Higher-order perturbative relativistic corrections to energies and properties

Relativistic effects need to be considered in quantum-chemical calculations on systems including heavy elements or when aiming at high accuracy for molecules containing only lighter elements. In the latter case, consideration of relativistic effects via perturbation theory is an attractive option. Among the available techniques, Direct Perturbation Theory (DPT) in its lowest order (DPT2) has become a standard tool for the calculation of relativistic corrections to energies and properties.In this work, the DPT treatment is extended to the next order (DPT4). It is demonstrated that the DPT4 correction can be obtained as a second derivative of the energy with respect to the relativistic perturbation parameter. Accordingly, differentiation of a suitable Lagrangian, thereby taking into account all constraints on the wave function, provides analytic expressions for the fourth-order energy corrections. The latter have been implemented at the Hartree-Fock level and within second-order Møller-Plesset perturbaton theory using standard analytic second-derivative techniques into the CFOUR program package. For closed-shell systems, the DPT4 corrections consist of higher-order scalar-relativistic effects as well as spin-orbit corrections with the latter appearing here for the first time in the DPT series.Relativistic corrections are reported for energies as well as for first-order electrical properties and compared to results from rigorous four-component benchmark calculations in order to judge the accuracy and convergence of the DPT expansion for both the scalar-relativistic as well as the spin-orbit contributions. Additionally, the importance of relativistic effects to the bromine and iodine quadrupole-coupling tensors is investigated in a joint experimental and theoretical study concerning the rotational spectra of CH2BrF, CHBrF2, and CH2FI.

Laserspektroskopie der Grundzustands-Hyperfeinstruktur des lithiumähnlichen 209 Bi 80+

Die theoretische und experimentelle Untersuchung von wasserstoffähnlichen Systemen hat in den letzten hundert Jahren immer wieder sowohl die experimentelle als auch die theoretische Physik entscheidend vorangebracht. Formulierung und Test der Quantenelektrodynamik (QED) standen und stehen in engen Zusammenhang mit der Untersuchung wasserstoffähnlicher Systeme. Gegenwärtig sind besonders wasserstoffähnliche Systeme schwerer Ionen von Interesse, um die QED in den extrem starken Feldern in Kernnähe zu testen. Laserspektroskopische Messungen der Hyperfeinstrukturaufspaltung des Grundzustandes bieten eine hohe Genauigkeit, ihre Interpretation wird jedoch durch die Unsicherheit in der Größe der Kernstruktureffekte erschwert. Beseitigt werden können diese durch die Kombination der Aufspaltung in wasserstoff- und lithiumähnlichen Ionen des gleichen Nuklids. In den letzten zwei Jahrzehnten scheiterten mehrere dadurch motivierte Versuche, den HFS-Übergang in lithiumähnlichen 209Bi80+ zu finden. Im Rahmen dieser Arbeit wurde kollineare Laserspektroskopie bei etwa 70% der Lichtgeschwindigkeit an 209Bi82+ und 209Bi80+ -Ionen im Experimentier- Speicherring an der GSI in Darmstadt durchgeführt. Dabei wurde der Übergang im lithiumähnlichen Bismut erstmals beobachtet und dessen Übergangswellenlänge zu 1554,74(74) nm bestimmt. Ein eigens für dieses Experiment optimiertes Fluoreszenz-Nachweissystem stellte dabei die entscheidende Verbesserung gegenüber den gescheiterten Vorgängerexperimenten dar. Der Wellenlängenfehler ist dominiert von der Unsicherheit der Ionengeschwindigkeit, die für die Transformation in das Ruhesystem der Ionen entscheidend ist. Für deren Bestimmung wurden drei Ansätze verfolgt: Die Geschwindigkeit wurde aus der Elektronenkühlerspannung bestimmt, aus dem Produkt von Orbitlänge und Umlauffrequenz und aus dem relativistischen Dopplereffekt unter Annahme der Korrektheit des früher bestimmten Überganges in wasserstoffähnlichen Bismut. Die Spannungskalibration des Elektronenkühlers wurde im Rahmen dieser Arbeit erstmals kritisch evaluiert und bislang unterschätzte systematische Unsicherheiten aufgezeigt, die derzeit einen aussagekräftigen QED-Test verhindern. Umgekehrt konnte unter Verwendung der QED-Berechnungen eine Ionengeschwindigkeit berechnet werden, die ein genaueres und konsistenteres Resultat für die Übergangswellenlängen beider Ionenspezies liefert. Daraus ergibt sich eine Diskrepanz zu dem früher bestimmten Wert des Überganges in wasserstoffähnlichen Bismut, die es weiter zu untersuchen gilt.

