Doctor of Philosophy / Department of Statistics / Juan Du / It is common to assume the spatial or spatio-temporal data are realizations of underlying random elds or stochastic processes. E ective approaches to modelling of the underlying autocorrelation structure of the same random eld and the association among multiple processes are of great demand in many areas including atmospheric sciences, meteorology and agriculture. To this end, this dissertation studies methods and application of the spatial modeling of large-scale dependence structure and spatio-temporal regression modelling. First, variogram and variogram matrix functions play important roles in modeling dependence structure among processes at di erent locations in spatial statistics. With more and more data collected on a global scale in environmental science, geophysics, and related elds, we focus on the characterizations of the variogram models on spheres of all dimensions for both stationary and intrinsic stationary, univariate and multivariate random elds. Some e cient approaches are proposed to construct a variety of variograms including simple polynomial structures. In particular, the series representation and spherical behavior of intrinsic stationary random elds are explored in both theoretical and simulation study. The applications of the proposed model and related theoretical results are demonstrated using simulation and real data analysis. Second, knowledge of the influential factors on the number of days suitable for fieldwork (DSFW) has important implications on timing of agricultural eld operations, machinery decision, and risk management. To assess how some global climate phenomena such as El Nino Southern Oscillation (ENSO) a ects DSFW and capture their complex associations in space and time, we propose various spatio-temporal dynamic models under hierarchical Bayesian framework. The Integrated Nested Laplace Approximation (INLA) is used and adapted to reduce the computational burden experienced when a large number of geo-locations and time points is considered in the data set. A comparison study between dynamics models with INLA viewing spatial domain as discrete and continuous is conducted and their pros and cons are evaluated based on multiple criteria. Finally a model with time- varying coefficients is shown to reflect the dynamic nature of the impact and lagged effect of ENSO on DSFW in US with spatio-temporal correlations accounted.

Traumatic injuries lead to articular cartilage lesion formation and result in the development of osteoarthritis. Recent research suggests that the early stage of mechanical injuries involve cell death (apoptosis and necrosis) and inflammation. In this thesis, we focus on building mathematical models to investigate the biological mechanism involving chondrocyte death and inflammatory responses in the process of cartilage degeneration. Chapter 1 describes the structure of articular cartilage, the process of carti- lage degeneration, and reviews of existing mathematical models. Chapter 2 presents a delay-diffusion-reaction model of cartilage lesion formation under cyclic loading. Computational methods were used to simulate the impact of varying loading stresses and erythropoietin levels. The model is parameterized with experimental results, and is therefore clinically relevant. Due to numerical limitations using delay differential equations, a new model is presented using tools for population dynamics. Chapter 3 presents an age and space-structured model of articular cartilage lesion formation un- der a single blunt impact. Age structure is introduced to represent the time delay in cytokine synthesis and cell transition. Numerical simulations produce similar tempo- ral and spatial patterns to our experimental data. In chapter 4, we extend our model under the cyclic loading setting. Chapter 5 builds a spatio-temporal model adapted from the former models, and investigates the distribution of model parameters using experimental data and statistical methods. Chapter 6 concludes.

In ecological studies, the goal is often to describe and gain further insight into ecological processes underlying the data collected during observational studies. Because of the nature of observational data, it can often be difficult to separate the variation in the data from the underlying process or `state dynamics.' In order to better address this issue, it is becoming increasingly common for researchers to use hierarchical models. Hierarchical spatial, temporal, and spatio-temporal models allow for the simultaneous modeling of both first and second order processes, thus accounting for underlying autocorrelation in the system while still providing insight into overall spatial and temporal pattern. In this particular study, I use two species of interest, the lesser and greater scaup (Aythya affnis and Aythya marila), as an example of how hierarchical models can be utilized in wildlife management studies. Scaup are the most abundant and widespread diving duck in North America, and are important game species. Since 1978, the continental population of scaup has declined to levels that are 16% below the 1955-2010 average and 34% below the North American Waterfowl Management Plan goal. The greatest decline in abundance of scaup appears to be occurring in the western boreal forest, where populations may have depressed rates of reproductive success, survival, or both. In order to better understand the causes of the decline, and better understand the biology of scaup in general, a level of high importance has been placed on retrospective analyses that determine the spatial and temporal changes in population abundance. In order to implement Bayesian hierarchical models, I used a method called Integrated Nested Laplace Approximation (INLA) to approximate the posterior marginal distribution of the parameters of interest, rather than the more common Markov Chain Monte Carlo (MCMC) approach. Based on preliminary analysis, the data appeared to be overdispersed, containing a disproportionately high number of zeros along with a high variance relative to the mean. Thus, I considered two potential data models, the negative binomial and the zero-inflated negative binomial. Of these models, the zero-inflated negative binomial had the lowest DIC, thus inference was based on this model. Results from this model indicated that a large proportion of the strata were not decreasing (i.e., the estimated slope of the parameter was not significantly different from zero). However, there were important exceptions with strata in the northwest boreal forest and southern prairie parkland habitats. Several strata in the boreal forest habitat had negative slope estimates, indicating a decrease in breeding pairs, while some of the strata in the prairie parkland habitat had positive slope estimates, indicating an increase in this region. Additionally, from looking at plots of individual strata, it seems that the strata experiencing increases in breeding pairs are experiencing dramatic increases. Overall, my results support previous work indicating a decline in population abundance in the northern boreal forest of Canada, and additionally indicate that the population of scaup has increased rapidly in the prairie pothole region since 1957. Yet, by accounting for spatial and temporal autocorrelation in the data, it appears that declines in abundance are not as widespread as previously reported.

