Les méthodes de trajectographie conventionnelles par mesures d’angle supposent que la source est en mouvement rectiligne uniforme tandis que l’observateur est manœuvrant. Dans cette thèse, nous remettons en cause cette hypothèse en proposant un autre modèle de cinématique de la source : le mouvement circulaire uniforme. Nous prouvons qu’une telle trajectoire est observable à partir d’un observateur en mouvement rectiligne uniforme. Puis, nous étudions l’apport de mesures additionnelles de fréquence ou la faisabilité de la trajectographie par mesures de distances. Le cas d’une source en mouvement rectiligne uniforme et d’un observateur manœuvrant est étudié pour ce dernier type de mesures. Chaque cas donne lieu à une analyse de l’observabilité de la trajectoire de la source et à la mise au point de l’estimateur du maximum de vraisemblance. Nous montrons que ce dernier s’avère le plus souvent efficace. / The conventional bearings-only target motion analysis methods assume that the source is in constant velocity motion (constant speed and heading) while the observer maneuvers. In this thesis, we reassess this hypothesis and propose another model of the kinematics of the source: the constant turn motion (an arc of circle followed at constant speed). We prove that this kind of trajectory is observable by an observer in constant velocity motion. Then, we study the contribution of the addition of frequency measurements or the feasibility of target motion analysis methods that use range only measurements. The case of a source in constant velocity motion with a maneuvering observer is examined for this last type of measurements. Each case leads to an analysis of the observability of the trajectory of the source and to the development of the associated maximum likelihood estimator. We show that this estimator often appears to be efficient.

La nécessité d’économiser de l'énergie est l’un des axes importants de ces dernières décennies, d’où le besoin de surveiller la consommation d'énergie des processus résidentiels et industriels. Le travail de recherche présenté dans ce manuscrit s’inscrit plus particulièrement dans le suivi de la consommation électrique afin de permettre l’économie d’énergie. Le but final étant d'avoir une connaissance précise et fiable d'un réseau électrique donné. Cela passe par la décomposition de la consommation électrique globale du réseau électrique étudié afin de fournir une analyse détaillée de l'énergie consommée par usage. L’objectif de cette thèse est la mise en place d’une approche non-intrusive permettant de réaliser les étapes de détection d’évènements et d’extraction de caractéristiques, qui précédent les étapes de classification et d’estimation de la consommation électrique par usage. L’algorithme résultant des travaux effectués durant cette thèse permet de détecter les évènements qui surviennent sur le courant et d’y associer un vecteur d’information contenant des paramètres caractérisant le régime permanent et le régime transitoire. Ce vecteur d’information permet ensuite de reconnaître tous les évènements liés à la même charge électrique. / The need to save energy is an important focus of recent decades, hence the need to monitor the energy consumption of residential and industrial processes. The research works presented in this manuscript are within the monitoring power consumption area in order to enable energy saving. The final goal is to have a clear and reliable knowledge of a given grid. This involves the decomposition of the overall power consumption of the electrical network to provide a detailed analysis of the consumed energy. The objective of this thesis is to develop a non-intrusive approach to achieve the event detection and feature extraction steps, which precede the classification and the power consumption estimation steps. The algorithm resulting from the works performed in this thesis can detect events which occur on the current and associates to them an information vector containing the parameters characterizing the steady and transient states. Then this information vector is used to recognize all the events linked to the same electrical load.

