This project is associated with statistical methods to find the unknown parameters of a model. It is the statistical investigation of the algorithm with respect to accuracy (the Cramer-Rao bound and L-curve technique) and optimization of the algorithmic parameters. This project aims to estimate the true temperature (final temperature) of a certain liquid in a container by using initial measurements (readings) from a temperature probe with a known time constant. Basically, the final temperature of the liquid was estimated, before the probe reached its final reading. The probe obeys a simple first-order differential equation model. Based on the model of the probe and the measurement data the estimate was calculated of the ’true’ temperature in the container by using a maximum likelihood approach to parameter estimation.  The initial temperature was also investigated. Modelling, analysis, calculations, and simulations of this problem were explored.

Embarqué sous le radôme du missile, les autodirecteurs existants utilisent une rotation mécanique du plan d’antenne pour balayer le faisceau en direction d’une cible. Les recherches actuelles examinent le remplacement des composantes mécaniques de rotation de l’antenne par un nouveau réseau d’antennes 3D conformes à balayage électronique. Les antennes 3D conformes pourraient offrir des avantages significatifs, tels qu’un balayage plus rapide et une meilleure couverture angulaire mais qui pourraient aussi offrir de nouveaux challenges résultant d’un diagramme de rayonnement plus complexes en 3D qu’en 2D. Le nouvel autodirecteur s’affranchit du système mécanique de rotation ce qui libère de l’espace pour le design d’une nouvelle antenne 3D conforme. Pour tirer le meilleur parti de cet espace, différentes formes de réseaux sont étudiées, ainsi l’impact de la position, de l’orientation et de la conformation des éléments est établi sur les performances de l’antenne, en termes de directivité, ellipticité et de polarisation. Pour faciliter cette étude de réseaux 3D conformes, un programme Matlab a été développé, il permet de générer rapidement le diagramme de rayonnement en polarisation d’un réseau donné dans toutes les directions. L’une des tâches de l’autodirecteur consiste à estimer la position d’une cible donnée afin de corriger la trajectoire du missile. Ainsi, l’impact de la forme du réseau sur l’erreur entre la direction d’arrivée mesurée de l’écho de la cible et sa vraie valeur est analysé. La borne inférieure de Cramer-Rao est utilisée pour calculer l’erreur minimum théorique. Ce modèle suppose que chaque élément est alimenté séparément et permet ainsi d’évaluer le potentiel des réseaux 3D conformes actifs.Finalement, l’estimateur du monopulse en phase est étudié pour des réseaux 3D conformes dont les quadrants n’auraient pas les mêmes caractéristiques. Un nouvel estimateur, plus adapté à des quadrants non identiques, est aussi proposé. / Embedded below the radome of a missile, existing RF-seekers use a mechanical rotating antenna to steer the radiating beam in the direction of a target. Latest research is looking at replacing the mechanical antenna components of the RF-seeker with a novel 3D conformal antenna array that can steer the beam electronically. 3D antennas may offer significant advantages, such as faster beam steering and better coverage but, at the same time, introduce new challenges resulting from a much more complex radiation pattern than that of 2D antennas. Thanks to the mechanical system removal, the new RF-seeker has a wider available space for the design of a new 3D conformal antenna. To take best benefits of this space, different array shapes are studied, hence the impact of the position, orientation and conformation of the elements is assessed on the antenna performance in terms of directivity, ellipticity and polarisation. To facilitate this study of 3D conformal arrays, a Matlab program has been developed to compute the polarisation pattern of a given array in all directions. One of the task of the RF-seeker consists in estimating the position of a given target to correct the missile trajectory accordingly. Thus, the impact of the array shape on the error between the measured direction of arrival of the target echo and its true value is addressed. The Cramer-Rao lower bound is used to evaluate the theoretical minimum error. The model assumes that each element receives independently and allows therefore to analyse the potential of active 3D conformal arrays. Finally, the phase monopulse estimator is studied for 3Dconformal arrays whose quadrants do not have the same characteristics. A new estimator more adapted to non-identical quadrants is also proposed.

Cognitive radio is a recent novel approach for the realization of intelligent and sophisticated wireless systems. Although the research and development on cognitive radio is still in the stage of infancy, there are significant interests and efforts towards realization of cognitive radio. Cognitive radio systems are envisioned to support context awareness and related systems. The context can be spectrum, environment, location, waveform, power and other radio resources. Significant amount of the studies related to cognitive radio in the literature focuses on the spectrum awareness since it is one of the most crucial features of cognitive radio systems. However, the rest of the features of cognitive radio such as location and environment awareness have not been investigated thoroughly. For instance, location aware systems are widespread and the demand for more advanced ones are growing. Therefore, the main objective of this dissertation is to develop an underlying location awareness architecture for cognitive radio systems, which is described as location awareness engine, in order to support goal driven and autonomous location aware systems. A cognitive radio conceptual model with location awareness engine and cycle is developed by inspiring from the location awareness features of human being and bat echolocation systems. Additionally, the functionalities of the engine are identified and presented. Upon providing the functionalities of location awareness engine, the focus is given to the development of cognitive positioning systems. Furthermore, range accuracy adaptation, which is a cognitive behavior of bats, is developed for cognitive positioning systems. In what follows, two main approaches are investigated in order to improve the performance of range accuracy adaptation method. The first approach is based on idea of improving the spectrum availability through hybrid underlay and overlay dynamic spectrum access method. On the other hand, the second approach emphasizes on spectrum utilization, where we study performance of range accuracy adaptation from both theoretical and practical perspectives considering whole spectrum utilization approach. Furthermore, we introduced a new spectrum utilization technique that is referred as dispersed spectrum utilization. The performance analysis of dispersed spectrum utilization approach is studied considering time delay estimation problem in cognitive positioning systems. Afterward, the performance of whole and dispersed spectrum utilization approaches are compared in the context of cognitive positioning systems. Finally, some representative advanced location aware systems for cognitive radio networks are presented in order to demonstrate some potential applications of the proposed location awareness engine in cognitive radio systems.

La capture de mouvement ambulatoire est un sujet en plein essor pour des applications aussi diverses que le suivi des personnes âgées, l'assistance des sportifs de haut niveau, la réhabilitation fonctionnelle, etc. Ces applications exigent que le mouvement ne soit pas contraint par un système externe, qu’il puisse être réalisé dans différentes situations, y compris en extérieur, que l’équipement soit léger et à un faible coût, qu’il soit réellement ambulatoire et sans procédure complexe de calibration.Actuellement, seuls les systèmes utilisant un exosquelette ou bien des modules inertiels (souvent combinés avec des modules magnétiques) permettent d'effectuer de la capture de mouvement de façon ambulatoire. Le poids de l’exosquelette est très important et il impose des contraintes sur les mouvements de la personne, ce qui le rend inutilisable pour certaines applications telles que le suivi de personnes âgées. La technologie inertielle est plus légère. Elle permet d'effectuer la capture du mouvement sans contrainte sur l’espace de mesure ou sur les mouvements réalisés. Par contre, elle souffre de dérives des gyromètres, et le système doit être recalibré.L'objectif de cette thèse est de développer un système de capture de mouvement de chaînes articulées, bas-coût et temps réel, réellement ambulatoire, ne nécessitant pas d'infrastructure de capture spécifique, permettant une utilisation dans de nombreux domaines applicatifs (rééducation, sport, loisirs, etc.).On s'intéresse plus particulièrement à des mesures intra-corporelles. Ainsi, tous les capteurs sont placés sur le corps et aucun dispositif externe n'est utilisé. Outre un démonstrateur final permettant de valider l'approche proposée, on s'astreint à développer également des outils qui permettent de dimensionner le système en termes de technologie, nombre et position des capteurs, mais également à évaluer différents algorithmes de fusion des données. Pour ce faire, on utilise la borne de Cramer-Rao.Le sujet est donc pluridisciplinaire. Il traite des aspects de modélisation et de dimensionnement de systèmes hybrides entièrement ambulatoires. Il étudie des algorithmes d'estimation adaptés au domaine de la capture de mouvement corps entier en traitant les problématiques d'observabilité de l'état et en tenant compte des contraintes biomécaniques pouvant être appliquées. Ainsi, un traitement adapté permet de reconstruire en temps réel la posture du sujet à partir de mesures intra-corporelles, la source étant également placée sur le corps. / Ambulatory motion capture is of great interest for applications ranging for the monitoring of elderly people, sporty performances monitoring, functional rehabilitation, etc. These applications require that the movement is not constrained by an external system, that it can be performed in different situations, including outdoor environment. It requires lightweight and low cost equipment; it must be truly ambulatory without complex process of calibration.Currently, only systems using an exoskeleton or inertial modules (often combined with magnetic modules) can be used in such situations. Unfortunately, the exoskeleton weight is not affordable and it imposes constraints on the movements of the person, which makes it unusable for certain applications such as monitoring of the elderly.Inertial technology is lighter. Itcan be used for the capture of movement without constraints on the capture space or on the movements. However, it suffers from gyros drift, and the system must be recalibrated.The objective of this thesis is to develop a system of motion capture for an articulated chain, low-cost, real-time truly ambulatory that does not require specific capture infrastructure, that can be used in many application fields (rehabilitation, sport, leisure, etc.).We focus on intra-corporal measurements. Thus, all sensors are placed on the body and no external device is used. In addition to a final demonstrator to validate the proposed approach, we also develop tools to evaluate the system in terms of technology, number and position of sensors, but also to evaluate different algorithms for data fusion. To do this, we use the Cramer-Rao lower bound. \\The subject is multidisciplinary. It addresses aspects of modelling and design of fully ambulatory hybrid systems. It studies estimation algorithms adapted to the field of motion capture of a whole body by considering the problem of observability of the state and taking into account the biomechanical constraints that can be taken into account. Thus, with an appropriate treatment, the pose of a subject can be reconstructed in real time from intra-body measurements.

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Nonstationary signals are common in many environments such as radar, sonar, bioengineering and power systems. The nonstationary nature of the signals found in these environments means that classicalspectralanalysis techniques are notappropriate for estimating the parameters of these signals. Therefore it is important to develop techniques that can accommodate nonstationary signals. This thesis seeks to achieve this by firstly, modelling each component of the signal as having a polynomial phase and by secondly, developing techniques for estimating the parameters of these components. Several approaches can be used for estimating the parameters of polynomial phase signals, eachwithvarying degrees ofsuccess.Criteria to consider in potential estimation algorithms are (i) the signal-to-noise (SNR) ratio threshold of the algorithm, (ii) the amount of computation required for running the algorithm, and (iii) the closeness of the resulting estimates' mean-square errors to the minimum theoretical bound. These criteria will be used to compare the new techniques developed in this thesis with existing techniques. The literature on polynomial phase signal estimation highlights the recurring trade-off between the accuracy of the estimates and the amount of computation required. For example, the Maximum Likelihood (ML) method provides near-optimal estimates above threshold, but also incurs a heavy computational cost for higher order phase signals. On the other hand, multi-linear techniques such as the high-order ambiguity function (HAF) method require little computation, but have a significantly higher SNR threshold than the ML method. Of the existing techniques, the cubic phase (CP) function method is a promising technique because it provides an attractive SNR threshold and computational complexity trade-off. For this reason, the analysis techniques developed in this thesis will be derived from the CP function. A limitation of the CP function is its inability to accurately process phase orders greater than three. Therefore, the first novel contribution to this thesis develops a broadened class of discrete-time higher order phase (HP)functions to address this limitation.This broadened class is achieved by providing a multi-linear extension of the CP function. Monte Carlo simulations are performed to demonstrate the statistical advantage of the HP functions compared to the HAFs. A first order statistical analysis of the HP functions is presented. This analysis verifies the simulation results. The next novel contribution is a technique called the lower SNR cubic phase function (LCPF)method. It is an extension of the CP function, with the extension enabling performance at lower signal-to-noise ratios (SNRs). The improvement of the SNR threshold's performance is achieved by coherently integrating the CP function over a compact interval in the two-dimensional CP function space. The computation of the new algorithm is quite moderate, especially when compared to the ML method. Above threshold, the LCPF method's parameter estimates are asymptotically efficient. Monte Carlo simulation results are presented and a threshold analysis of the algorithm closely predicts the thresholds observed in these results. The next original contribution to this research involves extending the LCPF method so that it is able to process multicomponent cubic phase signals and higher order phase signals. The LCPF method is extended to higher orders by applying a windowing technique as opposed to adjusting the order of the kernel as implemented in the HP function method. To demonstrate the extension of the LCPF method for processing higher order phase signals and multicomponent cubic phase signals, some Monte Carlo simulations are presented. Finally, these estimation techniques are applied to real-worldscenarios in the fields of Power Systems Analysis, Neuroethology and Speech Analysis.