Design of a GNSS receiver for the ESEO mission

This thesis was carried out inside the ESA's ESEO mission and focus in the design of one of the secondary payloads carried on board the spacecraft: a GNSS receiver for orbit determination. The purpose of this project is to test the technology of the orbit determination in real time applications by using commercial components. The architecture of the receiver includes a custom part, the navigation computer, and a commercial part, the front-end, from Novatel, with COCOM limitation removed, and a GNSS antenna. This choice is motivated by the goal of demonstrating the correct operations in orbit, enabling a widespread use of this technology while lowering the cost and time of the device’s assembly. The commercial front-end performs GNSS signal acquisition, tracking and data demodulation and provides raw GNSS data to the custom computer. This computer processes this raw observables, that will be both transferred to the On-Board Computer and then transmitted to Earth and provided as input to the recursive estimation filter on-board, in order to obtain an accurate positioning of the spacecraft, using the dynamic model. The main purpose of this thesis, is the detailed design and development of the mentioned GNSS receiver up to the ESEO project Critical Design Review, including requirements definition, hardware design and breadboard preliminary test phase design.

Oberflächenuntersuchungen von Metalla-Tetraazaporphyrinen

Ziel dieser Arbeit war es, ein System zu entwickeln, in dem ein durch Licht induzierter Elektronentransfer stattfinden kann. Dazu wurden ein Kupfer(II)- und ein Zink(II)Tetraazaporphyrin mit acht 4-tert-Butylphenyl-Substituenten synthetisiert (Cu4Dinit, Zn4Dinit). Die Energielücke von 1,85 eV zwischen HOMO und LUMO von Cu4Dinit in Lösung wurde mit Hilfe von Cyclovoltammetrie und UV/Vis-Messungen bestimmt. Somit ist sie größer als für Cu4Dinit Moleküle, die auf einer Oberfläche (Wolfram(100)) liegen und mit STM-, STS-Messungen untersucht wurden. Hier beträgt die Energielücke 1,35 eV, was durch eine Drehung der Phenylringe in die Ebene der Pyrrolringe des Makrozyklus und somit durch eine bessere Überlappung der Orbitale erklärt werden kann. Um die Wechselwirkung der Moleküle mit der Oberfläche zu untersuchen, wurde Cu4Dinit, wie oben beschrieben, auf Magnetit aufgedampft. Dadurch wurde ausschließlich die Wechselwirkung zwischen den Elektronenspins des Kupfer(II)-ions und den Elektronenspins des Eisens im Magnetit betrachtet. Durch Messungen der Röntgenabsorption und des XMCD-Effektes konnten das Spinmoment, Bahnmoment und das Gesamtmoment des Kupfers berechnet und eine anisotrope Kopplung des Elektronenspins des Kupferions zum Magnetit, in Abhängigkeit der Magnetisierungsrichtung des Magnetits, festgestellt werden. Wenn der Magnetit senkrecht zur Oberfläche (out-of-plane) magnetisiert ist, ist die Kopplung ferromagnetisch, während bei einer Magnetisierungsrichtung parallel zur Ebene (in-plane) des Magnetits der Elektronenspin des Kupfers antiferromagnetisch mit dem des Eisens koppelt. Dadurch muss der Hamiltonian, der die Wechselwirkung zwischen zwei Spins beschreibt, bei einer anisotropen Kopplung um einen ansiotropen Term ergänzt werden. Das Ergebnis, dass der Elektronenspin des Kupferions durch die Richtung der Magnetisierung des Magnetits beeinflusst werden kann, eröffnet neue Wege, um die Spinkonfiguration von auf der Oberfläche liegenden Molekülen mit ungepaarten Elektronen, wie die zentralen Metallionen der Makrozyklen aber auch die Elektronenspins anderer metallorganischer Komplexe oder molekulare Magnete, durch ein externes Magnetfeld