vortices has been modeled and simulated. The equation of the motion has been derived and the methodology to compute the raindrops' trajectory and distribution in the flow induced by the wake vortices has been proposed. Secondly, two simulators have been developed for evaluating the radar signatures of raindrops in wake vortices. One simulator is based on the simulation of radar signal time series, by superimposing the radar backscattered signal from each raindrop in the wake vortex region. The other one is based on the raindrops' number concentration and velocity distribution in wake vortices, enabling the computation of radar signatures much more eciently. Those simulators have been used to reproduce experimental configurations and the comparison between measured and simulated signature has shown an interesting agreement at X and W band. Lastly, the interpretation of radar signatures of raindrops in wake vortices has been presented. Based on the computation of three spectral moments, the dependence of radar signatures on rain rate, vortex circulation and radar parameters has been studied for vortices generated by different aircraft types. A wake vortex detection method based on the analysis of Doppler spectrum width of raindrops has been proposed. Considering radar scanning under flight path, a methodology to estimate the wake vortex characteristics has been proposed. Preliminary simulation results have shown its effectiveness. The radar signatures of wake vortices in rainy weather have been modeled and analyzed in this thesis. The simulation results have demonstrated the capability of radar to detect wake vortex in rainy weather. The methodologies developed in this thesis can be further exploited for designing new wake vortex radar systems.

Les dispositifs passifs ne sont pas parfaitement linéaires aux très fortes puissances. Ils créent des harmoniques et des produits d’intermodulation pairs et impairs. Ces produits peuvent perturber fortement les performances des récepteurs utilisant les mêmes équipements passifs ou simplement installés sur le même site que les émetteurs. Ces produits n’obéissent pas à la loi classique de croissance en fonction de la puissance d’entrée avec une pente en dB/dB égale à l’ordre du produit. Ceci a interdit, jusqu’à présent, de modéliser correctement ces dispositifs. On propose une modélisation par des fonctions non analytiques qui permet de mieux reproduire cette caractéristique avec un nombre minimal de coefficients et à partir d’un nombre minimal de mesures.

This paper presents a demodulation algorithm for automatic identification system (AIS) signals received by a satellite. The main contribution of this work is to consider the phase recovery problem for an unknown modulation index, coupled with a time-varying phase shift. The proposed method is based on a demodulator introduced in a previous paper based on a Viterbi-type algorithm applied to an extended trellis. The states of this extended trellis are composed of a trellis-code state and of a cyclic redundancy check state. The bit stuffing mechanism is taken into account by defining special conditional transitions in the extended trellis. This algorithm estimates and tracks the phase shift by modifying the Euclidean distance used in the trellis. Simulation results obtained with and without phase tracking are presented and compared in the context of the AIS system.

This paper focuses on the performance of time of arrival estimators for distress beacon signals which are defined by pulses with smooth transitions. These signals are used in the satellite-based search and rescue Cospas-Sarsat system. We propose a signal model based on sigmoidal functions. Closed-form expressions for the modified Cram´er-Rao bounds associated with the parameters of this model are derived. The obtained expressions are easy to interpret since they analytically depend on the system parameters. Simulations conducted on realistic search and rescue signals show good agreement with the theoretical results.

This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér–Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.

For precise positioning techniques, performance of phase lock loop (PLL) is of utmost importance since the estimated receiver’s position is intimately linked to phase measurement. Unfortunately, conventional PLLs suffer from a lack of noise robustness that is mostly due to cycle slips. Cycle slips are phase measurement biases that occur during the phase tracking and damage the quality of phase estimation. The purpose of this paper is to propose a new PLL design embedding a multifrequency phase unwrapping technique. Indeed, with the modernization of GPS and the arrival of the future European positioning system Galileo, users will have access to numerous civilian multicarrier signals. We exploit this diversity within a phase unwrapping structure that allows the incoming phase dynamics to be predicted and subsequently the dynamics estimated by the discriminator to be reduced. Compared with a conventional PLL, this new structure offers a better cycle slip robustness and reduces the probability of loss of lock.

Much attention has been recently devoted to the analysis of coastal altimetric waveforms. When approaching the coast, altimetric waveforms are sometimes corrupted by peaks caused by high reflective areas inside the illuminated land surfaces or by the modification of the sea state close to the shoreline. This paper introduces a new parametric model for these peaky altimetric waveforms. This model assumes that the received alti- metric waveform is the sum of a Brown echo and an asymmetric Gaussian peak. The asymmetric Gaussian peak is parameterized by a location, an amplitude, a width, and an asymmetry coefficient. A maximum-likelihood estimator is studied to estimate the Brown plus peak model parameters. The Cramér–Rao lower bounds of the model parameters are then derived providing minimum variances for any unbiased estimator, i.e., a reference in terms of estimation error. The performance of the proposed model and the resulting estimation strategy are evaluated via many simulations conducted on synthetic and real data. Results obtained in this paper show that the proposed model can be used to retrack efficiently standard oceanic Brown echoes as well as coastal echoes corrupted by symmetric or asymmetric Gaussian peaks. Thus, the Brown with Gaussian peak model is useful for analyzing altimetric measurements closer to the coast.

This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters.