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Le problème de filtrage consiste à estimer l'état d'un système dynamique, appelé signal qui est souvent un processus markovien, à partir d'observation bruitées des états passés du système. Dans ce mémoire, nous considérons un modèle de filtrage en temps continu pour le processus de diffusion. Le but est d'étudier la stabilité du filtre optimal par rapport à sa condition initiale au-delà de l'hypothèse de mélange (fort) pour le noyau de transition en ignorant l'ergodicité du signal / The filtering problem consists of estimating the state of a dynamic, called signal which is often a Markov process, from the noisy observation of the past states. In this thesis, we consider a filtering model in continuous time for the diffusion process. The aim is to study the stability of the optimal filter with respect to its initial condition beyond the mixing (or quasi – mixing) hypothesis for the transition kernel

Effort to estimate unknown time-varying channels as a part of high-speed mobile communication systems is of interest especially for next-generation wireless systems. The high computational complexity of the optimal Wiener estimator usually makes its use impractical in fast time-varying channels. As a powerful candidate, the adaptive least mean squares (LMS) algorithm offers a computationally efficient solution with its simple first-order weight-vector update equation. However, the performance of the LMS algorithm deteriorates in time-varying channels as a result of the eigenvalue disparity, i.e., spread, of the input correlation matrix in such chan nels. In this work, we incorporate the L MS algorithm into the well-known bidirectional processing idea to produce an extension called the bidirectional LMS. This algorithm is shown to be robust to the adverse effects of time-varying channels such as large eigenvalue spread. The associated tracking performance is observed to be very close to that of the optimal Wiener filter in many cases and the bidirectional LMS algorithm is therefore referred to as near-optimal. The computational complexity is observed to increase by the bidirectional employment of the LMS algorithm, but nevertheless is significantly lower than that of the optimal Wiener filter. The tracking behavior of the bidirectional LMS algorithm is also analyzed and eventually a steady-state step-size dependent mean square error (MSE) expression is derived for single antenna flat-fading channels with various correlation properties. The aforementioned analysis is then generalized to include single-antenna frequency-selective channels where the so-called ind ependence assumption is no more applicable due to the channel memory at hand, and then to multi-antenna flat-fading channels. The optimal selection of the step-size values is also presented using the results of the MSE analysis. The numerical evaluations show a very good match between the theoretical and the experimental results under various scenarios. The tracking analysis of the bidirectional LMS algorithm is believed to be novel in the sense that although there are several works in the literature on the bidirectional estimation, none of them provides a theoretical analysis on the underlying estimators. An iterative channel estimation scheme is also presented as a more realistic application for each of the estimation algorithms and the channel models under consideration. As a result, the bidirectional LMS algorithm is observed to be very successful for this real-life application with its increased but still practical level of complexity, the near-optimal tracking performa nce and robustness to the imperfect initialization.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-25T13:40:30Z No. of bitstreams: 1 marcosviniciusteixeira.pdf: 5877294 bytes, checksum: 8fe056549285d49782c2d9ec8e16f786 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-04-25T15:26:43Z (GMT) No. of bitstreams: 1 marcosviniciusteixeira.pdf: 5877294 bytes, checksum: 8fe056549285d49782c2d9ec8e16f786 (MD5) / Made available in DSpace on 2017-04-25T15:26:43Z (GMT). No. of bitstreams: 1 marcosviniciusteixeira.pdf: 5877294 bytes, checksum: 8fe056549285d49782c2d9ec8e16f786 (MD5) Previous issue date: 2015-08-21 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho tem como objetivo o estudo de técnicas para a estimação da amplitude de sinais no calorímetro de telhas (TileCal) do ATLAS no LHC em cenários de alta luminosidade. Em alta luminosidade, sinais provenientes de colisões adjacentes são observados, ocasionando o efeito de empilhamento de sinais. Neste ambiente, o método COF (do inglês, Constrained Optimal Filter), apresenta desempenho superior ao algoritmo atualmente implementado no sistema. Entretanto, o COF requer a inversão de matrizes para o cálculo da pseudo-inversa de uma matriz de convolução, dificultando sua implementação online. Para evitar a inversão de matrizes, este trabalho apresenta métodos interativos, para a daptação do COF, que resultam em operações matemáticas simples. Baseados no Gradiente Descendente, os resultados demonstraram que os algoritmos são capazes de estimar a amplitude de sinais empilhados, além do sinal de interesse com eficiência similar ao COF. Visando a implementação online, este trabalho apresenta estudos sobre a complexidade dos métodos iterativos e propõe uma arquitetura de processamento em FPGA. Baseado em uma estrutura sequencial e utilizando lógica aritmética em ponto fixo, os resultados demonstraram que a arquitetura desenvolvida é capaz executar o método iterativo, atendendo os requisitos de tempo de processamento exigidos no TileCal. / This work aims at the study of techniques for online energy estimation in the ATLAS hadronic Calorimeter (TileCal) on the LHC collider. During further periods of the LHC operation, signals coming from adjacent collisions will be observed within the same window, producing a signal superposition. In this environment, the energy reconstruction method COF (Constrained Optimal Filter) outperforms the algorithm currently implemented in the system. However , the COF method requires an inversion of matrices and its online implementation is not feasible. To avoid such inversion of matrices, this work presents iteractive methods to implement the COF, resulting in simple mathematical operations. Based on the Gradient Descent, the results demonstrate that the algorithms are capable of estimating the amplitude of the superimposed signals with efficiency similar to COF. In addition, a processing architecture for FPGA implementation is proposed. The analysis has shown that the algorithms can be implemented in the new TilaCal electronics, reaching the processing time requirements.

