For synthetic aperture imaging, position and orientation deviation is of great concern. Unknown motions of a Synthetic Aperture Sonar (SAS) can blur the reconstructed images and degrade image quality considerably. Considering the high sensitivity of synthetic aperture imaging technique to sonar deviation, this research aims at providing a thorough navigation solution for a free-towed synthetic aperture sonar (SAS) comprising aspects from the design and construction of the navigation card through to data postprocessing to produce position, velocity, and attitude information of the sonar. The sensor configuration of the designed navigation card is low-cost Micro-Electro-Mechanical-Systems (MEMS) Magnetic, Angular Rate, and Gravity (MARG) sensors including three angular rate gyroscopes, three dual-axial accelerometers, and a triaxial magnetic hybrid. These MARG sensors are mounted orthogonally on a standard 180mm Eurocard PCB to monitor the motions of the sonar in six degrees of freedom. Sensor calibration algorithms are presented for each individual sensor according to its characteristics to precisely determine sensor parameters. The nonlinear least square method and two-step estimator are particularly used for the calibration of accelerometers and magnetometers. A quaternion-based extended Kalman filter is developed based on a total state space model to fuse the calibrated navigation data. In the model, the frame transformations are described using quaternions instead of other attitude representations. The simulations and experimental results are demonstrated in this thesis to verify the capability of the sensor fusion strategy.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-17Bitstream added on 2014-06-13T18:30:54Z : No. of bitstreams: 1 barreiro_rc_me_sjrp.pdf: 585027 bytes, checksum: 039155145a6c7b9e6e1fc03a02180b55 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo deste trabalho ée estabelecer similaridades entre a análise complexa e os quatérnios. Nele é feito um estudo da regularidade de funções quaterniônicas e são estabelecidas as funções exponencial e logarítmica para os quatérnios sendo feito um estudo da hiperpe- riodicidade dessas funções. Outro resultado apresentado é a generalização quaterniônica da fórmula integral de Cauchy um dos principais teoremas da análise complexa. / The objective of this work is to establish similarities between the complex analysis and the quaternions. In it is made a study of the regularity of quaternionic functions and are established the exponential and logarithmic functions for the quaternions being made a study of the hiperperiodicity of these functions. Another presented result is the quater- nionic generalization of the Cauchy's integral formula one of the main theorems of the complex analysis.

A simplicial cell complex K is the face poset of a regular CW complex W such that the boundary complex of each cell is isomorphic to the boundary complex of a simplex of same dimension. If a topological space X is homeomorphic to W then we say that K is a pseudotriangulation of X. For d 1, a (d + 1)-colored graph is a graph = (V; E) with a proper edge coloring : E ! f0; : : : ; dg. Such a graph is called contracted if (V; E n 1(i)) is connected for each color A contracted graph = (V; E) with an edge coloring : E ! f0; : : : ; dg determines a d-dimensional simplicial cell complex K( ) whose vertices have one to one correspondence with the colors 0; : : : ; d and the facets (d-cells) have one to one correspondence with the vertices in V . If K( ) is a pseudotriangulation of a manifold M then ( ; ) is called a crystallization of M. In [71], Pezzana proved that every connected closed PL manifold admits a crystallization. This thesis addresses many important results of crystallization theory in combinatorial topology. The main contributions in this thesis are the followings. We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of vertices of any crystallization of a connected closed 3-manifold M is at least the weight of the fundamental group of M. This lower bound is sharp for the 3-manifolds RP3, L(3; 1), L(5; 2), S1 S1 S1, S2 S1, S2 S1 and S3=Q8, where Q8 is the quaternion group. Moreover, there is a unique such vertex minimal crystallization in each of these seven cases. We have also constructed crystallizations of L(kq 1; q) with 4(q + k 1) vertices for q 3, k 2 and L(kq +1; q) with 4(q + k) vertices for q 4, k 1. In [22], Casali and Cristofori found similar crystallizations of lens spaces. By a recent result of Swartz [76], our crystallizations of L(kq + 1; q) are vertex minimal when kq + 1 are even. In [47], Gagliardi found presentations of the fundamental group of a manifold M in terms of a crystallization of M. Our construction is the converse of this, namely, given a presentation of the fundamental group of a 3-manifold M, we have constructed a crystallization of M. These results are in Chapter 3. We have de ned the weight of the pair (hS j Ri; R) for a given presentation hS j R of a group, where the number of generators is equal to the number of relations. We present an algorithm to construct crystallizations of 3-manifolds whose fundamental group has a presentation with two generators and two relations. If the weight of (hS j Ri; R) is n then our algorithm constructs all the n-vertex crystallizations which yield (hS j Ri; R). As an application, we have constructed some new crystallization of 3-manifolds. We have generalized our algorithm for presentations with three generators and a certain class of relations. For m 3 and m n k 2, our generalized algorithm gives a 2(2m + 2n + 2k 6 + n2 + k2)-vertex crystallization of the closed connected orientable 3-manifold Mhm; n; ki having fundamental group hx1; x2; x3 j xm1 = xn2 = xk3 = x1x2x3i. These crystallizations are minimal and unique with respect to the given presentations. If `n = 2' or `k 3 and m 4' then our crystallization of Mhm; n; ki is vertex-minimal for all the known cases. These results are in Chapter 4. We have constructed a minimal crystallization of the standard PL K3 surface. The corresponding simplicial cell complex has face vector (5; 10; 230; 335; 134). In combination with known results, this yields minimal crystallizations of all simply connected PL 4-manifolds of \standard" type, i.e., all connected sums of CP2, CP2, S2 S2, and the K3 surface. In particular, we obtain minimal crystallizations of a pair 4-manifolds which are homeomorphic but not PL-homeomorphic. We have also presented an elementary proof of the uniqueness of the 8-vertex crystallization of CP2. These results are in Chapter 5. For any crystallization ( ; ) the number f1(K( )) of 1-simplices in K( ) is at least d+1 . It is easy to see that f1(K( )) = d+1 if and only if (V; 1(A)) is connected for each d 2 2 1)-set A called simple. All the crystallization in Chapter 5 (. Such a crystallization is are simple. Let ( ; ) be a crystallization of M, where = (V; E) and : E ! f0; : : : ; dg. We say that ( ; ) is semi-simple if (V; 1(A)) has m + 1 connected components for each (d 1)-set A, where m is the rank of the fundamental group of M. Let ( ; ) be a connected (d +1)-regular (d +1)-colored graph, where = (V; E) and : E ! f0; : : : ; dg. An embedding i : ,! S of into a closed surface S is called regular if there exists a cyclic permutation ("0; "1; : : : ; "d) (of the color set) such that the boundary of each face of i( ) is a bi-color cycle with colors "j; "j+1 for some j (addition is modulo d+1). Then the regular genus of ( ; ) is the least genus (resp., half of genus) of the orientable (resp., non-orientable) surface into which embeds regularly. The regular genus of a closed connected PL 4-manifold M is the minimum regular genus of its crystallizations. For a closed connected PL 4-manifold M, we have provided the following: (i) a lower bound for the regular genus of M and (ii) a lower bound of the number of vertices of any crystallization of M. We have proved that all PL 4-manifolds admitting semi-simple crystallizations, attain our bounds. We have also characterized the class of PL 4-manifolds which admit semi-simple crystallizations. These results are in Chapter 6.

Dans ce travail de thèse on s’intéresse à l’estimation de l’attitude d’un corps rigideen mouvement dans l’espace 3D en utilisant les quaternions comme représentation. Cetteproblématique a été largement étudiée dans la littérature sous divers domaines d’application.L’objectif de la thèse est de proposer de nouvelles méthodes de fusion de données en combinantdes mesures inertielles et magnétiques. Dans un premier temps, nous nous sommesintéressés à l’estimation de l’attitude en cas de mouvement accéléré où l’accélération linéairedu corps n’est plus négligeable devant la gravité. Deux approches ont été proposées dans cecadre. La première utilise un filtre de Kalman adaptatif pour la compensation des accélérationslinéaires. Précisément, des lois de détection ont été développées pour distinguer d’unefaçon automatique les différentes phases de mouvement (statiques et dynamiques). Ainsi, lamatrice de covariance associée à l’accélération linéaire est estimée afin d’ajuster le gain dufiltre. La deuxième approche consiste à intégrer un filtre singulier élaboré sur la base d’unnouveau modèle, dans lequel le modèle du processus est défini en se basant sur les mesuresissues de l’accéléromètre tandis que le modèle d’observation est défini par les mesures issuesdu gyromètres et du magnétomètres. Cette formulation permet de prendre en compte l’effetdes accélérations linéaires d’une manière efficace. Dans un deuxième temps, on s’est focalisésur l’estimation de l’attitude avec utilisation intermittente de gyromètres, considérés commecapteurs énergivores. Nous avons étudié dans ce cas la façon la plus adéquate afin de réduirel’acquisition des mesures de vitesse angulaire tout en gardant une qualité acceptable de l’estimationde l’attitude. Toutes les approches développées ont été validées par des simulationsnumériques ainsi que des expérimentations utilisant des données réelles. / In this PhD. thesis we deal with attitude estimation of accelerated rigid body moving in the 3D space using quaternion parameterization. This problem has been widely studied in the literature in various application areas. The main objective of the thesis is to propose new methods for data fusion to combine inertial gyros) and magnetic measurements. The first challenge concerns the attitude estimation during dynamic cases, in which external acceleration of the body is not negligible compared to the Gravity. Two main approaches are proposed in this context. Firstly, a quatenion-based adaptive Kalman filter (q-AKF) was designed in order to compensate for such external acceleration. Precisely, a smart detector is designed to decide whether the body is in static or dynamic case. Then, the covariance matrix of the external acceleration is estimated to tune the filter gain. Second, we developed descriptor filter based on a new formulation of the dynamic model where the process model is fed by accelerometer measurements while observation model is fed by gyros and magnetometer measurements. Such modeling gives rise to a descriptor system. The resulting model allows taking the external acceleration of the body into account in a very efficient way. The second challenge is related to the energy consumption issue of gyroscope, considered as the most power consuming sensor. We study the way to reduce the gyro measurements acquisition by switching on/off the sensor while maintaining an acceptable attitude estimation. The effciency of the proposed methods is evaluated by means of numerical simulations and experimental tests.