O modelo TF-ORM (Temporal Functionality in Objects With Roles Model) é um modelo de dados temporal orientado a objetos que utiliza o conceito de papeis para representar os diferentes comportamentos dos objetos. 0 modelo permite a modelagem dos aspectos estáticos e dinâmicos da aplicação pois considera todos os estados dos objetos ao longo de sua evolução. Sua linguagem de consulta e baseada na linguagem SQL e possibilita a recuperação de diferentes histórias do banco de dados. Este trabalho apresenta um sistema visual de consulta para o modelo TFORM. O VQS TF-ORM (Visual Query System TF-ORM) é um ambiente para recuperação de informações temporais. O sistema permite que as consultas sejam elaboradas de três formas alternativas: textual, gráfica ou por formulários. A linguagem gráfica possui o mesmo poder de expressão da linguagem textual, permitindo que a consulta seja elaborada diretamente sobre o esquema conceitual gráfico do modelo com o auxilio de um conjunto de janelas e elementos visuais. A recuperação de informações utilizando-se formulários não possui o mesmo poder de expressão da linguagem textual, mas possibilita a recuperação dos valores das propriedades de um determinado objeto através de uma hierarquia de janelas. A recuperação de informações através do sistema visual de consulta do modelo apresenta algumas facilidades tais como: representação visual dos operadores temporais do modelo, definição de níveis de detalhe e navegação sobre o esquema gráfico, armazenamento das consultas para posterior utilizando, possibilidade de representar uma consulta textual na forma visual e vice-versa, entre outras. Alem da preocupação com a definição de restrições temporais, o ambiente considera ainda as diferentes formas de apresentação do resultado da consulta que podem ser selecionadas pelo usuário. No sistema apresentado neste trabalho, o modelo TF-ORM é implementado em um banco de dados relacional que utiliza a linguagem SQL para recuperação de informações. Para a implementação do modelo em um banco de dados relacional foi feito um mapeamento, que determina como os conceitos de orientação a objetos, papel e tempo devem ser mapeados para tabelas e atributos no modelo relacional. As consultas realizadas na linguagem TF-ORM são então traduzidas para a linguagem de consulta do banco de dados relacional. O ambiente foi implementado utilizando a ferramenta para desenvolvimento de aplicações Delphi e o banco de dados Watcom, um banco de dados relacional que permite a recuperação de informações no padrão SQL/ANSI. / TF-ORM model (Temporal Functionality in Objects with Roles Model) is an object-oriented temporal data model which uses the role concept to represent different behaviors of objects. The model allows modelling of the static and the dynamic aspects of an application representing all the states of its evolution. The TF-ORM query language is based on the SQL language and enables the recovery of different database histories. This work represents a visual query system for the TF-ORM model. The VQS TF-ORM (Visual Query System TF-ORM) is an environment for recovery of temporal information. The system allows queries to be elaborated in three alternatives way: textual, graphic or by forms. The graphic language has the same functionality of the textual lan g uage permitting the query to be elaborated directly on the graphic conceptual schema of the model this operation is supported by a set of windows and visual elements. The information recovery using forms doesn't have the same functionality of the textual lan guage, but enables recovery of property values of an object through window hierarchies. Information recovery using the visual query system of the model presents some facilities: the visual representation of temporal operators, different levels of details for the navigation on the graphic schema, query storage for later use, possibility of representing a textual query in a visual way and vice-versa. The environment supports the definition of temporal constraints and the selection by the user of different representations forms for the results of a query. In the presented system, the TF-ORM model is implemented in a relational database which uses SQL language for information recovery. In order to implement the model in a relational database, a mapping was done - the concepts of the object orientation, roles and time were mapped in to tables and attributes to the relational model. The queries performed in the TF-ORM language are translated into the query lan guage of relational database. The environment was implemented using Delphi and the Watcom database, a relational database which allows information recovery in SQL/ANSI standard.