Cette thèse porte sur l'estimation bayésienne d'état dans les séries temporelles modélisées à l'aide des variables latentes hybrides, c'est-à-dire dont la densité admet une composante discrète-finie et une composante continue. Des algorithmes généraux d'estimation des variables d'états dans les modèles de Markov partiellement observés à états hybrides sont proposés et comparés avec les méthodes de Monte-Carlo séquentielles sur un plan théorique et appliqué. Le résultat principal est que ces algorithmes permettent de réduire significativement le coût de calcul par rapport aux méthodes de Monte-Carlo séquentielles classiques / This thesis addresses the Bayesian estimation of hybrid-valued state variables in time series. The probability density function of a hybrid-valued random variable has a finite-discrete component and a continuous component. Diverse general algorithms for state estimation in partially observable Markov processesare introduced. These algorithms are compared with the sequential Monte-Carlo methods from a theoretical and a practical viewpoint. The main result is that the proposed methods require less processing time compared to the classic Monte-Carlo methods

Am Large Hadron Collider und am ATLAS-Detektor werden umfangreiche Aufrüstungsarbeiten vorgenommen. Diese Arbeiten sind in mehrere Phasen gegliedert und umfassen unter Anderem Änderungen an der Ausleseelektronik der Flüssigargonkalorimeter; insbesondere ist es geplant, während der letzten Phase ihren Primärpfad vollständig auszutauschen. Die Elektronik besteht aus einem analogen und einem digitalen Teil: während ersterer die Signalpulse verstärkt und sie zur leichteren Abtastung verformt, führt letzterer einen Algorithmus zur Energierekonstruktion aus. Beide Teile müssen während der Aufrüstung verbessert werden, damit der Detektor interessante Kollisionsereignisse präzise rekonstruieren und uninteressante effizient verwerfen kann. In dieser Dissertation werden Simulationsstudien präsentiert, die sowohl die analoge als auch die digitale Auslese der Flüssigargonkalorimeter optimieren. Die Korrektheit der Simulation wird mithilfe von Kalibrationsdaten geprüft, die im sog. Run 2 des ATLAS-Detektors aufgenommen worden sind. Der Einfluss verschiedener Parameter der Signalverformung auf die Energieauflösung wird analysiert und die Nützlichkeit einer erhöhten Abtastrate von 80 MHz untersucht. Des Weiteren gibt diese Arbeit eine Übersicht über lineare und nichtlineare Energierekonstruktionsalgorithmen. Schließlich wird eine Auswahl von ihnen hinsichtlich ihrer Leistungsfähigkeit miteinander verglichen. Es wird gezeigt, dass ein Erhöhen der Ordnung des Optimalfilters, der gegenwärtig verwendete Algorithmus, die Energieauflösung um 2 bis 3 % verbessern kann, und zwar in allen Regionen des Detektors. Der Wiener Filter mit Vorwärtskorrektur, ein nichtlinearer Algorithmus, verbessert sie um bis zu 10 % in einigen Regionen, verschlechtert sie aber in anderen. Ein Zusammenhang dieses Verhaltens mit der Wahrscheinlichkeit fälschlich detektierter Kalorimetertreffer wird aufgezeigt und mögliche Lösungen werden diskutiert.:1 Introduction 2 An Overview of High-Energy Particle Physics 2.1 The Standard Model of Particle Physics 2.2 Verification of the Standard Model 2.3 Beyond the Standard Model 3 LHC, ATLAS, and the Liquid-Argon Calorimeters 3.1 The Large Hadron Collider 3.2 The ATLAS Detector 3.3 The ATLAS Liquid-Argon Calorimeters 4 Upgrades to the ATLAS Liquid-Argon Calorimeters 4.1 Physics Goals 4.2 Phase-I Upgrade 4.3 Phase-II Upgrade 5 Noise Suppression With Digital Filters 5.1 Terminology 5.2 Digital Filters 5.3 Wiener Filter 5.4 Matched Wiener Filter 5.5 Matched Wiener Filter Without Bias 5.6 Timing