Seja p um número primo e seja uma raiz p - ésima primitiva da unidade. Considere os seguintes elementos i := 1 + + 2 + ... + i-1 para todo 1 i k do anel Z[] onde k = (p-1)/2. Nesta tese nós descrevemos explicitamente um conjunto gerador para o grupo das unidades do anel de grupo integral ZC2p; representado por U(ZC2p); onde C2p representa o grupo cíclico de ordem 2p e p satisfaz as seguintes condições: S := { -1, , u2, ... uk } gera U(Z[]) e U(Zp) = ou U(Zp)2 = e -1 U(Zp); que são verificadas para p = 7; 11; 13; 19; 23; 29; 53; 59; 61 e 67. Com o intuito de estender tais ideias encontramos um conjunto gerador para U(Z(C2p x C2) e U(Z(C2p x C2 x C2) onde p satisfaz as mesmas condições anteriores acrescidas de uma nova hipótese. Finalmente com o auxílio dos resultados anteriores apresentamos um conjunto gerador das unidades centrais do anel de grupo Z(Cp x Q8); onde Q8 representa o grupo dos quatérnios, ou seja, Q8 := <a; b : a4 = 1; a2 = b2; b-1 a b = a-1 >. / Let p be an odd prime integer, be a pth primitive root of unity, Cn be the cyclic group of order n, and U(ZG) the units of the Integral Group Ring ZG: Consider ui := 1++2 +: : :+i1 for 2 i p + 1 2 : In our study we describe explicitly the generator set of U(ZC2p); where p is such that S := f1; ; u2; : : : ; up1 2 g generates U(Z[]) and U(Zp) is such that U(Zp) = 2 or U(Zp)2 = 2 and 1 =2 U(Zp)2; which occurs for p = 7; 11; 13; 19; 23; 29; 37; 53; 59; 61, and 67: For another values of p we don\'t know if such conditions hold. In addition, under suitable hypotheses, we extend these ideas and build a generator set of U(Z(C2p C2)) and U(Z(C2p C2 C2)): Besides that, using the previous results, we exhibit a generator set for the central units of the group ring Z(Cp Q8) where Q8 represents the quaternion group.

