Abstract The multiple–input multiple–output (MIMO) technique, applying several transmit and receive antennas in wireless communications, has emerged as one of the most prominent technical breakthroughs of the last decade. Wideband MIMO parameter estimation and its applications to the MIMO orthogonal frequency division multiplexing (MIMO–OFDM) channel estimation and mobile positioning are studied in this thesis. Two practical MIMO channel models, i.e., correlated-receive independent-transmit channel and correlated-transmit-receive channel, and associated space-time parameter estimation algorithms are considered. Thanks to the specified structure of the proposed training signals for multiple transmit antennas, the iterative quadrature maximum likelihood (IQML) algorithm is applied to estimate the time delay and spatial signature for the correlated-receive independent-transmit MIMO channels. For the correlated-transmit-receive MIMO channels, the spatial signature matrix corresponding to a time delay can be further decomposed in such a way that the angle of arrival (AOA) and the angle of departure (AOD) can be estimated simultaneously by the 2-D unitary ESPRIT algorithm. Therefore, the combination of the IQML algorithm and the 2-D unitary ESPRIT algorithm provides a novel solution to jointly estimate the time delay, the AOA and the AOD for the correlated-transmit-receive MIMO channels. It is demonstrated from the numerical examples that the proposed algorithms can obtain good performance at a reasonable cost. Considering the correlated-receive independent-transmit MIMO channels, channel coefficient estimation for the MIMO–OFDM system is studied. Based on the parameters of the correlated-receive independent-transmit MIMO channels, the channel statistics in terms of the correlation matrix are developed. By virtue of the derived channel statistics, a joint spatial-temporal (JST) filtering based MMSE channel estimator is proposed which takes full advantage of the channel correlation properties. The mean square error (MSE) of the proposed channel estimator is analyzed, and its performance is also demonstrated by Monte Carlo computer simulations. It is shown that the proposed JST minimum mean square error (MMSE) channel estimator outperforms the more conventional temporal MMSE channel estimator in terms of the MSE when the signals in the receive antenna array elements are significantly correlated. The closed form bit error probability of the space-time block coded OFDM system with correlation at the receiver is also developed by taking the channel estimation errors and channel statistics, i.e., correlation at the receiver, into account. Mobile positioning in the non-line of sight (NLOS) scenarios is studied. With the knowledge of the time delay, the AOA and the AOD associated with each NLOS propagation path, a novel geometric approach is proposed to calculate the MS's position by only exploiting two NLOS paths. On top of this, the least squares and the maximum likelihood (ML) algorithms are developed to utilize multiple NLOS paths to improve the positioning accuracy. Moreover, the ML algorithm is able to estimate the scatterers' positions as well as those of the MSs. The Cramer-Rao lower bound related to the position estimation in the NLOS scenarios is derived. It is shown both analytically and through computer simulations that the proposed algorithms are able to estimate the mobile position only by employing the NLOS paths.

Non-contact life detection is a significant component of both civilian and military rescue applications. As a consequence, this interest has resulted in a very active area of research. The primary goal of this research is reliable detection of a human breathing signal. Additional goals of this research are to carry out detection under realistic conditions, to distinguish between two targets, to determine human breathing rate and estimate the posture. Range gating and Singular Value Decomposition (SVD) have been used to remove clutter in order to detect human breathing under realistic conditions. However, the information of the target range or what principal component contains target information may be unknown. DFT and Short Time Fourier Transform (STFT) algorithms have been used to detect the human breathing and discriminate between two targets. However, the algorithms result in many false alarms because they detect breathing when no target exists. The unsatisfactory performance of the DFT-based estimators in human breathing rate estimation is due to the fact that the second harmonic of the breathing signal has higher magnitude than the first harmonic. Human posture estimation has been performed by measuring the distance of the chest displacements from the ground. This requires multiple UWB receivers and a more complex system. In this thesis, monostatic UWB radar is used. Initially, the SVD method was combined with the skewness test to detect targets, discriminate between two targets, and reduce false alarms. Then, a novel human breathing rate estimation algorithm was proposed using zero-crossing method. Subsequently, a novel method was proposed to distinguish between human postures based on the ratios between different human breathing frequency harmonics magnitudes. It was noted that the ratios depend on the abdomen displacements and higher harmonic ratios were observed when the human target was sitting or standing. The theoretical analysis shows that the distribution of the skewness values of the correlator output of the target and the clutter signals in a single range-bin do not overlap. The experimental results on human breathing detection, breathing rate, and human posture estimation show that the proposed methods improve performance in human breathing detection and rate estimation.