zu beeinflussen. rnDurch die stöchiometrische Templatreaktion von Pyrazino[2,3-f][1,10]-phenanthrolin-2,3-di-carbonitril (Dicnq), Bis(4-tert-Butylphenyl)-fumarodinitril (Dinit) und Kupfer(II)-acetat wurde eine Koordinationsmöglichkeit für ein Ruthenium(II)-ion in einem Tetraazaporphyrin hergestellt und so die Makrozyklen Cu3Dinit1Dicnq und Zn3Dinit1Dicnq synthetisiert, mit Rutheniumionen versetzt und ebenfalls mit Hilfe von Röntgenabsorptionsmessungen und XMCD untersucht. Durch die Vergleiche mit Zn3Dinit1Dicnq und den jeweiligen Verbindungen mit koordinierten Rutheniumionen (Cu3Dinit1Dicnq-1Ru, Zn3Dinit1Dicnq-1Ru) konnte gezeigt werden, dass eine Verschiebung der Elektronendichte des Rutheniumions zu dem zentralen Kupferion des Makrozyklus stattgefunden hat und durch die Koordination eines Rutheniumions in der Peripherie des Tetraazaporphyrins die energetische Lage der Kupferorbitale beeinflusst wird.rnDer Einfluss von vier koordinierten Ruthenium(II)-ionen auf das zentrale Kupferion wurde an Hand des in dieser Arbeit hergestellten Kupfer(II)phenanthralocyanins (Cu4Dicnq) untersucht, das aus vier Dicnq-Liganden und Kupfer(II)-acetat synthetisiert wurde. Auf Grund der schlechten Löslichkeit wurde für die Koordination der Rutheniumionen der Prekursor [Ru(bipy)2Dicnq](PF6)2 hergestellt und daraus der Makrozyklus in einer Templatsynthese mit Kufper(II)-ionen gebildet. Durch diese neue Syntheseroute war es möglich, die Verbindung Cu4Dicnq-4Ru herzustellen und ebenfalls durch Röntgenabsorption und XMCD zu untersuchen und so das Spin- und Bahnmoment zu ermitteln. Ein Teil der Elektronendichte des Rutheniumions in dieser Verbindung wird auf die zusätzlich an das Rutheniumion koordinierten 2,2'-Bipyridine und nicht auf den Makrozyklus, wie in Cu3Dinit1Dicnq-1Ru, geschoben. Trotzdem konnte die Funktionsweise als Modell des Photosystems II durch eine Oxidation durch die Bestrahlung mit einer Quecksilberlampe mit para-Benzochinon beobachtet werden. Dies bestätigte die Funktionsweise des Kupfer(II)phenanthralocyanins mit koordinierten Rutheniumionen, da ein durch Licht induzierter Elektronenübergang auf das para-Benzochinon stattgefunden hat.rn

The role of postoperative prophylactic antibiotics in the treatment of facial fractures: a randomised, double-blind, placebo-controlled pilot clinical study. Part 1: orbital fractures in 62 patients

The aim of this study was to evaluate the difference between the effects of a 5-day and a 1-day course of antibiotics on the incidence of postoperative infection after displaced fractures of the orbit. A total of 62 patients with orbital blow-out fractures were randomly assigned to two groups, both of which were given amoxicillin/clavulanic acid 1.2g intravenously every 8h from the time of admission to 24h postoperatively. The 5-day group were then given amoxicillin/clavulanic acid 625mg orally every 8h for 4 further days. The 1-day group were given placebo orally at the same time intervals. Follow up appointments were 1, 2, 4, 6, and 12 weeks, and 6 months, postoperatively. An infection in the orbital region was the primary end point. Sixty of the 62 patients completed the study. Two of the 29 patients in the 5-day group (6.8%) and 1/31 patients in the 1-day group (3.2%) developed local infections. In the 5-day group 1 patient developed diarrhoea. In the 1-day group 1 patient developed a rash on the trunk. There were no significant differences in the incidence of infection or side effects between the groups. We conclude that in displaced orbital fractures a postoperative 1-day course of antibiotics is as effective in preventing infective complications as a 5-day regimen.

