Cyber-Physical Systems theory is a new concept that is about to revolutionize the way computers interact with the physical world by integrating physical knowledge into the computing systems and tailoring such computing systems in a way that is more compatible with the way processes happen in the physical world. In this master’s thesis, Field Programmable Gate Arrays (FPGA) are studied as a potential technological asset that may contribute to the enablement of the Cyber-Physical paradigm. As an example application that may benefit from cyber-physical system support, the Electro-Slag Remelting process - a process for remelting metals into better alloys - has been chosen due to the maturity of its related physical models and controller designs. In particular, the Particle Filter that estimates the state of the process is studied as a candidate for FPGA-based computing enhancements. In comparison with CPUs, through the designs and experiments carried in relationship with this study, the FPGA reveals itself as a serious contender in the arsenal of v computing means for Cyber-Physical Systems, due to its capacity to mimic the ubiquitous parallelism of physical processes. / text

<p>In this report a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms based on resampling quality and on computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in resampling quality and computational complexity.</p>

Wildfires have significant impact on both ecosystems and human society. To effectively manage wildfires, simulation models are used to study and predict wildfire spread. The accuracy of wildfire spread simulations depends on many factors, including GIS data, fuel data, weather data, and high-fidelity wildfire behavior models. Unfortunately, due to the dynamic and complex nature of wildfire, it is impractical to obtain all these data with no error. Therefore, predictions from the simulation model will be different from what it is in a real wildfire. Without assimilating data from the real wildfire and dynamically adjusting the simulation, the difference between the simulation and the real wildfire is very likely to continuously grow. With the development of sensor technologies and the advance of computer infrastructure, dynamic data driven application systems (DDDAS) have become an active research area in recent years. In a DDDAS, data obtained from wireless sensors is fed into the simulation model to make predictions of the real system. This dynamic input is treated as the measurement to evaluate the output and adjust the states of the model, thus to improve simulation results. To improve the accuracy of wildfire spread simulations, we apply the concept of DDDAS to wildfire spread simulation by dynamically assimilating sensor data from real wildfires into the simulation model. The assimilation system relates the system model and the observation data of the true state, and uses analysis approaches to obtain state estimations. We employ Sequential Monte Carlo (SMC) methods (also called particle filters) to carry out data assimilation in this work. Based on the structure of DDDAS, this dissertation presents the data assimilation system and data assimilation results in wildfire spread simulations. We carry out sensitivity analysis for different densities, frequencies, and qualities of sensor data, and quantify the effectiveness of SMC methods based on different measurement metrics. Furthermore, to improve simulation results, the image-morphing technique is introduced into the DDDAS for wildfire spread simulation.

In this report a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms based on resampling quality and on computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in resampling quality and computational complexity.

In this thesis the radar target tracking problem in Bayesian estimation framework is studied. Traditionally, linear or linearized models, where the uncertainty in the system and measurement models is typically represented by Gaussian densities, are used in this area. Therefore, classical sub-optimal Bayesian methods based on linearized Kalman filters can be used. The sequential Monte Carlo methods, i.e. particle filters, make it possible to utilize the inherent non-linear state relations and non-Gaussian noise models. Given the sufficient computational power, the particle filter can provide better results than Kalman filter based methods in many cases. A survey over relevant radar tracking literature is presented including aspects as estimation and target modeling. In various target tracking related estimation applications, particle filtering algorithms are presented.

