This thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional nonlinear filtering problems. The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon- Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own. The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates visà-vis those obtained through the parent filtering schemes. In Chapter 4, we explore the possibility of unscented transformation on Gaussian random variables, as employed within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. We propose in Chapter 5 an iterated gain-based particle filter that is consistent with the form of the nonlinear filtering (Kushner-Stratonovich) equation in our attempt to treat larger dimensional filtering problems with enhanced estimation accuracy. A crucial aspect of the proposed filtering set-up is that it retains the simplicity of implementation of the ensemble Kalman filter (EnKF). The numerical results obtained via EnKF-like simulations with or without a reduced-rank unscented transformation also indicate substantively improved filter convergence. The final contribution, reported in Chapter 6, is an iterative, gain-based filter bank incorporating an artificial diffusion parameter and may be viewed as an extension of the iterative filter in Chapter 5. While the filter bank helps in exploring the phase space of the state variables better, the iterative strategy based on the artificial diffusion parameter, which is lowered to zero over successive iterations, helps improve the mixing property of the associated iterative update kernels and these are aspects that gather importance for highly nonlinear filtering problems, including those involving significant initial mismatch of the process states and the measured ones. Numerical evidence of remarkably enhanced filter performance is exemplified by target tracking and structural health assessment applications. The thesis is finally wound up in Chapter 7 by summarizing these developments and briefly outlining the future research directions

Contexte: Le retard de croissance intra-utérin (RCIU) désigne l’incapacité du fœtus à atteindre son potentiel de croissance déterminé génétiquement en raison de diverses causes. Il est défini le plus souvent par un poids de naissance inférieur au 10ème percentile pour l’âge gestationnel sur les courbes néonatales. Ce travail de thèse a comme objectif de répondre aux questions non-résolues sur la définition et les conséquences du RCIU dans le contexte de la grande prématurité: (1) Quelle est la meilleure définition du RCIU à utiliser pour identifier les enfants à risque ? (2) Quels sont les risques de mortalité et de morbidités néonatales respiratoires et neurologiques associés au RCIU et existe-t-il des interactions avec les pathologies de la grossesse responsables de cette naissance très prématurée ? (3) Quel est l’impact du RCIU sur le devenir neuro-développemental à 2 ans, en particulier chez les enfants nés extrêmement prématurément ? Méthodes: Nous avons utilisé deux sources de données. L’étude MOSAIC (Models for OrganiSing Access to Intensive Care for Very Preterm Babies in Europe) est une étude européenne en population qui porte sur l’ensemble des naissances survenues entre 22 et 31 semaines d’aménorrhée en 2003 dans dix régions européennes. Les enfants ont été suivis jusqu’à la sortie d’hospitalisation (population d’étude : 4525 enfants). La deuxième source est une cohorte d’enfants nés avant 27SA qui ont été hospitalisés dans le service de réanimation néonatale à l'hôpital de Port-Royal de 1999 à 2008 et qui ont eu un examen pédiatrique et une évaluation selon l’échelle de Brunet-Lézine qui inclut quatre domaines du développement global de l’enfant : la motricité globale, la motricité fine, le langage et l’interaction sociale (445 enfants admis, 268 enfants suivis à 2 ans). Résultats: Dans les deux populations, les risques de décès et de dysplasie broncho-pulmonaire étaient plus élevés pour les enfants ayant un poids de naissance <10éme percentile des courbes néonatales, mais également pour des enfants avec un poids plus élevé (entre le 10éme et le 24éme percentile des courbes néonatales ou <10ème percentile des courbes fœtales). Par contre, il n’y avait pas de lien entre les complications neurologiques et le faible poids, ni d’interaction avec les pathologies de la grossesse. Le RCIU était associé à un risque élevé du retard neurocognitif à deux ans d’âge corrigé chez les extrêmes prématurés, surtout dans le domaine de la motricité fine et de l’interaction sociale mais pas dans le domaine du langage et de la motricité globale. Nous n’avons pas trouvé d’association entre le RCIU et le risque d’infirmité motrice cérébrale à deux ans d’âge corrigé. Conclusions: L’utilisation du 10ème percentile des courbes néonatales n’est pas adaptée pour identifier l’impact du RCIU chez les grands prématurés ; l’utilisation de multiples seuils ou de courbes de croissance fœtale est nécessaire. Le RCIU accroit les risques de mortalité et de dysplasie broncho-pulmonaire, mais n’est pas associé aux lésions cérébrales sévères ; ces associations sont observées dans différents contextes périnatals (pathologies vasculaires et infectieuses, et naissances à des âges gestationnels très précoces). Le RCIU représente un facteur pronostic défavorable pour le neuro-développement à moyen terme. Nos résultats soulèvent de nouvelles questions sur le suivi adapté pour les enfants ayant un RCIU après leur sortie de l’hôpital et aussi sur les éventuels mécanismes biologiques pouvant expliquer les liens entre le RCIU avec une morbidité respiratoire et certains domaines du développement neurocognitif à moyen terme. / Background: Intrauterine growth restriction (IUGR) refers to the inability of the fetus to achieve its genetically determined growth potential due to various causes. Most often, it is defined by a birth weight less than the 10th percentile for gestational age using neonatal growth curves. This thesis aims to answer unresolved questions about the definition and consequences of IUGR in the context of very preterm birth: (1) what is the best definition of IUGR for identifying children at risk? (2) What are the risks of mortality and neonatal respiratory and neurological morbidity associated with