Orientadores: Reginaldo Palazzo Júnior, Cátia Regina de Oliveira Quilles Queiroz / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-25T14:53:45Z (GMT). No. of bitstreams: 1 Benedito_CintyaWinkdeOliveira_D.pdf: 1485856 bytes, checksum: 50adbb3cffa1343c4a0cd9b3d7586173 (MD5) Previous issue date: 2014 / Resumo: Na busca por novos sistemas de comunicações muitos trabalhos têm sido realizados com o objetivo de obter constelações de sinais e códigos geometricamente uniformes no plano hiperbólico. Neste contexto, nossa proposta é identificar uma estrutura algébrica e geométrica para que códigos e reticulados possam ser construídos neste espaço. O problema central deste trabalho consiste em construir grupos fuchsianos provenientes de tesselações hiperbólicas regulares {p,q} utilizando diversos tipos de emparelhamentos e identificá-los com álgebras e ordens dos quatérnios, definindo-os assim como aritmético. Desta forma, propomos um algoritmo para construir grupos fuchsianos aritméticos provenientes de tesselações hiperbólicas regulares {p,q} cujo polígono hiperbólico regular gera uma superfície orientada de gênero maior ou igual a dois. Para isso, fornecemos uma condição necessária para que estes grupos possam ser obtidos, esta condição será denominada condição de Fermat devido a sua identificação com os números de Fermat. Através da construção destes grupos, mostramos que existe um isomorfismo entre dois grupos fuchsianos aritméticos provenientes de uma tesselação {p,q} a partir de emparelhamentos diferentes. Além disso, descrevemos alguns dos corpos de números que utilizamos para construir grupos fuchsianos aritméticos, como subcorpos maximais reais de corpos ciclotômicos, a fim de propor uma relação entre os reticulados hiperbólicos e os reticulados euclidianos. Reticulados hiperbólicos completos obtidos através da identificação de grupos fuchsianos com ordens maximais dos quatérnios também são apresentados. Desta forma, obtemos um rotulamento completo dos pontos da constelação de sinal associada / Abstract: In the search for new communications systems many studies have been conducted with the goal of obtaining signal constellations and geometrically uniform codes in the hyperbolic plane. In this context, our proposal is to identify an algebraic and geometric structures for constructing codes and lattices in this space. The central problem of this work is to construct fuchsian groups derived from hyperbolic tessellations {p,q} using different edge-pairings sets and identify them with quaternion algebras and quaternion orders, by setting it as arithmetic. We also propose an algorithm to construct arithmetic fuchsian groups from a tessellation {p,q} whose regular hyperbolic polygon generates an oriented and compact surface with genus greater or equal than 2. For that we provide a necessary condition for these groups to be obtained, this necessary condition is called Fermat condition due to its identification with the Fermat numbers. By the construction of these groups, it is also shown an isomorphism between two arithmetic fuchsian groups derived from a tessellation {p,q} via different edge-pairings sets. Furthermore, we will describe some of the number fields that we use to construct arithmetic fuchsian groups as maximal real subfields of cyclotomic fields in order to propose a relationship between hyperbolic lattices and euclidean lattices. Complete hyperbolic lattices obtained by identifying fuchsian groups with maximal quaternion orders will also be presented. In this way we have a complete labeling of the points of the corresponding signal constellation / Doutorado / Telecomunicações e Telemática / Doutora em Engenharia Elétrica

This dissertation presents a novel approach to develop a system for real-time tracking of the position and orientation of the human hand in three-dimensional space, using MEMS inertial measurement units (IMUs) and infrared cameras. This research focuses on the study and implementation of an algorithm to correct the gyroscope drift, which is a major problem in orientation tracking using commercial-grade IMUs. An algorithm to improve the orientation estimation is proposed. It consists of: 1.) Prediction of the bias offset error while the sensor is static, 2.) Estimation of a quaternion orientation from the unbiased angular velocity, 3.) Correction of the orientation quaternion utilizing the gravity vector and the magnetic North vector, and 4.) Adaptive quaternion interpolation, which determines the final quaternion estimate based upon the current conditions of the sensor. The results verified that the implementation of the orientation correction algorithm using the gravity vector and the magnetic North vector is able to reduce the amount of drift in orientation tracking and is compatible with position tracking using infrared cameras for real-time human hand motion tracking. Thirty human subjects participated in an experiment to validate the performance of the hand motion tracking system. The statistical analysis shows that the error of position tracking is, on average, 1.7 cm in the x-axis, 1.0 cm in the y-axis, and 3.5 cm in the z-axis. The Kruskal-Wallis tests show that the orientation correction algorithm using gravity vector and magnetic North vector can significantly reduce the errors in orientation tracking in comparison to fixed offset compensation. Statistical analyses show that the orientation correction algorithm using gravity vector and magnetic North vector and the on-board Kalman-based orientation filtering produced orientation errors that were not significantly different in the Euler angles, Phi, Theta and Psi, with the p-values of 0.632, 0.262 and 0.728, respectively. The proposed orientation correction algorithm represents a contribution to the emerging approaches to obtain reliable orientation estimates from MEMS IMUs. The development of a hand motion tracking system using IMUs and infrared cameras in this dissertation enables future improvements in natural human-computer interactions within a 3D virtual environment.