Reconstruction, Optimal Filtering, and Selection Criteria 5.7 Forward Correction 5.8 Sparse Signal Restoration 5.9 Artificial Neural Networks 6 Simulation of the ATLAS Liquid-Argon Calorimeter Readout Electronics 6.1 AREUS 6.2 Hit Generation and Sampling 6.3 Pulse Shapes 6.4 Thermal Noise 6.5 Quantization 6.6 Digital Filters 6.7 Statistical Analysis 7 Results of the Readout Electronics Simulation Studies 7.1 Statistical Treatment 7.2 Simulation Verification Using Run-2 Data 7.3 Dependence of the Noise on the Shaping Time 7.4 The Analog Readout Electronics and the ADC 7.5 The Optimal Filter (OF) 7.6 The Wiener Filter 7.7 The Wiener Filter with Forward Correction (WFFC) 7.8 Final Comparison and Conclusions 8 Conclusions and Outlook Appendices / The Large Hadron Collider and the ATLAS detector are undergoing a comprehensive upgrade split into multiple phases. This effort also affects the liquid-argon calorimeters, whose main readout electronics will be replaced completely during the final phase. The electronics consist of an analog and a digital portion: the former amplifies the signal and shapes it to facilitate sampling, the latter executes an energy reconstruction algorithm. Both must be improved during the upgrade so that the detector may accurately reconstruct interesting collision events and efficiently suppress uninteresting ones. In this thesis, simulation studies are presented that optimize both the analog and the digital readout of the liquid-argon calorimeters. The simulation is verified using calibration data that has been measured during Run 2 of the ATLAS detector. The influence of several parameters of the analog shaping stage on the energy resolution is analyzed and the utility of an increased signal sampling rate of 80 MHz is investigated. Furthermore, a number of linear and non-linear energy reconstruction algorithms is reviewed and the performance of a selection of them is compared. It is demonstrated that increasing the order of the Optimal Filter, the algorithm currently in use, improves energy resolution by 2 to 3 % in all detector regions. The Wiener filter with forward correction, a non-linear algorithm, gives an improvement of up to 10 % in some regions, but degrades the resolution in others. A link between this behavior and the probability of falsely detected calorimeter hits is shown and possible solutions are discussed.:1 Introduction 2 An Overview of High-Energy Particle Physics 2.1 The Standard Model of Particle Physics 2.2 Verification of the Standard Model 2.3 Beyond the Standard Model 3 LHC, ATLAS, and the Liquid-Argon Calorimeters 3.1 The Large Hadron Collider 3.2 The ATLAS Detector 3.3 The ATLAS Liquid-Argon Calorimeters 4 Upgrades to the ATLAS Liquid-Argon Calorimeters 4.1 Physics Goals 4.2 Phase-I Upgrade 4.3 Phase-II Upgrade 5 Noise Suppression With Digital Filters 5.1 Terminology 5.2 Digital Filters 5.3 Wiener Filter 5.4 Matched Wiener Filter 5.5 Matched Wiener Filter Without Bias 5.6 Timing Reconstruction, Optimal Filtering, and Selection Criteria 5.7 Forward Correction 5.8 Sparse Signal Restoration 5.9 Artificial Neural Networks 6 Simulation of the ATLAS Liquid-Argon Calorimeter Readout Electronics 6.1 AREUS 6.2 Hit Generation and Sampling 6.3 Pulse Shapes 6.4 Thermal Noise 6.5 Quantization 6.6 Digital Filters 6.7 Statistical Analysis 7 Results of the Readout Electronics Simulation Studies 7.1 Statistical Treatment 7.2 Simulation Verification Using Run-2 Data 7.3 Dependence of the Noise on the Shaping Time 7.4 The Analog Readout Electronics and the ADC 7.5 The Optimal Filter (OF) 7.6 The Wiener Filter 7.7 The Wiener Filter with Forward Correction (WFFC) 7.8 Final Comparison and Conclusions 8 Conclusions and Outlook Appendices