This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reßectances result froma nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The Þrst step of the proposedmethod estimates the abundance vectors for all the image pixels using a Bayesian approach an aGaussian process latent variable model for the nonlinear function (relating the abundance vectors to the observations). The endmembers are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is Þrst evaluated on synthetic data. The proposed method provides accurate abundance and endmember estimations when compared to other linear and nonlinear unmixing strategies. An interesting property is its robustness to the absence of pure pixels in the image. The analysis of a real hyperspectral image shows results that are in good agreement with state of the art unmixing strategies and with a recent classiÞcation method.

Periodic nonuniform sampling of order three (PNS3) is a sampling scheme composed of three periodic sequences with the same period. It is well-known that this sampling scheme can be useful to remove aliasing. Previous studies have provided conditions on the spectrum support for exact reconstruction in the case of functions. This paper deals more generally with the best mean-square interpolation for stationary processes with any known power spectrum, from PNS3 and possibly aliasing. We show that the best estimation is based upon particular linear filters, which depend on the gap between the sampling sequences. The mean-time error also depends on this gap. The errorless interpolation is a particular case. It requires the knowledge of the spectral support rather than the spectral true values.

Multifractal analysis has matured into a widely used signal and image processing tool. Due to the statistical nature of multifractal processes (strongly non-Gaussian and intricate dependence) the accurate estimation of multifractal parameters is very challenging in situations where the sample size is small (notably including a range of biomedical applications) and currently available estimators need to be improved. To overcome such limitations, the present contribution proposes a Bayesian estimation procedure for the multifractality (or intermittence) parameter. Its originality is threefold : First, the use of wavelet leaders, a recently introduced multiresolution quantity that has been shown to yield significant benefits for multifractal analysis ; Second, the construction of a simple yet generic semi-parametric model for the marginals and covariance structure of wavelet leaders for the large class of multiplicative cascade based multifractal processes ; Third, the construction of original Bayesian estimators associated with the model and the constraints imposed by multifractal theory. Performance are numerically assessed and illustrated for synthetic multifractal processes for a range of multifractal parameter values. The proposed procedure yields significantly improved estimation performance for small sample sizes.

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.

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.