This study looked at what components are in student solutions to computational estimation problems involving fractions. Past computational estimation research has focused on strategies used for estimating with whole numbers and decimals while neglecting those used for fractions. An extensive literature review revealed one study specifically directed toward estimating with fractions (Hanson & Hogan, 2000) that researched adult estimation strategies and not children's strategies. Given the lack of research on estimation strategies that children use to estimate with fractions, this study used qualitative research methods to find which estimation components were in 10 eighth-grade students' solutions to estimation problems involving fractions. Analysis of this data differs from previous estimation studies in that it considers actions as the unit of analysis, providing a smaller grain size that reveals the components used in each estimation solution. The analysis revealed new estimation components as well as a new structure for categorizing the components. The new categories are whole number and decimal estimation components, fraction estimation components, and components used with either fractions or whole numbers and decimals. The results from this study contribute to the field of mathematics education by identifying new components to consider when conducting future studies in computational estimation. The findings also suggest that future research on estimation should use a smaller unit of analysis than a solution response to a task, the typical unit of analysis in previous research. Additionally, these results contribute to mathematics teaching by suggesting that all components of an estimation solution be considered when teaching computational estimation, not just the overarching strategy.

Dans cette thèse, nous nous intéressons à l'estimation de paramètres dans les chaînes de Markov cachées. Nous considérons tout d'abord le problème de l'estimation en ligne (sans sauvegarde des observations) au sens du maximum de vraisemblance. Nous proposons une nouvelle méthode basée sur l'algorithme Expectation Maximization appelée Block Online Expectation Maximization (BOEM). Cet algorithme est défini pour des chaînes de Markov cachées à espace d'état et espace d'observations généraux. Dans le cas d'espaces d'états généraux, l'algorithme BOEM requiert l'introduction de méthodes de Monte Carlo séquentielles pour approcher des espérances sous des lois de lissage. La convergence de l'algorithme nécessite alors un contrôle de la norme Lp de l'erreur d'approximation Monte Carlo explicite en le nombre d'observations et de particules. Une seconde partie de cette thèse se consacre à l'obtention de tels contrôles pour plusieurs méthodes de Monte Carlo séquentielles. Nous étudions enfin des applications de l'algorithme BOEM à des problèmes de cartographie et de localisation simultanées. La dernière partie de cette thèse est relative à l'estimation non paramétrique dans les chaînes de Markov cachées. Le problème considéré est abordé dans un cadre précis. Nous supposons que (Xk) est une marche aléatoire dont la loi des incréments est connue à un facteur d'échelle a près. Nous supposons que, pour tout k, Yk est une observation de f(Xk) dans un bruit additif gaussien, où f est une fonction que nous cherchons à estimer. Nous établissons l'identifiabilité du modèle statistique et nous proposons une estimation de f et de a à partir de la vraisemblance par paires des observations. / This document is dedicated to inference problems in hidden Markov models. The first part is devoted to an online maximum likelihood estimation procedure which does not store the observations. We propose a new Expectation Maximization based method called the Block Online Expectation Maximization (BOEM) algorithm. This algorithm solves the online estimation problem for general hidden Markov models. In complex situations, it requires the introduction of Sequential Monte Carlo methods to approximate several expectations under the fixed interval smoothing distributions. The convergence of the algorithm is shown under the assumption that the Lp mean error due to the Monte Carlo approximation can be controlled explicitly in the number of observations and in the number of particles. Therefore, a second part of the document establishes such controls for several Sequential Monte Carlo algorithms. This BOEM algorithm is then used to solve the simultaneous localization and mapping problem in different frameworks. Finally, the last part of this thesis is dedicated to nonparametric estimation in hidden Markov models. It is assumed that the Markov chain (Xk) is a random walk lying in a compact set with increment distribution known up to a scaling factor a. At each time step k, Yk is a noisy observations of f(Xk) where f is an unknown function. We establish the identifiability of the statistical model and we propose estimators of f and a based on the pairwise likelihood of the observations.