Io volcano observer (IVO) integrated approach to optimizing system design for radiation challenges

One of the major challenges for a mission to the Jovian system is the radiation tolerance of the spacecraft (S/C) and the payload. Moreover, being able to achieve science observations with high signal to noise ratios (SNR), while passing through the high flux radiation zones, requires additional ingenuity on the part of the instrument provider. Consequently, the radiation mitigation is closely intertwined with the payload, spacecraft and trajectory design, and requires a systems-level approach. This paper presents a design for the Io Volcano Observer (IVO), a Discovery mission concept that makes multiple close encounters with Io while orbiting Jupiter. The mission aims to answer key outstanding questions about Io, especially the nature of its intense active volcanism and the internal processes that drive it. The payload includes narrow-angle and wide-angle cameras (NAC and WAC), dual fluxgate magnetometers (FGM), a thermal mapper (ThM), dual ion and neutral mass spectrometers (INMS), and dual plasma ion analyzers (PIA). The radiation mitigation is implemented by drawing upon experiences from designs and studies for missions such as the Radiation Belt Storm Probes (RBSP) and Jupiter Europa Orbiter (JEO). At the core of the radiation mitigation is IVO's inclined and highly elliptical orbit, which leads to rapid passes through the most intense radiation near Io, minimizing the total ionizing dose (177 krads behind 100 mils of Aluminum with radiation design margin (RDM) of 2 after 7 encounters). The payload and the spacecraft are designed specifically to accommodate the fast flyby velocities (e.g. the spacecraft is radioisotope powered, remaining small and agile without any flexible appendages). The science instruments, which collect the majority of the high-priority data when close to Io and thus near the peak flux, also have to mitigate transient noise in their detectors. The cameras use a combination of shielding and CMOS detectors with extremely fast readout to mi- imize noise. INMS microchannel plate detectors and PIA channel electron multipliers require additional shielding. The FGM is not sensitive to noise induced by energetic particles and the ThM microbolometer detector is nearly insensitive. Detailed SNR calculations are presented. To facilitate targeting agility, all of the spacecraft components are shielded separately since this approach is more mass efficient than using a radiation vault. IVO uses proven radiation-hardened parts (rated at 100 krad behind equivalent shielding of 280 mils of Aluminum with RDM of 2) and is expected to have ample mass margin to increase shielding if needed.

An Instrument Design for Space-Based Optical Observation of Space Debris

Currently, observations of space debris are primarily performed with ground-based sensors. These sensors have a detection limit at some centimetres diameter for objects in Low Earth Orbit (LEO) and at about two decimetres diameter for objects in Geostationary Orbit (GEO). The few space-based debris observations stem mainly from in-situ measurements and from the analysis of returned spacecraft surfaces. Both provide information about mostly sub-millimetre-sized debris particles. As a consequence the population of centimetre- and millimetre-sized debris objects remains poorly understood. The development, validation and improvement of debris reference models drive the need for measurements covering the whole diameter range. In 2003 the European Space Agency (ESA) initiated a study entitled “Space-Based Optical Observation of Space Debris”. The first tasks of the study were to define user requirements and to develop an observation strategy for a space-based instrument capable of observing uncatalogued millimetre-sized debris objects. Only passive optical observations were considered, focussing on mission concepts for the LEO, and GEO regions respectively. Starting from the requirements and the observation strategy, an instrument system architecture and an associated operations concept have been elaborated. The instrument system architecture covers the telescope, camera and onboard processing electronics. The proposed telescope is a folded Schmidt design, characterised by a 20 cm aperture and a large field of view of 6°. The camera design is based on the use of either a frame-transfer charge coupled device (CCD), or on a cooled hybrid sensor with fast read-out. A four megapixel sensor is foreseen. For the onboard processing, a scalable architecture has been selected. Performance simulations have been executed for the system as designed, focussing on the orbit determination of observed debris particles, and on the analysis of the object detection algorithms. In this paper we present some of the main results of the study. A short overview of the user requirements and observation strategy is given. The architectural design of the instrument is discussed, and the main tradeoffs are outlined. An insight into the results of the performance simulations is provided.