Delade Augmented reality (AR) system är ofta implementerade på ett sådant sätt att de är hårt kopplade av hårdvaran eller utnyttjar stora ramverk eller grafikmotorer för att implementera den grafiska delen av projektet. Detta är ett problem då system som är hårtkopplade till hårdvara inte är lika enkla att distribuera och minskar användarsegmentet som kan använda systemet. Implementationer som nyttjar stora grafikmotorer använder ofta bara en liten del av funktionaliteten som motorn erbjuder och denna funktionalitet som inte används utgör en förlust i prestanda. För att lösa detta måste ett system abstraherat från hårdvara med den minsta nödvändiga funktionaliteten nödvändig för delad Augmented reality implementeras.  Rapporten arbetar med abstraktion av hårdvara för ett projicerat delat Augmented reality med hjälp av maskinlärning. Detta utförs genom uppdelning av systemet i två delar. En del fångar upp individen framför kameran och beräknar hur personen är positionerad med hjälp av en maskinlärning-modell, medan den andra delen hanterar projiceringen genom att ta in data från maskinlärning-modellen, som skickas över via socketkommunikation, för att knyta samman punkterna till ett tredimensionellt skelett. Tester gjordes om denna typ av abstraktion innebär för signifikanta fördröjningar samt påfrestningar på prestanda. Testerna visade att programmet körs med 50 millisekunder fördröjning på 80 bilder per sekund. Detta tyder på att det är gynnsamt att abstrahera applikationen för distribution av dess olika moduler eller byta ut dem. En slutgiltig projektion enlig med personen kunde inte tas fram men abstraktionen som är nödvändig för att tillhandahålla systemet är godtycklig nog för att vara oberoende av hårdvara och visa vilken funktionalitet som krävs av system inom delad AR. / Shared augmented reality (AR) systems are often implemented in a way that tightly couples them to the hardware or relies on large frameworks or graphics engines to implement the graphical part of the project. This is a problem because systems tightly coupled to hardware are not as easy to distribute and reduce the user segment that can use the system. Implementations that rely on large graphics engines often utilize only a small portion of the engine's functionality, resulting in a loss of performance for unused functionality. To solve this, a hardware-agnostic system with the minimal necessary functionality for shared augmented reality must be implemented.  The report works with hardware abstraction for a projected shared augmented reality using machine learning. This is accomplished by dividing the system into two parts. One part captures the individual in front of the camera and calculates their positioning using a machine learning model, while the other part handles projection by receiving data from the machine learning model, transmitted via socket communication, to connect the points into a three-dimensional skeleton. Tests were conducted to determine if this type of abstraction results in significant delays and performance strain. The tests showed that the program runs with a 50-millisecond delay at 80 frames per second. This suggests that it is beneficial to abstract the application for the distribution of its different modules or to replace them. A final projection aligned with the individual could not be produced, but the abstraction necessary to provide the system is arbitrary enough to be independent of hardware and demonstrate the required functionality of shared AR systems.

Apresentamos duas construções para unidades de uma ordem em uma classe de álgebras de quatérnios que é anel de divisão: as unidades de Pell e as unidades de Gauss. Classificamos os anéis de inteiros de extensões quadráticas racionais, $R$, cujo grupo de unidades $\\U (R G)$ é hiperbólico para um certo grupo $G$ fixado. Também classificamos os semigrupos finitos $S$, tal que, para a álgebra unitária $\\Q S$ e para toda $\\Z$-ordem $\\Gamma$ de $\\Q S$, o grupo de unidades $\\U (\\Gamma)$ é hiperbólico. Nesse mesmo contexto, classificamos os {\\it RA}-loops $L$ cujo loop de unidades $\\U (\\Z L)$ não contém um subgrupo abeliano livre de posto dois. / For a given division algebra of a quaternion algebra, we construct and define two types of units of its $\\Z$-orders: Pell units and Gauss units. Also, for the quadratic imaginary extensions over the racionals and some fixed group $G$, we classify the algebraic integral rings for which the unit group ring is a hyperbolic group. We also classify the finite semigroups $S$, for which all integral orders $\\Gamma$ of $\\Q S$ have hyperbolic unit group $\\U(\\Gamma)$. We conclude with the classification of the $RA$-loops $L$ for which the unit loop of its integral loop ring does not contain a free abelian subgroup of rank two.

São estudados alguns aspectos das álgebras alternativas, como o bar-radical de uma álgebra bárica alternativa e as identidades de grau 4 e 5 nas álgebras de Cayley-Dickson. Neste estudo fazemos uso da decomposição de Peirce e de diversas propriedades importantes das álgebras alternativas. Concluímos mostrando que as únicas identidades de grau 4 são as triviais e as de grau 5 são conseqüência de outras duas identidades conhecidas / We studied some aspects of alternative algebras, in special the bar radical of an alternative baric algebra and identities of degree 4 and 5 of Cayley-Dickson algebras. We made significant use of the Peirce decomposition and several properties of the alternative algebras, in order to show that the only identities of degree four are the trivial ones, and the identities of degree five are consequences of other two known identities.