A new method for predicting the uncertainty in a nonlinear dynamical system is developed and analyzed in the context of uncertainty evolution for resident space objects (RSOs) in the near-geosynchronous orbit regime under the influence of central body gravitational acceleration, third body perturbations, and attitude-dependent solar radiation pressure (SRP) accelerations and torques. The new method, termed the splitting Gaussian mixture unscented Kalman filter (SGMUKF), exploits properties of the differential entropy or Renyi entropy for a linearized dynamical system to determine when a higher-order prediction of uncertainty reaches a level of disagreement with a first-order prediction, and then applies a multivariate Gaussian splitting algorithm to reduce the impact of induced nonlinearity. In order to address the relative accuracy of the new method with respect to the more traditional approaches of the extended Kalman filter (EKF) and unscented Kalman filter (UKF), several concepts regarding the comparison of probability density functions (pdfs) are introduced and utilized in the analysis. The research also describes high-fidelity modeling of the nonlinear dynamical system which drives the motion of an RSO, and includes models for evaluation of the central body gravitational acceleration, the gravitational acceleration due to other celestial bodies, and attitude-dependent SRP accelerations and torques when employing a macro plate model of an RSO. Furthermore, a high-fidelity model of the measurement of the line-of-sight of a spacecraft from a ground station is presented, which applies light-time and stellar aberration corrections, and accounts for observer and target lighting conditions, as well as for the sensor field of view. The developed algorithms are applied to the problem of forward predicting the time evolution of the region of uncertainty for RSO tracking, and uncertainty rectification via the fusion of incoming measurement data with prior knowledge. It is demonstrated that the SGMUKF method is significantly better able to forward predict the region of uncertainty and is subsequently better able to utilize new measurement data. / text

Atom Interferometrie ist eine sehr genaue und sensitive Methode mit einer Vielzahl von Anwendungsmöglichkeiten, zu der auch die Messung der Erdbeschleunigung zählt. Während die meisten Atom Interferometer aus großen, ortsfesten Aufbauten bestehen, werden auf diesem Gebiet häufig mobile Messgeräte benötigt. Das Gravimetric Atom Interferometer (GAIN) Projekt wurde ins Leben gerufen, um dieser zusätzlichen Anforderung bei bestmöglicher Messgenauigkeit gerecht zu werden. Es soll eine Alternative zu anderen modernsten Gravimetertypen geschaffen werden, die wichtige funktionale Eigenschaften wie eine hohe Auflösung und absolute Genauigkeit in einem Gerät vereint. Der GAIN Sensor verwendet lasergekühlte Rb87 Atome in einer 1 m hohen Fontäne. Mit Hilfe von stimulierten Raman Übergängen wird ein beschleunigungssensitives Interferometer realisiert. In dieser Arbeit wurde der Sensor mit Blick auf mobile und driftfreie Langzeitmessungen weiterentwickelt. Dafür wurden einzelne Subsysteme des Laseraufbaus auf die daraus resultierenden Anforderungen hin angepasst oder neu entwickelt. Mit derselben Zielstellung wurden weiterhin systematische Effekte in dem Messaufbau untersucht und Maßnahmen für ihre Reduzierung realisiert. Der Aufbau wurde transportiert und in relevanten Umgebungen getestet. Dabei konnte gezeigt werden, dass die Leistungsfäigkeit dieses Aufbaus mit denen der wichtigsten und modernsten Gravimeter konkurieren kann, sie teilweise übertrifft und dass dieser Sensor zur präzisen Kalibrierung der relativen Gravimeter verwendet werden kann. In den Messungen wurde eine Sensitivität von 138 nm/s^2/Sqrt(Hz) sowie eine Langzeitstabilität von 5 x 10^−11 g über 10^5 s erreicht. / Atom interferometry offers a very precise and sensitive measurement tool for various areas of application whereof one is the registration of the gravity acceleration. While the vast majority of atom interferometers include large and stationary setups, this field very often implies the additional request for a mobile apparatus. The Gravimetric Atom Interferometer (GAIN) project has been started to meet this requirement and to provide best possible accuracy at the same time. It aims to realize an alternative to other types of gravimeters and to combine important qualities such as high sensitivity and absolute accuracy in one instrument. The GAIN sensor is based on laser-cooled Rb87 atoms in a 1 m atomic fountain. Stimulated Raman transitions form a Mach-Zehnder type interferometer which is sensitive to accelerations. In this work it has been advanced to meet all requirements for mobile and drift-free long-term operation. Therefore, selected parts of the laser system have been improved or redeveloped. A second focus has been on systematic effects for the same objective. They have been analyzed and measures for their suppression have been undertaken. The apparatus has been transported, tested in relevant environments, and compared to the most important state-of-the-art gravimeter types where a competitive performance has been achieved. It is demonstrated, that the gravity signal of this sensor allows for a precise calibration of the relative gravimeter types. During the measurements a best sensitivity of 138 nm/s^2/Sqrt(Hz) and a stability of 5 x 10^−11 g after 10^5 s has been reached.