Orbital manifestation of whipple's disease: an atypical case

BACKGROUND: Whipple's disease is a systemic disorder caused by an infection with a gram-positive bacillus, Tropheryma whipplei. Almost every organ system can be affected in Whipple's disease, resulting in varying clinical symptoms. CASE REPORT: As far as we are aware, this report of a 61-year-old male is the first presenting with a periorbital manifestation of the disease, with severe exophthalmos and optic nerve involvement, leading to rapid visual loss. This emergency case was successfully treated by a surgical orbital decompression combined with systemic use of antibiotics and steroids. CONCLUSION: Whipple's disease can affect the periorbital tissues and the optic nerve, causing massive exophthalmos and serious transient visual loss. In such a case surgical decompression of the affected orbit combined with antibiotics and steroids is a recommended valid treatment option.

Late-onset posttraumatic septal hematoma and abscess formation in a six-year-old Tamil girl--case report and literature review

Nasal septal hematoma with abscess (NSHA) is an uncommon complication of trauma and studies on children are especially rare. We discuss the case of a 6-year-old girl, who was initially evaluated independently by three doctors for minor nasal trauma but had to be re-hospitalized 6 days later with NSHA. Although septal hematoma had initially been excluded (5, 7 and 24 hours after trauma), a secondary accumulation of blood seems to have occured. Delayed hematoma formation has been described in the orbit as a result of possible venous injuries after endoscopic sinus surgery. However, such an observation is new for septal hematoma in children. Thus, we recommend re-evaluation for septal hematoma 48h to 72h after paediatric nasal trauma. Such a scheduled re-examination offers a chance to treat delayed subperichondral hematoma on time before almost inevitable superinfection leads to abscess formation and destruction of the nasal infrastructure. We suggest that parents should be vigilant for delayed nasal obstruction as possible herald of hematoma accumulation within the first week.

Development of a direct evaporation bismuth Hall thruster

Hall thrusters have been under active development around the world since the 1960’s. Thrusters using traditional propellants such as xenon have been flown on a variety of satellite orbit raising and maintenance missions with an excellent record. To expand the mission envelope, it is necessary to lower the specific impulse of the thrusters but xenon and krypton are poor performers at specific impulses below 1,200 seconds. To enhance low specific impulse performance, this dissertation examines the development of a Hall-effect thruster which uses bismuth as a propellant. Bismuth, the heaviest non-radioactive element, holds many advantages over noble gas propellants from an energetics as well as a practical economic standpoint. Low ionization energy, large electron-impact crosssection and high atomic mass make bismuth ideal for low-specific impulse applications. The primary disadvantage lies in the high temperatures which are required to generate the bismuth vapors. Previous efforts carried out in the Soviet Union relied upon the complete bismuth vaporization and gas phase delivery to the anode. While this proved successful, the power required to vaporize and maintain gas phase throughout the mass flow system quickly removed many of the efficiency gains expected from using bismuth. To solve these problems, a unique method of delivering liquid bismuth to the anode has been developed. Bismuth is contained within a hollow anode reservoir that is capped by a porous metallic disc. By utilizing the inherent waste heat generated in a Hall thruster, liquid bismuth is evaporated and the vapors pass through the porous disc into the discharge chamber. Due to the high temperatures and material compatibility requirements, the anode was fabricated out of pure molybdenum. The porous vaporizer was not available commercially so a method of creating a refractory porous plate with 40-50% open porosity was developed. Molybdenum also does not respond well to most forms of welding so a diffusion bonding process was also developed to join the molybdenum porous disc to the molybdenum anode. Operation of the direct evaporation bismuth Hall thruster revealed interesting phenomenon. By utilizing constant current mode on a discharge power supply, the discharge voltage settles out to a stable operating point which is a function of discharge current, anode face area and average pore size on the vaporizer. Oscillations with a 40 second period were also observed. Preliminary performance data suggests that the direct evaporation bismuth Hall thruster performs similar to xenon and krypton Hall thrusters. Plume interrogation with a Retarding Potential Analyzer confirmed that bismuth ions were being efficiently accelerated while Faraday probe data gave a view of the ion density in the exhausted plume.

