Integrated attitude determination system using a combination of magnetometer and horizon sensor data

Thesis (MScEng)--Stellenbosch University, 2003.ENGLISH ABSTRACT: A different approach of employing attitude sensors with incomplete measurements in an attitude determination system is investigated. The amount of available attitude sensors on small satellites are limited, and the failure of sensors can be fatal when accurate attitude determination is necessary. The problem with sensors with incomplete measurements is that they must be used in combination with other sensors to obtain three dimensional attitude information. The aim is to enhance the possible number of sensor combinations that can be employed, in an attempt to improve the ability of the attitude determination system to tolerate sensor failures. An alternative sensor structure consisting of a magnetometer and two horizon sensors is presented. A method to obtain vector observations of the attitude from a combination between magnetometer and horizon sensor measurements is derived and tested. A full state Extended Kalman Filter is used to determine the satellite's attitude, attitude rate and disturbance torque from these vector observations. A second Extended Kalman Filter structure, using only magnetometer measurements, is implemented. The magnetometer Extended Kalman Filter and the horizon/magnetometer Extended Kalman Filter are integrated to obtain a single Extended Kalman Filter structure to determine the satellite's full attitude state. Integration is done by switching between the different pairs of vector information. A systematic analysis of the integrated filter's dynamic behaviour during the switching stages is done by means of a series of case studies.AFRIKAANSE OPSOMMING: Die gebruik van oriëntasiesensore met onvolledige metingsdata in oriëntasiebepalingsstelsels is ondersoek. Slegs 'n beperkte aantal oriëntasiesensore is beskikbaar op mikro satelliete. 'n Foutiewe sensor kan dus noodlottig wees wanneer akkurate oriëntasiebepaling nodig is. Die probleem met sensore met onvolledige metingsdata is dat dit in sensor kombinasies gebruik moet word om drie dimensionele oriëntasieinligting te verkry. Die doel is dus om die moontlike aantal sensor kombinasies sodanig te vermeerder dat die oriëntasiebepalingsstelsel beter bestand sal wees teen moontlike sensor falings. 'n Alternatiewe sensor struktuur, bestaande uit 'n magnetometer en twee horison sensore, is ondersoek. 'n Metode vir die verkryging van 3-as oriëntasie inligting vanaf 'n kombinasie van magnetometer en horison sensor metingsdata is afgelei en getoets. 'n Vol toestand uitgebreide Kalmanfilter is gebruik om the satelliet se oriëntasie, oriëntasie snelheid en versteurings draairnoment vanaf die vektor observasies af te lei. 'n Tweede uitgebreide Kalmanfilter struktuur, wat slegs magnetometer metingsdata gebruik, is geïmplementeer. Die magnetometer filter en die horison/magnetometer filter is geïntegreer sodat een uitgebreide Kalmanfilter struktuur volle oriëntasie inligting kan aflei vanaf verskillende pare vektors met oriëntasie inligting. Integrasie is gedoen deur te skakel tussen die verskillende vektorpare. 'n Sistematiese analise van die geïntegreerde filter se dinamiese gedrag gedurende die oorskakelingstye is gedoen deur middel van 'n reeks gevallestudies

Scaling behavior in economics: II. Modeling of company growth

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an ``optimal'' size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France (April 1997

SL(2,Z) Multiplets in N=4 SYM Theory

We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in the superconformal phase. The modular property of the operator's scaling dimension determines whether the operator transforms as a singlet, or covariantly, as part of a finite or infinite dimensional multiplet under the SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the non-perturbative local operators dual to the Konishi multiplet.Comment: 14 pages, harvmac; v2: published version with minor change

Scaling behavior in economics: I. Empirical results for company growth

We address the question of the growth of firm size. To this end, we analyze the Compustat data base comprising all publicly-traded United States manufacturing firms within the years 1974-1993. We find that the distribution of firm sizes remains stable for the 20 years we study, i.e., the mean value and standard deviation remain approximately constant. We study the distribution of sizes of the ``new'' companies in each year and find it to be well approximated by a log-normal. We find (i) the distribution of the logarithm of the growth rates, for a fixed growth period of one year, and for companies with approximately the same size $S$ displays an exponential form, and (ii) the fluctuations in the growth rates -- measured by the width of this distribution $\sigma_1$ -- scale as a power law with $S$, $\sigma_1\sim S^{-\beta}$. We find that the exponent $\beta$ takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain: $\beta=0.20\pm0.03$ for sales, $\beta=0.18\pm0.03$ for number of employees, $\beta=0.18\pm0.03$ for assets, $\beta=0.18\pm0.03$ for cost of goods sold, and $\beta=0.20\pm0.03$ for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France (April 1997