This dissertation studies several aspects of the interface between information theory and signal processing. Several new and existing results in information theory are researched from the perspective of signal processing. Similarly, some fundamental results in signal processing and statistics are studied from the information theoretic viewpoint. The first part of this dissertation focuses on illustrating the equivalence between Stein's identity and De Bruijn's identity, and providing two extensions of De Bruijn's identity. First, it is shown that Stein's identity is equivalent to De Bruijn's identity in additive noise channels with specific conditions. Second, for arbitrary but fixed input and noise distributions, and an additive noise channel model, the first derivative of the differential entropy is expressed as a function of the posterior mean, and the second derivative of the differential entropy is expressed in terms of a function of Fisher information. Several applications over a number of fields, such as statistical estimation theory, signal processing and information theory, are presented to support the usefulness of the results developed in Section 2. The second part of this dissertation focuses on three contributions. First, a connection between the result, proposed by Stoica and Babu, and the recent information theoretic results, the worst additive noise lemma and the isoperimetric inequality for entropies, is illustrated. Second, information theoretic and estimation theoretic justifications for the fact that the Gaussian assumption leads to the largest Cramer-Rao lower bound (CRLB) is presented. Third, a slight extension of this result to the more general framework of correlated observations is shown. The third part of this dissertation concentrates on deriving an alternative proof for an extremal entropy inequality (EEI), originally proposed by Liu and Viswanath. Compared with the proofs, presented by Liu and Viswanath, the proposed alternative proof is simpler, more direct, and more information-theoretic. An additional application for the extremal inequality is also provided. Moreover, this section illustrates not only the usefulness of the EEI but also a novel method to approach applications such as the capacity of the vector Gaussian broadcast channel, the lower bound of the achievable rate for distributed source coding with a single quadratic distortion constraint, and the secrecy capacity of the Gaussian wire-tap channel. Finally, a unifying variational and novel approach for proving fundamental information theoretic inequalities is proposed. Fundamental information theory results such as the maximization of differential entropy, minimization of Fisher information (Cramer-Rao inequality), worst additive noise lemma, entropy power inequality (EPI), and EEI are interpreted as functional problems and proved within the framework of calculus of variations. Several extensions and applications of the proposed results are briefly mentioned.

The amount of carbon dioxide in the Earth’s atmosphere has significantly increased in the last few decades as compared to the last 80,000 years approximately. The increase in carbon dioxide levels are affecting the temperature and therefore need to be understood better. In order to study the effects of global events on the carbon dioxide levels, one need to properly estimate the trends in carbon dioxide in the previous years. In this project, we will perform the task of estimating the trend in carbon dioxide measurements taken in Mauna Loa for the last 46 years, also known as the Keeling Curve, using estimation techniques based on a Taylor and Fourier series model equation. To perform the estimation, we will employ Maximum Likelihood Estimation (MLE) and the Cramér-Rao Lower Bound (CRLB) and review our results by comparing it to other estimation techniques. The estimation of the trend in Keeling Curve is well-posed however, the estimation for the first derivative of the trend is an ill-posed problem. We will further calculate if the estimation error is under a suitable limit and conduct statistical analyses for our estimated results.

Indoor positioning is desired in many areas for various reasons, such as positioning products in industrial environments, hospital equipment or firefighters inside a building on fire. One even tougher situation where indoor positioning can be useful is locating a specific object on a shelf in a commercial setting. This thesis aims to investigate and design different network deployment strategies in an indoor environment in order to achieve both high position estimation accuracy and availability. The investigation considers the two positioning techniques downlink time difference of arrival, DL-TDOA, and round trip time, RTT. Simulations of several deployments are performed in two standard scenarios which mimic an indoor open office and an indoor factory, respectively. Factors having an impact on the positioning accuracy and availability are found to be deployment geometry, number of base stations, line-of-sight conditions and interference, with the most important being deployment geometry. Two deployment strategies are designed with the goal of optimising the deployment geometry. In order to achieve both high positioning accuracy and availability in a simple, sparsely cluttered environment, the strategy is to deploy the base stations evenly around the edges of the deployment area. In a more problematic, densely cluttered environment the approach somewhat differs. The proposed strategy is now to identify and strategically place some base stations in the most cluttered areas but still place a majority of the base stations around the edges of the deployment area. A robust positioning algorithm is able to handle interference well and to decrease its impact on the positioning accuracy. The cost, in terms of frequency resources, of using more orthogonal signals may not be worth the small improvement in accuracy and availability.

