Relative global positioning system (GPS) navigation is currently used for autonomous rendezvous and docking of two spacecraft as well as formation flying applications. GPS receivers deliver measurements to flight software that use this information to determine estimates of the current states of the spacecraft. The success of autonomous proximity operations in the presence of an uncertain environment and noisy measurements depends primarily on the navigation accuracy. This thesis presents the implementation and calibration of a spaceborne GPS receiver model, a visibility analysis for multiple GPS antenna cone angles, the implementation of four different extended Kalman filter architectures and a comparison of the advantages and disadvantages of each filter used for relative GPS navigation. A spaceborne GPS model is developed to generate simulated GPS measurements for a spacecraft located on any orbit around the Earth below the GPS constellation. Position and velocity estimation algorithms for GPS receivers are developed and implemented. A visibility analysis is performed to determine the number of visible satellites throughout the duration of the rendezvous. Multiple constant fields of view are analyzed and results compared to develop an understanding of how the GPS constellation evolves during the proximity operations. The comparison is used to choose a field of view with adequate satellite coverage. The advantages and disadvantages of the relative navigation architectures are evaluated based on a trade study involving several parameters. It is determined in this thesis that a reduced pseudorange filter provides the best overall performance in both relative and absolute navigation with less computational cost than the slightly more accurate pseudorange lter. A relative pseudorange architecture experiences complications due to multipath rich environments and performs well in only relative navigation. A position velocity architecture performs well in absolute state estimation but the worst of the four filters studied in relative state estimation.

Les propriétés de transport à haute température dans les gaz et/ou dans les plasmas ont une importance capitale dans différents domaines, à savoir dans le domaine de technologie de coupure à arc, plasmas de coupure, de soudure ou de gravure. La connaissance des coefficients de transport est nécessaire pour toute modélisation faisant intervenir les équations hydrodynamiques. Dans le cadre de la théorie cinétique des gaz dilués, une solution approchée de l’équation intégro-différentielle de Boltzmann régissant les fonctions de distribution a été proposée par Chapman-Enskog. Les coefficients de transport sont calculés classiquement par la méthode de Chapman-Enskog via les intégrales de collision. Dans le cadre de notre étude nous avons développé, dans un premier temps, un code numérique permettant l’obtention de ces intégrales de collision en tenant compte des singularités qui peuvent apparaître dans le calcul des sections efficaces relatives aux interactions entre les particules constituant les gaz et/ou les plasmas. Dans un second temps nous avons étudié l’influence du choix des paramètres des potentiels d’interaction sur les coefficients de transport. Par la suite, nous avons utilisé le code numérique ainsi développé pour évaluer les coefficients de transport du plasma d’hélium en étudiant l’influence du choix de la méthode de calcul de composition chimique sur ces coefficients. Enfin, un modèle simplifié d’une interaction entre une onde électromagnétique et un plasma d’hélium a été proposé comme une application directe des coefficients de transport. / Transport properties at high temperature in gases and/or in plasmas are of very importance in various fields, namely in the field of breaking technology in arc, cutting plasma, welding or burning. Knowledge of transport coefficients is necessary for any modeling involving hydrodynamic equations. As part of the kinetic theory of diluted gas, an approximate solution of the integro-differential Boltzmann equation governing distribution functions was proposed by Chapman-Enskog. Transport coefficients are classically computed using the method of Chapman-Enskog through the collision integrals. In our study we have developed, initially, a numerical code to obtain these collision integral taking into account the singularities that may occur in the calculation of the cross sections relating to interactions between particles forming the gas and/or plasmas. Secondly, we have studied the influence of the choice of parameters of interaction potentials on transport coefficients. Subsequently, we have used the numerical code developed for evaluating and helium plasma transport coefficients by studying the influence of the choice of method for calculating chemical composition on these coefficients. Finally, a simplified model of an interaction between an electromagnetic wave and a helium plasma has been proposed as a direct application of the transport coefficients.

Includes Van Allen thesis (M.S.)--University of Iowa, 1936, and thesis (Ph.D.)--University of Iowa, 1939.