O modelo TF-ORM (Temporal Functionality in Objects With Roles Model) é um modelo de dados temporal orientado a objetos que utiliza o conceito de papeis para representar os diferentes comportamentos dos objetos. 0 modelo permite a modelagem dos aspectos estáticos e dinâmicos da aplicação pois considera todos os estados dos objetos ao longo de sua evolução. Sua linguagem de consulta e baseada na linguagem SQL e possibilita a recuperação de diferentes histórias do banco de dados. Este trabalho apresenta um sistema visual de consulta para o modelo TFORM. O VQS TF-ORM (Visual Query System TF-ORM) é um ambiente para recuperação de informações temporais. O sistema permite que as consultas sejam elaboradas de três formas alternativas: textual, gráfica ou por formulários. A linguagem gráfica possui o mesmo poder de expressão da linguagem textual, permitindo que a consulta seja elaborada diretamente sobre o esquema conceitual gráfico do modelo com o auxilio de um conjunto de janelas e elementos visuais. A recuperação de informações utilizando-se formulários não possui o mesmo poder de expressão da linguagem textual, mas possibilita a recuperação dos valores das propriedades de um determinado objeto através de uma hierarquia de janelas. A recuperação de informações através do sistema visual de consulta do modelo apresenta algumas facilidades tais como: representação visual dos operadores temporais do modelo, definição de níveis de detalhe e navegação sobre o esquema gráfico, armazenamento das consultas para posterior utilizando, possibilidade de representar uma consulta textual na forma visual e vice-versa, entre outras. Alem da preocupação com a definição de restrições temporais, o ambiente considera ainda as diferentes formas de apresentação do resultado da consulta que podem ser selecionadas pelo usuário. No sistema apresentado neste trabalho, o modelo TF-ORM é implementado em um banco de dados relacional que utiliza a linguagem SQL para recuperação de informações. Para a implementação do modelo em um banco de dados relacional foi feito um mapeamento, que determina como os conceitos de orientação a objetos, papel e tempo devem ser mapeados para tabelas e atributos no modelo relacional. As consultas realizadas na linguagem TF-ORM são então traduzidas para a linguagem de consulta do banco de dados relacional. O ambiente foi implementado utilizando a ferramenta para desenvolvimento de aplicações Delphi e o banco de dados Watcom, um banco de dados relacional que permite a recuperação de informações no padrão SQL/ANSI. / TF-ORM model (Temporal Functionality in Objects with Roles Model) is an object-oriented temporal data model which uses the role concept to represent different behaviors of objects. The model allows modelling of the static and the dynamic aspects of an application representing all the states of its evolution. The TF-ORM query language is based on the SQL language and enables the recovery of different database histories. This work represents a visual query system for the TF-ORM model. The VQS TF-ORM (Visual Query System TF-ORM) is an environment for recovery of temporal information. The system allows queries to be elaborated in three alternatives way: textual, graphic or by forms. The graphic language has the same functionality of the textual lan g uage permitting the query to be elaborated directly on the graphic conceptual schema of the model this operation is supported by a set of windows and visual elements. The information recovery using forms doesn't have the same functionality of the textual lan guage, but enables recovery of property values of an object through window hierarchies. Information recovery using the visual query system of the model presents some facilities: the visual representation of temporal operators, different levels of details for the navigation on the graphic schema, query storage for later use, possibility of representing a textual query in a visual way and vice-versa. The environment supports the definition of temporal constraints and the selection by the user of different representations forms for the results of a query. In the presented system, the TF-ORM model is implemented in a relational database which uses SQL language for information recovery. In order to implement the model in a relational database, a mapping was done - the concepts of the object orientation, roles and time were mapped in to tables and attributes to the relational model. The queries performed in the TF-ORM language are translated into the query lan guage of relational database. The environment was implemented using Delphi and the Watcom database, a relational database which allows information recovery in SQL/ANSI standard.