Cette thèse traite de l'estimation et de la stabilisation de l'état des compliances passives présentes dans les chevilles du robot humanoïde HRP-2. Ces compliances peuvent être vues comme un degré de liberté unique et observable, sous quelques hypothèses qui sont explicitées. L'estimateur utilise des mesures provenant de la centrale inertielle située dans le torse du robot et éventuellement des capteurs de forces situés dans ses pieds. Un filtre de Kalman étendu est utilisé pour l'estimation d'état. Ce filtre utilise un modèle complet de la dynamique du robot, pour lequel la dynamique interne du robot, considérée comme parfaitement connue et contrôlée, a été découplée de la dynamique de la compliance passive du robot. L'observabilité locale de l'état a été montrée en considérant ce modèle et les mesures provenant de la centrale inertielle seule. Il a de plus été montré que l'ajout des mesures des capteurs de forces dans les pieds du robot permet de compléter l'état avec des mesures d'erreurs dans le modèle dynamique du robot. L'estimateur a été validé expérimentalement sur le robot humanoïde HRP-2. Sur cet estimateur a été construit un stabilisateur de l'état de la compliance d'HRP-2. L'état commandé est la position et vitesse du centre de masse (contrôle indirecte de la quantité de mouvement) du robot, l'orientation et la vitesse angulaire de son tronc (contrôle indirecte du moment cinétique), ainsi que l'orientation et la vitesse angulaire de la compliance. Les grandeurs de commande sont l'accélération du centre de masse du robot et l'accélération angulaire de son tronc. Un régulateur quadratique linéaire (LQR) a été utilisé pour calculer les gains du retour d'état, basé sur un modèle appelé "pendule inverse flexible à roue d'inertie" qui consiste en un pendule inverse dont la base est flexible et où une répartition de masse en rotation autour du centre de masse du robot représente le tronc du robot. Des tests ont été effectués sur le robot HRP-2 en double support, utilisant l'estimateur décrit précédemment avec ou sans les capteurs de forces. / This PhD thesis covers the estimation and stabilization of the passive compliances state wich are located in the HRP-2 humanoid robot ankles. These compliances can be seen as a unique compliance under some assumptions that are presented. The estimator uses measurements coming from an Inertial Measurement Unit (IMU) located in the robot's chest. It also uses measurements coming from forces sensors located in its feet. An Extended Kalman Filter (EKF) is used for state estimation. This filter uses a complete model of the robot dynamics, in which the internal dynamics of the robot, considered as known, is decoupled from the dynamics of its passive compliance. The local observability of the state is shown by considering this model and the measurements coming from the IMU only. Furthermore, it has been shown that, by adding the measurements coming from the forces sensors in the robot's feet, we are able to complete the state with some errors measurements in the dynamical model of the robot. The estimator was validated experimentaly on the HRP-2 humanoid robot. Based on this estimator, a stabilizer of the compliance state of the HRP-2 robot was build. The control state is the position and velocity of the center of mass of the robot, the orientation and angular velocity of its trunk, and the orientation and the angular velocity of the compliance. The control values are the acceleration of the robot's center of mass and the angular acceleration of its trunk. A Linear Quadratic Regulator (LQR) is used to compute the feed-back gains, based on a Viscoelastic Reaction Mass Pendulum model which consist in an inverse pendulum whith a flexible base and where a mass repartition rotating around the center of mass is modeling the robot's trunk. Some tests were made on the HRP-2 robot in double support, using the previous estimator with and without the use of forces sensors