Ce travail de thèse poursuit une perspective double dans l'usage conjoint des méthodes de Monte Carlo séquentielles (MMS) et de l'algorithme Espérance-Maximisation (EM) dans le cadre des modèles de Markov cachés présentant une structure de dépendance markovienne d'ordre supérieur à 1 au niveau de la composante inobservée. Tout d'abord, nous commençons par un exposé succinct de l'assise théorique des deux concepts statistiques à travers les chapitres 1 et 2 qui leurs sont consacrés. Dans un second temps, nous nous intéressons à la mise en pratique simultanée des deux concepts au chapitre 3 et ce dans le cadre usuel où la structure de dépendance est d'ordre 1. L'apport des méthodes MMS dans ce travail réside dans leur capacité à approximer efficacement des fonctionnelles conditionnelles bornées, notamment des quantités de filtrage et de lissage dans un cadre non linéaire et non gaussien. Quant à l'algorithme EM, il est motivé par la présence à la fois de variables observables et inobservables (ou partiellement observées) dans les modèles de Markov Cachés et singulièrement les mdèles de volatilité stochastique étudié. Après avoir présenté aussi bien l'algorithme EM que les méthodes MCs ainsi que quelques unes de leurs propriétés dans les chapitres 1 et 2 respectivement, nous illustrons ces deux outils statistiques au travers de la calibration d'un modèle de volatilité stochastique. Cette application est effectuée pour des taux change ainsi que pour quelques indices boursiers au chapitre 3. Nous concluons ce chapitre sur un léger écart du modèle de volatilité stochastique canonique utilisé ainsi que des simulations de Monte Carlo portant sur le modèle résultant. Enfin, nous nous efforçons dans les chapitres 4 et 5 à fournir les assises théoriques et pratiques de l'extension des méthodes Monte Carlo séquentielles notamment le filtrage et le lissage particulaire lorsque la structure markovienne est plus prononcée. En guise d'illustration, nous donnons l'exemple d'un modèle de volatilité stochastique dégénéré dont une approximation présente une telle propriété de dépendance.

abstract: The radar performance of detecting a target and estimating its parameters can deteriorate rapidly in the presence of high clutter. This is because radar measurements due to clutter returns can be falsely detected as if originating from the actual target. Various data association methods and multiple hypothesis filtering approaches have been considered to solve this problem. Such methods, however, can be computationally intensive for real time radar processing. This work proposes a new approach that is based on the unsupervised clustering of target and clutter detections before target tracking using particle filtering. In particular, Gaussian mixture modeling is first used to separate detections into two Gaussian distinct mixtures. Using eigenvector analysis, the eccentricity of the covariance matrices of the Gaussian mixtures are computed and compared to threshold values that are obtained a priori. The thresholding allows only target detections to be used for target tracking. Simulations demonstrate the performance of the new algorithm and compare it with using k-means for clustering instead of Gaussian mixture modeling. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2016