O modelo TF-ORM (Temporal Functionality in Objects With Roles Model) é um modelo de dados temporal orientado a objetos que utiliza o conceito de papeis para representar os diferentes comportamentos dos objetos. 0 modelo permite a modelagem dos aspectos estáticos e dinâmicos da aplicação pois considera todos os estados dos objetos ao longo de sua evolução. Sua linguagem de consulta e baseada na linguagem SQL e possibilita a recuperação de diferentes histórias do banco de dados. Este trabalho apresenta um sistema visual de consulta para o modelo TFORM. O VQS TF-ORM (Visual Query System TF-ORM) é um ambiente para recuperação de informações temporais. O sistema permite que as consultas sejam elaboradas de três formas alternativas: textual, gráfica ou por formulários. A linguagem gráfica possui o mesmo poder de expressão da linguagem textual, permitindo que a consulta seja elaborada diretamente sobre o esquema conceitual gráfico do modelo com o auxilio de um conjunto de janelas e elementos visuais. A recuperação de informações utilizando-se formulários não possui o mesmo poder de expressão da linguagem textual, mas possibilita a recuperação dos valores das propriedades de um determinado objeto através de uma hierarquia de janelas. A recuperação de informações através do sistema visual de consulta do modelo apresenta algumas facilidades tais como: representação visual dos operadores temporais do modelo, definição de níveis de detalhe e navegação sobre o esquema gráfico, armazenamento das consultas para posterior utilizando, possibilidade de representar uma consulta textual na forma visual e vice-versa, entre outras. Alem da preocupação com a definição de restrições temporais, o ambiente considera ainda as diferentes formas de apresentação do resultado da consulta que podem ser selecionadas pelo usuário. No sistema apresentado neste trabalho, o modelo TF-ORM é implementado em um banco de dados relacional que utiliza a linguagem SQL para recuperação de informações. Para a implementação do modelo em um banco de dados relacional foi feito um mapeamento, que determina como os conceitos de orientação a objetos, papel e tempo devem ser mapeados para tabelas e atributos no modelo relacional. As consultas realizadas na linguagem TF-ORM são então traduzidas para a linguagem de consulta do banco de dados relacional. O ambiente foi implementado utilizando a ferramenta para desenvolvimento de aplicações Delphi e o banco de dados Watcom, um banco de dados relacional que permite a recuperação de informações no padrão SQL/ANSI. / TF-ORM model (Temporal Functionality in Objects with Roles Model) is an object-oriented temporal data model which uses the role concept to represent different behaviors of objects. The model allows modelling of the static and the dynamic aspects of an application representing all the states of its evolution. The TF-ORM query language is based on the SQL language and enables the recovery of different database histories. This work represents a visual query system for the TF-ORM model. The VQS TF-ORM (Visual Query System TF-ORM) is an environment for recovery of temporal information. The system allows queries to be elaborated in three alternatives way: textual, graphic or by forms. The graphic language has the same functionality of the textual lan g uage permitting the query to be elaborated directly on the graphic conceptual schema of the model this operation is supported by a set of windows and visual elements. The information recovery using forms doesn't have the same functionality of the textual lan guage, but enables recovery of property values of an object through window hierarchies. Information recovery using the visual query system of the model presents some facilities: the visual representation of temporal operators, different levels of details for the navigation on the graphic schema, query storage for later use, possibility of representing a textual query in a visual way and vice-versa. The environment supports the definition of temporal constraints and the selection by the user of different representations forms for the results of a query. In the presented system, the TF-ORM model is implemented in a relational database which uses SQL language for information recovery. In order to implement the model in a relational database, a mapping was done - the concepts of the object orientation, roles and time were mapped in to tables and attributes to the relational model. The queries performed in the TF-ORM language are translated into the query lan guage of relational database. The environment was implemented using Delphi and the Watcom database, a relational database which allows information recovery in SQL/ANSI standard.