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Radio Tomographic imaging (RTI) is an exciting new field that utilizes a sensor network of a large number of relatively simple radio nodes for inverse imaging, utilizing similar mathematical algorithms to those used in medical imaging. Previous work in this field has almost exclusively focused on device-free object location and tracking. In this thesis, the application of RTI to propagation problems will be studied-- specifically using RTI to measure the strength and location of attenuating objects in an area of interest, then using this knowledge of the shadowing present in an area for radio coverage prediction. In addition to radio coverage prediction, RTI can be used to improve the quality of RSS-based position location estimates. Because the traditional failing of RSS-based multilateration is ranging error due to attenuating objects, RTI has great potential for improving the accuracy of these estimates if shadowing objects are accounted for. In this thesis, these two problems will primarily be studied. A comparison with other inverse imaging, remote sensing, and propagation modeling techniques of interest will be given, as well as a description of the mathematical theory used for tomographic image reconstruction. Proof-of-concept of the efficacy of applying RTI to position location will be given by computer simulation, and then physical experiments with an RTI network consisting of 28 Zigbee radio sensors will be used to verify the validity of these assertions. It will be shown in this thesis that RTI does provide noticeable improvement in RSS-based position location accuracy in cluttered environments, and it produces much more accurate RSS estimates than a standard exponential path-loss model is able to provide. / Master of Science

La recherche présentée dans cette thèse est divisée en trois parties. Notre objectif dans la première partie est l’amélioration de la compression de l’image par stéganographie. Dans cette étude, la compression de données est effectuée en deux étapes. Tout d’abord, nous profitons du compactage d’énergie en utilisant JPEG pour réduire les données redondantes. Ensuite, nous intégrons des blocs de bits dans les blocs suivants de la même image stéganographie. Les bits intégrés servent à non seulement augmenter la taille du fichier de l’image compressée, mais aussi à diminuer davantage la taille du fichier. Les résultats expérimentaux montrent que notre méthode donne de meilleurs taux de compression tout en conservant une haute qualité de l’image. Le deuxième sujet de cette thèse propose un formalisme bayésien pour la stéganalyse d’image numérique qui permet la détection d’images stego, l’identification de l’algorithme de stéganographie utilisé, l’estimation de la longueur du message et l’emplacement, et l’anticipation dans le cas de l’intégration en utilisant un algorithme de stéganographie inconnu. La détection, l’identification et l’anticipation impliquent l’apprentissage discriminant dans l’espace des fonctions. L’estimation nécessite la fusion de classificateurs permettant la discrimination entre les sous-images et une intégration entière des couvertures de tailles différentes. La validation sur des images JPEG montre que le système proposé est efficace et permet d’anticiper des algorithmes de stéganographie inconnus. Le troisième sujet de la thèse décrit une méthode d’estimation du regard de l’oeil humain pendant un mouvement normal de la tête. Dans ce procédé, la position et l’orientation de la tête sont acquises par des données de profondeur fournies par Kinect. La direction de l’oeil est obtenue à partir d’images à haute résolution. Nous nous proposons la régression logistique multinomiale pour construire une fonction de mappage du regard et de vérifier l’état de l’iris. L’efficacité de la méthode proposée est validée par une évaluation de la performance pour plusieurs personnes avec différentes distances et poses par rapport à la caméra et dans différents états de l’oeil.

When studying detection systems, parameters associated with the Receiver Operating Characteristic (ROC) curve are often estimated to assess system performance. In some applied settings it is often not possible to test the detection system with large numbers of stimuli. The resulting small sample statistics many have undesirable properties. The characteristics of these small sample ROC estimators were examined in a Monte Carlo simulation. Three popular ROC parameters were chosen for study. One of the parameters was a single parameter index of system performance, Area under the ROC curve. The other parameters, ROC intercept and slope, were considered as a pair. ROC intercept and slope were varied along with sample size and points on the certainty rating scale to form a four way factorial design. Several types of estimators were examined. For the parameter, Area under the curve, Maximum Likelihood (ML), three types of Least Squares (LS), and Distribution Free (DF) estimators were considered. Except for the DF estimator, the same estimators were considered for the parameters, intercept and slope. These estimators were compared with respect to three characteristics: bias, efficiency, and consistency. For Area under the curve, the ML estimator was the least biased. The DF estimator was the most efficient, and all the estimators except the DF estimator appeared to be consistent. For intercept and slope the LS estimator that minimized vertical error of the points from the ROC curve (line) was the least biased for both estimators. This LS estimator was also the most efficient. This estimator along with the ML estimator also appeared to be the most consistent. The other two estimators had no significant trend toward consistency. These results along with other findings, illustrate that different estimators may be "best" for different sample sizes and for different parameters. Therefore, researchers should carefully consider the characteristics of ROC estimators before using them as indices of system performance.