Orbits design for Leo space based solar power satellite system

Space Based Solar Power satellites use solar arrays to generate clean, green, and renewable electricity in space and transmit it to earth via microwave, radiowave or laser beams to corresponding receivers (ground stations). These traditionally are large structures orbiting around earth at the geo-synchronous altitude. This thesis introduces a new architecture for a Space Based Solar Power satellite constellation. The proposed concept reduces the high cost involved in the construction of the space satellite and in the multiple launches to the geo-synchronous altitude. The proposed concept is a constellation of Low Earth Orbit satellites that are smaller in size than the conventional system. For this application a Repeated Sun-Synchronous Track Circular Orbit is considered (RSSTO). In these orbits, the spacecraft re-visits the same locations on earth periodically every given desired number of days with the line of nodes of the spacecraft’s orbit fixed relative to the Sun. A wide range of solutions are studied, and, in this thesis, a two-orbit constellation design is chosen and simulated. The number of satellites is chosen based on the electric power demands in a given set of global cities. The orbits of the satellites are designed such that their ground tracks visit a maximum number of ground stations during the revisit period. In the simulation, the locations of the ground stations are chosen close to big cities, in USA and worldwide, so that the space power constellation beams down power directly to locations of high electric power demands. The j2 perturbations are included in the mathematical model used in orbit design. The Coverage time of each spacecraft over a ground site and the gap time between two consecutive spacecrafts visiting a ground site are simulated in order to evaluate the coverage continuity of the proposed solar power constellation. It has been observed from simulations that there always periods in which s spacecraft does not communicate with any ground station. For this reason, it is suggested that each satellite in the constellation be equipped with power storage components so that it can store power for later transmission. This thesis presents a method for designing the solar power constellation orbits such that the number of ground stations visited during the given revisit period is maximized. This leads to maximizing the power transmission to ground stations.

Quantification of relativistic perturbation forces on spacecraft trajectories

The intent of the work presented in this thesis is to show that relativistic perturbations should be considered in the same manner as well known perturbations currently taken into account in planet-satellite systems. It is also the aim of this research to show that relativistic perturbations are comparable to standard perturbations in speciffc force magnitude and effects. This work would have been regarded as little more then a curiosity to most engineers until recent advancements in space propulsion methods { e.g. the creation of a artiffcial neutron stars, light sails, and continuous propulsion techniques. These cutting-edge technologies have the potential to thrust the human race into interstellar, and hopefully intergalactic, travel in the not so distant future. The relativistic perturbations were simulated on two orbit cases: (1) a general orbit and (2) a Molniya type orbit. The simulations were completed using Matlab's ODE45 integration scheme. The methods used to organize, execute, and analyze these simulations are explained in detail. The results of the simulations are presented in graphical and statistical form. The simulation data reveals that the speciffc forces that arise from the relativistic perturbations do manifest as variations in the classical orbital elements. It is also apparent from the simulated data that the speciffc forces do exhibit similar magnitudes and effects that materialize from commonly considered perturbations that are used in trajectory design, optimization, and maintenance. Due to the similarities in behavior of relativistic versus non-relativistic perturbations, a case is made for the development of a fully relativistic formulation for the trajectory design and trajectory optimization problems. This new framework would afford the possibility of illuminating new more optimal solutions to the aforementioned problems that do not arise in current formulations. This type of reformulation has already showed promise when the previously unknown Space Superhighways arose as a optimal solution when classical astrodynamics was reformulated using geometric mechanics.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

GPS-only gravity field determination from GOCE data

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) is now in orbit for more than four years. This is longer than the originally planned lifetime of the satellite and after three years on the same altitude the satellite has been lowered to 235 km in several steps. In the frame of the GOCE High-level Processing Facility the Astronomical Institute of the University of Bern (AIUB) is responsible for the determination of the official Precise Science Orbit (PSO) product. Kinematic GOCE orbits are part of this product and are used by several institutions in- and outside the HPF for determining the low degrees of the Earth’s gravity field. AIUB GOCE GPS-only gravity field solutions using the Celestial Mechanics Approach and covering the Release 4 period as well as a more recent time interval at the lower orbit altitude are shown and discussed. Special attention is paid to the impact of systematic deficiencies in the kinematic orbits on the resulting gravity fields, e.g., related to the geomagnetic equator, and on possibilities to get rid of them.