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L’objectif général de cette thèse est de caractériser la dynamique des transferts des bactéries fécales à l’aide d’une modélisation spatio-temporelle, à l’échelle du bassin versant (BV) dans une région agricole et à l’échelle événementielle. Ce projet vise à mieux comprendre l'influence des processus hydrologiques, les facteurs environnementaux et temporels impliqués dans l’explication des épisodes de contamination microbienne des eaux récréatives. Premièrement, un modèle bayésien hiérarchique a été développé pour quantifier et cartographier les niveaux de probabilité des eaux à être contaminées par des effluents agricoles, sur la base des données spectrales et des variables géomorphologiques. Par cette méthode, nous avons pu calculer les relations pondérées entre les concentrations d’Escherichia coli et la distribution de l’ensemble des paramètres agro-pédo-climatiques qui régissent sa propagation. Les résultats ont montré que le modèle bayésien développé peut être utilisé en mode prédictif de la contamination microbienne des eaux récréatives. Ce modèle avec un taux de succès de 71 % a mis en évidence le rôle significatif joué par la pluie qui est la cause principale du transport des polluants. Deuxièmement, le modèle bayésien a fait l’objet d'une analyse de sensibilité liée aux paramètres spatiaux, en utilisant les indices de Sobol. Cette démarche a permis (i) la quantification des incertitudes sur les variables pédologiques, d’occupation du sol et de la distance et (2) la propagation de ces incertitudes dans le modèle probabiliste c'est-à-dire le calcul de l’erreur induite dans la sortie par les incertitudes des entrées spatiales. Enfin, une analyse de sensibilité des simulations aux différentes sources d’incertitude a été effectuée pour évaluer la contribution de chaque facteur sur l’incertitude globale en prenant en compte leurs interactions. Il apparaît que sur l’ensemble des scénarios, l’incertitude de la contamination microbienne dépend directement de la variabilité des sols argileux. Les indices de premier ordre de l’analyse de Sobol ont montré que parmi les facteurs les plus susceptibles d’influer la contamination microbienne, la superficie des zones agricoles est le premier facteur important dans l'évaluation du taux de coliformes. C’est donc sur ce paramètre que l’attention devra se porter dans le contexte de prévision d'une contamination microbienne. Ensuite, la deuxième variable la plus importante est la zone urbaine avec des parts de sensibilité d’environ 30 %. Par ailleurs, les estimations des indices totaux sont meilleures que celles des indices de premier ordre, ce qui signifie que l’impact des interactions paramétriques est nettement significatif pour la modélisation de la contamination microbienne Enfin, troisièmement, nous proposons de mettre en œuvre une modélisation de la variabilité temporelle de la contamination microbiologique du bassin versant du lac Massawippi, à partir du modèle AVSWAT. Il s'agit d'une modélisation couplant les composantes temporelles et spatiales qui caractérisent la dynamique des coliformes. La synthèse des principaux résultats démontrent que les concentrations de coliformes dans différents sous-bassins versants se révèlent influencées par l’intensité de pluie. La recherche a également permis de conclure que les meilleures performances en calage sont obtenues au niveau de l'optimisation multi-objective. Les résultats de ces travaux ouvrent des perspectives encourageantes sur le plan opérationnel en fournissant une compréhension globale de la dynamique de la contamination microbienne des eaux de surface. / Abstract : The aim of this study was to predict water faecal contamination from a bayesian probabilistic model, on a watershed scale in a farming area and on a factual scale. This project aims to better understand the influence of hydrological, environmental and temporal factors involved in the explanation of microbial contamination episodes of recreational waters. First, a bayesian probabilistic model: Weight of Evidence was developed to identify and map the probability of water levels to be contaminated by agricultural effluents, on the basis of spectrals data and geomorphologic variables. By this method, we were able to calculate weighted relationships between concentrations of Escherichia coli and distribution of key agronomic, pedologic and climatic parameters that influence the spread of these microorganisms. The results showed that the Bayesian model that was developed can be used as a prediction of microbial contamination of recreational waters. This model, with a success rate of 71%, highlighted the significant role played by the rain, which is the main cause of pollution transport. Secondly, the Bayesian probabilistic model has been the subject of a sensitivity analysis related to spatial parameters, using Sobol indications. This allowed (1) quantification of uncertainties on soil variables, land use and distance and (2) the spread of these uncertainties in the probabilistic model that is to say, the calculation of induced error in the output by the uncertainties of spatial inputs. Lastly, simulation sensitivity analysis to the various sources of uncertainty was performed to assess the contribution of each factor on the overall uncertainty taking into account their interactions. It appears that of all the scenarios, the uncertainty of the microbial contamination is directly dependent on the variability of clay soils. Sobol prime indications analysis showed that among the most likely to influence the microbial factors, the area of farmland is the first important factor in assessing the coliforms. Importance must be given on this parameter in the context of preparation for microbial contamination. Then, the second most important variable is the urban area with sensitivity shares of approximately 30%. Furthermore, estimates of the total indications are better than those of the first order, which means that the impact of parametric interaction is clearly significant for the modeling of microbial contamination. Thirdly, we propose to implement a temporal variability model of microbiological contamination on the watershed of Lake Massawippi, based on the AVSWAT model. This is a model that couples the temporal and spatial components that characterize the dynamics of coliforms. The synthesis of the main results shows that concentrations of Escherichia coli in different sub-watersheds are influenced by rain intensity. Research also concluded that best performance is obtained by multi-objective optimization. The results of these studies show the prospective of operationally providing a comprehensive understanding of the dynamics of microbial contamination of surface water.