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Turing degrees of limit sets of cellular automata

Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a computable point and that any non-trivial property on them is undecidable. We go one step further in this article by giving a full characterization of the sets of Turing degrees of cellular automata: they are the same as the sets of Turing degrees of effectively closed sets containing a computable point

A Comparison of 4-H and Other Youth Development Organizations in the Development of Life Skills

The article briefly describes the results of a study on the influence of 4-H and other youth development programs on the development of 36 life skills including critical thinking, goal setting, communication, decision-making and community service. Respondents (n=223) were high achieving 4-H alumni who participated it the Oklahoma 4-H Program between the years 1969 and 1998. Results suggest that while respondents credited 4-H with influencing the development of the majority of the identified life skills, other youth organizations were also identified as having some influence on the development in different life skills. Recommendations for 4-H programming are offered

The Use of Cafeteria Trials for the Selection of \u3ci\u3eDesmodium ovalifolium\u3c/i\u3e Genotypes

For the selection of tropical legumes which contain anti-nutritive components such as tannins, relative acceptability of genotypes to ruminants is of particular importance, since these plant components may influence selective grazing behaviour and subsequent animal productivity. Plant-animal interactions are not predictable from laboratory analyses. Involving grazing animals through the conduction of relative-acceptability (=cafeteria) trials at early stages of the germplasm selection process might therefore provide a convenient tool to adjust and confirm genotype selection based on laboratory quality analyses data. As part of a multilocational germplasm evaluation project, cafeteria-experiments were conducted at two contrasting environments in Colombia with a core collection of Desmodium ovalifolium, a tropical legume species containing tannins. The objective of these experiments was to assess the usefulness of such acceptability trials in the selection of D. ovalifolium genotypes. Relative acceptability indices for the 18 accessions confirm genotype selection based on a series of laboratory quality analyses during earlier stages of the project and indicate pronounced genotype-environment interactions. Moreover, animal activity profiles confirm the influence of plant-environment-animal interactions and thus the usefulness of cafeteriatrials for germplasm selection projects

Codariocalyx Gyroides- A New Forage Option for the Humid Tropics

The Southeast Asian shrub legume, Codariocalyx gyroides is adapted to acid, low-fertility soils with poor drainage. Data from 19 RIEPT (International Network for Evaluation of Tropical Pastures) trial sites conducted in the American humid and subhumid tropics were used to define the range of adaptation of C. gyroides. The results show that C. gyroides performs better under high rainfall conditions of the humid tropics with hardly any dry season, and it responds to soil fertility (Ca, P). Future research needs are identified. The release of a commercial cultivar in Colombia is being prepared

Neuronal assembly dynamics in supervised and unsupervised learning scenarios

The dynamic formation of groups of neurons—neuronal assemblies—is believed to mediate cognitive phenomena at many levels, but their detailed operation and mechanisms of interaction are still to be uncovered. One hypothesis suggests that synchronized oscillations underpin their formation and functioning, with a focus on the temporal structure of neuronal signals. In this context, we investigate neuronal assembly dynamics in two complementary scenarios: the first, a supervised spike pattern classification task, in which noisy variations of a collection of spikes have to be correctly labeled; the second, an unsupervised, minimally cognitive evolutionary robotics tasks, in which an evolved agent has to cope with multiple, possibly conflicting, objectives. In both cases, the more traditional dynamical analysis of the system’s variables is paired with information-theoretic techniques in order to get a broader picture of the ongoing interactions with and within the network. The neural network model is inspired by the Kuramoto model of coupled phase oscillators and allows one to fine-tune the network synchronization dynamics and assembly configuration. The experiments explore the computational power, redundancy, and generalization capability of neuronal circuits, demonstrating that performance depends nonlinearly on the number of assemblies and neurons in the network and showing that the framework can be exploited to generate minimally cognitive behaviors, with dynamic assembly formation accounting for varying degrees of stimuli modulation of the sensorimotor interactions