IUGR and are there interactions with the underlying pregnancy complications responsible for the very preterm birth? (3) What is the impact of IUGR on neurodevelopmental at 2 years, especially for children born extremely preterm ? Methods: We used two data sources. The MOSAIC study (Models for Organising Access to Intensive Care for Very Preterm Babies in Europe) is a European population-based study that included all births occurring between 22 and 31 weeks of gestation in 2003 in ten European regions. The children were followed until hospital discharge (study population = 4525 infants). The second source is a cohort of children born before 27 weeks of GA who were hospitalized in the neonatal intensive care unit at the Port Royal Hospital from 1999 to 2008 and had a pediatric examination and Brunet-Lézine (BL) neurodevelopmental assessment at 2 years of corrected age (445 children in the cohort, 268children followed at 2 years). The BL assessment includes four areas of child development: gross motor, fine motor, language and social interaction skills. Results: In both populations, the risk of death and bronchopulmonary dysplasia were higher for children with a birth weight <10th percentile of neonatal growth curves but also for children with a higher birth weight (between the 10th and the 24th percentile of neonatal growth curves or <10th percentile of fetal growth curves). In contrast, there was no link between neurological complications and low birth weight and no interactions with pregnancy complications. IUGR was associated with neurocognitive delay among extremely preterm children evaluated at two years of corrected age, especially for fine motor and social interaction skills, but not for language and gross motor skills. We did not find any association between IUGR and the risk of cerebral palsy at two years of corrected age. Conclusions: The use of the 10th percentile of neonatal growth curves is not suitable for identifying the impact of IUGR in very preterm infants; using higher thresholds or fetal growth curves is necessary. IUGR increased the risks of mortality and bronchopulmonary dysplasia, but was not associated with severe brain damage; these associations are observed in multiple clinical contexts (vascular and infectious pregnancy complications, and births at very early gestational ages). IUGR is a risk factor for poor medium-term neuro-development. Our results raise new questions about the appropriate surveillance for children with IUGR after discharge from the hospital and also about possible biological mechanisms that could explain the relationship between IUGR and respiratory morbidity and neurocognitive development.

Le nombre d'adultes porteurs de cardiopathies congénitales, de plus en plus sévères est constante progression. A moyen voire long terme certain d’entre eux posent des problèmes d’insuffisance cardiaque et de troubles du rythme parfois létaux. La physiologie de ces complications est multi factorielle et s’écarte souvent des schémas habituels. L’asynchronisme ventriculaire présentent chez un nombre important d’entre eux est connu pour favoriser un remodelage ventriculaire conduisant à l’insuffisance cardiaque sur cœur sain.Dans ce travail en couplant données expérimentales animales et études cliniques, nous avons étudié : 1) l’impact aigu puis chronique de la resynchronisation biventriculaire sur un modèle animal d’insuffisance cardiaque droite mimant la tétralogie de Fallot et sur une population de patients ; 2) le rôle et la conséquence d’une stimulation conventionnelle sur une physiologie de ventricule droit systémique ; 3) l’effet délétère de la stimulation VD prolongée sur un modèle de cœur animal en cours de développement.Nous avons appris que 1) la resynchronisation biventriculaire permet un bénéfice hémodynamique significatif chez l’animal mais aussi sur une population de Fallot implantées ; 2) que l’asynchronisme généré par la stimulation conventionnelle est délétère pour la fonction du ventricule systémique mais aussi pour le cœur de l’enfant en cours développement. La resynchronisation est un traitement prometteur pour traiter l’insuffisance cardiaque mais pourrait aussi l’être pour en prévenir sa survenue. De nouvelles techniques d’implantation nous permettent aujourd’hui d’implanter des patients qui présentent beaucoup d’obstacles anatomiques et d’éviter nombre de complications grave de la stimulation. / The number of adults with severe congenital heart disease is constantly growing. At medium to long-term follow up, these patients may present with heart failure or conduction disorders, which may lead to death. The pathophysiology and clinical course of these complications is multi-factorial and may be different from that in patients without congenital heart disease. In normal hearts, electromechanical dyssynchrony is known to induce ventricular remodeling and heart failure. Ventricular asynchrony is also present in a substantial number of adults with congenital heart disease. In this study, we combined animal experiments and clinical studies to investigate: 1) the acute and chronic effect of biventricular resynchronization therapy on cardiac function in an animal model mimicking right ventricular heart failure in Tetralogy of Fallot, as well as in patients with Tetralogy of Fallot; 2) the consequences of conventional ventricular pacing in patients with ‘systemic right ventricle physiology’; 3) the effects of chronic right ventricular pacing in an animal model of the developing heart.We found that: 1) biventricular resynchronization induces significant hemodynamic benefit in the animal model of Tetralogy of Fallot as well as in Fallot patients; 2) ventricular asynchrony induced by conventional ventricular pacing is deleterious to the function of the systemic right ventricle; 3) chronic right ventricular pacing is harmful to the developing (pediatric) heart with normal biventricular anatomy. Cardiac resynchronization therapy is promising as a treatment for heart failure, but may also prevent heart failure. Nowadays, new implantation techniques allow us to implant pacing devices in patients with limited anatomical access due to prior surgery and help to avoid numerous severe complications of conventional pacing therapy