La croissance des plantes en interaction avec l'environnement peut être décrite par des modèles mathématiques. Ceux-ci présentent des perspectives prometteuses pour un nombre considérable d'applications telles que la prévision des rendements ou l'expérimentation virtuelle dans le contexte de la sélection variétale. Dans cette thèse, nous nous intéressons aux différentes solutions capables d'améliorer les capacités prédictives des modèles de croissance de plantes, en particulier grâce à des méthodes statistiques avancées. Notre contribution se résume en quatre parties.Tout d'abord, nous proposons un nouveau modèle de culture (Log-Normal Allocation and Senescence ; LNAS). Entièrement construit dans un cadre probabiliste, il décrit seulement les processus écophysiologiques essentiels au bilan de la biomasse végétale afin de contourner les problèmes d'identification et d'accentuer l'évaluation des incertitudes. Ensuite, nous étudions en détail le paramétrage du modèle. Dans le cadre Bayésien, nous mettons en œuvre des méthodes Monte-Carlo Séquentielles (SMC) et des méthodes de Monte-Carlo par Chaînes de Markov (MCMC) afin de répondre aux difficultés soulevées lors du paramétrage des modèles de croissance de plantes, caractérisés par des équations dynamiques non-linéaires, des données rares et un nombre important de paramètres. Dans les cas où la distribution a priori est peu informative, voire non-informative, nous proposons une version itérative des méthodes SMC et MCMC, approche équivalente à une variante stochastique d'un algorithme de type Espérance-Maximisation, dans le but de valoriser les données d'observation tout en préservant la robustesse des méthodes Bayésiennes. En troisième lieu, nous soumettons une méthode d'assimilation des données en trois étapes pour résoudre le problème de prévision du modèle. Une première étape d'analyse de sensibilité permet d'identifier les paramètres les plus influents afin d'élaborer une version plus robuste de modèle par la méthode de sélection de modèles à l'aide de critères appropriés. Ces paramètres sélectionnés sont par la suite estimés en portant une attention particulière à l'évaluation des incertitudes. La distribution a posteriori ainsi obtenue est considérée comme information a priori pour l'étape de prévision, dans laquelle une méthode du type SMC telle que le filtrage par noyau de convolution (CPF) est employée afin d'effectuer l'assimilation de données. Dans cette étape, les estimations des états cachés et des paramètres sont mis à jour dans l'objectif d'améliorer la précision de la prévision et de réduire l'incertitude associée. Finalement, d'un point de vue applicatif, la méthodologie proposée est mise en œuvre et évaluée avec deux modèles de croissance de plantes, le modèle LNAS pour la betterave sucrière et le modèle STICS pour le blé d'hiver. Quelques pistes d'utilisation de la méthode pour l'amélioration du design expérimental sont également étudiées, dans le but d'améliorer la qualité de la prévision. Les applications aux données expérimentales réelles montrent des performances prédictives encourageantes, ce qui ouvre la voie à des outils d'aide à la décision en agriculture. / Plant growth models aim to describe plant development and functional processes in interaction with the environment. They offer promising perspectives for many applications, such as yield prediction for decision support or virtual experimentation inthe context of breeding. This PhD focuses on the solutions to enhance plant growth model predictive capacity with an emphasis on advanced statistical methods. Our contributions can be summarized in four parts. Firstly, from a model design perspective, the Log-Normal Allocation and Senescence (LNAS) crop model is proposed. It describes only the essential ecophysiological processes for biomass budget in a probabilistic framework, so as to avoid identification problems and to accentuate uncertainty assessment in model prediction. Secondly, a thorough research is conducted regarding model parameterization. In a Bayesian framework, both Sequential Monte Carlo (SMC) methods and Markov chain Monte Carlo (MCMC) based methods are investigated to address the parameterization issues in the context of plant growth models, which are frequently characterized by nonlinear dynamics, scarce data and a large number of parameters. Particularly, whenthe prior distribution is non-informative, with the objective to put more emphasis on the observation data while preserving the robustness of Bayesian methods, an iterative version of the SMC and MCMC methods is introduced. It can be regarded as a stochastic variant of an EM type algorithm. Thirdly, a three-step data assimilation approach is proposed to address model prediction issues. The most influential parameters are first identified by global sensitivity analysis and chosen by model selection. Subsequently, the model calibration is performed with special attention paid to the uncertainty assessment. The posterior distribution obtained from this estimation step is consequently considered as prior information for the prediction step, in which a SMC-based on-line estimation method such as Convolution Particle Filtering (CPF) is employed to perform data assimilation. Both state and parameter estimates are updated with the purpose of improving theprediction accuracy and reducing the associated uncertainty. Finally, from an application point of view, the proposed methodology is implemented and evaluated with two crop models, the LNAS model for sugar beet and the STICS model for winter wheat. Some indications are also given on the experimental design to optimize the quality of predictions. The applications to real case scenarios show encouraging predictive performances and open the way to potential tools for yield prediction in agriculture.

In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlying volatility process and of the unknown model parameters in the Heston model. The particle filter and the auxiliary particle filter are also employed to perform sequential inference. Next we extend the Heston model to the fractional Heston model, by replacing the Brownian motions that drive the underlying stochastic differential equations by fractional Brownian motions, so allowing a richer dependence structure across time. Again, we use a variety of methods to perform inference. We apply our methodology to simulated and real financial data with success. We then discuss how to make forecasts using both the Heston and the fractional Heston model. We make comparisons between the models and show that using our new fractional Heston model can lead to improve forecasts for real financial data.

Title: Sequential Monte Carlo Methods Author: David Coufal Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Viktor Beneš, DrSc. Abstract: The thesis summarizes theoretical foundations of sequential Monte Carlo methods with a focus on the application in the area of particle filters; and basic results from the theory of nonparametric kernel density estimation. The summary creates the basis for investigation of application of kernel meth- ods for approximation of densities of distributions generated by particle filters. The main results of the work are the proof of convergence of kernel estimates to related theoretical densities and the specification of the development of approx- imation error with respect to time evolution of a filter. The work is completed by an experimental part demonstrating the work of presented algorithms by simulations in the MATLABR⃝ computational environment. Keywords: sequential Monte Carlo methods, particle filters, nonparametric kernel estimates