Airborne angle-only geolocalization is the localization of objects on ground level from airborne vehicles (AV) using bearing measurements, namely azimuth and elevation. This thesis aims to introduce elevation data of the terrain to the airborne angle-only geolocalization problem and to demonstrate that it could be applicable for localization of jammers. Jammers are often used for deliberate interference with malicious intent which could interfere with the positioning system of a vehicle. It is important to locate the jammers to either avoid them or to remove them.    Three localization methods, i.e. the nonlinear least squares (NLS), the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are implemented and tested on simulated data. The methods are also compared to the theoretical lower bound, the Cramér-Rao Lower Bound (CRLB), to see if there is an efficient estimator. The simulated data are different scenarios where the number of AVs, the relative flight path of the AVs and the knowledge of the terrain can differ. Using the knowledge of the terrain elevation, the methods give more consistent localization than without it. Without elevation data, the localization relies on good geometry of the problem, i.e. the relative flight path of the AVs, while the geometry is not as critical when elevation data is available. However, the elevation data does not always improve the localization for certain geometries.    There is no method that is clearly better than the others when elevation data is used. The methods’ performances are very similar and they all converge to the CRLB but that could also be an advantage. This makes the usage of elevation data not restricted to a certain method and it leaves more up to the implementer which method they prefer.

With the increasing demand for faster communication systems, soon data rates in the terabit regime (100 Gbit/s and beyond) are required, which yields new challenges for the design of analog-to-digital converters (ADCs) since high bandwidths imply high sampling rates. For sampling rates larger than 300MHz, which we now achieve with 5G, the ADC power consumption per conversion step scales quadratically with the sampling rate. Thus, ADCs become a major energy consumption bottleneck. To circumvent this problem, we consider digital receivers based on 1-bit quantization and oversampling. We motivate this concept by a brief comparison of the energy efficiency of a recently proposed system employing 1-bit quantization and oversampling to the conventional approach using high resolution quantization and Nyquist rate sampling. Our numerical results show that the energy efficiency can be improved significantly by employing 1-bit quantization and oversampling at the receiver at the cost of increased bandwidth. The main part of this work is concerned with the synchronization of fully digital receivers using 1-bit quantization and oversampling. As a first step, we derive performance bounds for phase, timing, and frequency estimation in order to gain a deeper insight into the impact of 1-bit quantization and oversampling. We identify uniform phase and sample dithering as crucial to combat the non-linear behavior introduced by 1-bit quantization. This dithering can be implemented by sampling at an irrational intermediate frequency and with an oversampling factor with respect to the symbol rate that is irrational, respectively. Since oversampling results in noise correlation, a closed form expression of the likelihood function is not available. To enable an analytical treatment we thus study a system model with white noise by adapting the receive filter bandwidth to the sampling rate. Considering the aforementioned dithering, we obtain very tight closed form lower bounds on the Cramér-Rao lower bound (CRLB) in the large sample regime. We show that with uniform phase and sample dithering, all large sample properties of the CRLB of the unquantized receiver are preserved under 1-bit quantization, except for a signal-to-noise ratio (SNR) dependent performance loss that can be decreased by oversampling. For the more realistic colored noise case, we discuss a numerically computable upper bound of the CRLB and show that the properties of the CRLB for white noise still hold for colored noise except that the performance loss due to 1-bit quantization is reduced. Assuming a neglectable frequency offset, we use the least squares objective function to derive a typical digital matched filter receiver with a data-and timing-aided phase estimator and a timing estimator that is based on square time recovery. We show that both estimators are consistent under very general assumptions, e.g., arbitrary colored noise and stationary ergodic transmit symbols. Performance evaluations are done via simulations and are compared against the numerically computable upper bound of the CRLB. For low SNR the estimators perform well but for high SNR they converge to an error floor. The performance loss of the phase estimator due to decision-directed operation or estimated timing information is marginal. In summary, we have derived practical solutions for the design of fully digital receivers using 1-bit quantization and oversampling and presented a mathematical analysis of the proposed receiver structure. This is an important step towards enabling energy efficient future wireless communication systems with data rates of 100 Gbit/s and beyond.