Les caméras pushbroom sont omniprésentes en imagerie satellitaire. Ce capteur linéaire enregistre des images 1-D et utilise le défilement du satellite autour de la terre pour construire des bandeaux d’image ; son principe de fonctionnement est identique aux scanners et photocopieurs que l’on peut utiliser tous les jours. Les avantages liés à cette technologie sont principalement une résolution d’image étendue qui va bien au delà des caméras perspectives, un coût d’exploitation faible et une robustesse au contexte spatial. Pour reconstruire des images couleur, le plan focal d’un satellite embarque plusieurs caméras pushbroom sensibles à différentes bandes spectrales de la lumière. Ce mode d’acquisition dépendant du temps suppose que l’orientation du satellite, également appelée attitude dans cette étude, ne varie pas au cours du survol d’une scène. Les satellites ont jusqu’à maintenant été considérés comme stables du fait de leur inertie. Cependant les technologies récentes développées dans la recherche spatiale tendent à réduire leur taille et alléger leur poids pour les rendre plus agiles et moins coûteux en énergie lors de leur mise en orbite. La résolution des capteurs a également été améliorée, ce qui rend nettement plus critique la moindre oscillation de l’imageur. Ces facteurs cumulés font qu’un changement d’attitude de quelques microradians peut provoquer des déformations géométriques notables dans les images. Les solutions actuelles utilisent les capteurs de positionnement du satellite pour asservir son attitude et rectifier les images, mais elles sont coûteuses et limitées en précision. Les images contiennent pourtant une information cohérente sur les mouvements du satellite de par leurs éventuelles déformations. Nous proposons dans cette étude de retrouver les variations d’attitude par recalage des images enregistrées par le satellite. Nous exploitons la disposition des caméras pushbroom dans le plan focal ainsi que la nature stationnaire des oscillations pour conduire l’estimation. Le tout est présenté dans un cadre bayesien, où les données images peuvent se mêler avec une information a priori sur le mouvement ainsi que des mesures exogènes fournies par un capteur stellaire couramment appelé star tracker. Différentes solutions sont décrites et comparées sur des jeux de données satellitaires fournis par le constructeur de satellite EADS Astrium. / Linear pushbroom cameras are widely used for earth observation applications. This sensor acquires 1-D images over time and uses the straight motion of the satellite to sweep out a region of space and build 2-D image ; it operates in the same way as a usual flatbed scanner. Main advantages of such technology are : robustness in the space context, higher resolution than classical 2-D CCD sensors and low production cost. To build color images, several pushbroom cameras of different modalities are set in parallel onto the satellite’s focal plane. This acquisition process is dependent of the time and assumes that the satellite’s attitude remains constant during the image recording. However, the recent manufacture of smal- ler satellites with higher sampling resolution has weakened this assumption. The satellite may oscillates around its rotations axis, and an angular variation of a few microradians can result in noticeable warps in images. Current solutions use inertial sensors on board the satellite to control the attitude and correct the images, but they are costly and of limited precision. As warped images do contain the information of attitude variations, we suggest to use image registration to es- timate them. We exploit the geometry of the focal plane and the stationary nature of the disturbances to recover undistorted images. To do so, we embed the estimation process in a Bayesian framework where image registration, prior on attitude variations and mea- surements of a star tracker are fused to retrieve the motion of the satellite. We illustrate the performance of our algorithm on four satellite datasets provided by EADS Astrium.