Kalman filtering is a well-established method for fusing sensor data in order to accuratelyestimate unknown variables. Recently, the unscented Kalman filter (UKF) has beenused due to its ability to propagate the first and second moments of the probability distribution of an estimated state through a non-linear transformation. The design of ageneric algorithm which implements this filter occupies the first part of this thesis. The generality and functionality of the filter were tested on a toy example and the results are within machine accuracy when compared to those of an equivalent C++ implementation.Application of this filter to the attitude navigation problem becomes non-trivial when coupled to quaternions. Challenges present include the non-commutation of rotations and the dimensionality difference between quaternions and the degrees of freedom of the motion. The second part of this thesis deals with the formulation of the UKF in the quaternion space. This was achieved by implementing an error-state formulation of the process model, bounding estimation in the infinitesimal space and thus de-coupling rotations from non-commutation and bridging the dimensionality discrepancy of quaternions and their respective covariances.The attitude navigation algorithm was then tested using an IMU and a magnetometer.Results show a bounded estimation error which settles to around 1 degree. A detailed look of the filter mechanization process was also presented showing expected behavior for estimation of the initial attitude with error tolerance of 1 mdeg. The structure and design of the proposed formulation allows for trivially incorporating other sensors inthe estimation process and more intricate modelling of the stochastic processes present,potentially leading to greater estimation accuracy. / Kalman filtrering är en vältablerad metod for att sammanväga sensordata för att erhålla noggranna estimat av okända variabler. Nyligen har den typ av kalman filter som kallas unscented Kalman filter (UKF) ökat i populäritet pa grund av dess förmåga att propagera de första och andra momenten för sannolikhetsfördelningen för ett estimera tillstånd genom en ickelinjär transformation. Designen av en generisk algoritm som implementerar denna typ av filter upptar den första delen av denna avhandling. Generaliteten och funktionaliteten för detta filter testades på ett minimalt exempel och resultaten var identiska med de för en ekvivalent C++-implementation till den noggrannhet som tillåts av den nita maskinprecisionen. Användandet av detta filter för attitydnavigering blir icke-trivialt när det anvands forkvaternioner. De utmaningar som uppstar inkluderar att rotationer inte kommuterar och att de finns en skillnad i dimensionalitet mellan kvaternioner och antalet frihetsgrader i rörelsen. Den andra delen av denna avhandling behandlar formuleringen av ett UKF för ett tillstånd som inkluderar en kvaternion. Detta gjordes genom att implementera en så kallad error state-formulering av processmodellen, vilken begränsar estimeringen till ett innitesimalt tillstånd och därigenom undviker problemen med att kvaternionmultiplikation inte kommuterar och överbryggar skillnaden i dimensionalitet hos kvaternioner och deras motsvarande vinkelosäkerheter.Attitydnavigeringen testades sedan med hjälp av en IMU och en magnetometer.Resultaten visade ett begränsat estimeringsfel som ställer in sig kring 1 grad. Strukturen och designen av den föreslagna formuleringen möjliggör på ett rattframt satt tillägg av andra sensorer i estimeringsprocessen och mer detaljerad modellering av de stokastiska processerna, vilket potentiellt leder till högre estimering noggrannhet.

Technology advances each day, with every advancement new and improved products are accompanied. Robots come in various shapes and sizes, from the size of a fly to the size of a human being. The purpose of this project is to further our understanding in how to build a robot, more specifically, a mono wheeled robot and design control systems enabling it to balance by itself. The robot is a one-wheeler with ducted fans on top. It is to balance with the help of the wheel in one direction and with ducted fans in the perpendicular direction.The robot succeeded in balancing with the wheel. However with help of the fans the robot only managed to balance for approximately 20 seconds. Analysing the frequency content from figures 5.2, 5.4, 5.3 resulted in finding frequencies under 1Hz being dominant in the output signals from the control system, observing this a clear oscillation frequency was only determined for the ducted fan system while the wheel system was non periodic. The study concluded that one cannot stabilize the control systems individually because that can lead to disturbances for the other. The results showed that even though the wheel’s control system was stable, it was affected by the second control system, causing disturbances. / För varje dag som går tar tekniken ett steg frammåt, hela tiden med nya och förbättrade produkter. Robotar kommer i olika former och storlekar, från storleken av en insekt till storleken av en människa. Syftet med detta projekt är att utvidga förståelsen över hur man bygger en robot, mer specifikt, en enhjulig robot samt hur man konstruerar ett reglersystem för att få roboten att balansera på egen hand. Roboten är en enhjuling med fläktar. Syftet är att bygga och programmera den till att balansera på egen hand, i ena riktningen med hjulet och i andra riktningen med fläktarna. Roboten lyckades balansera med hjälp av hjulet, men med fläktsystemet balancerade roboten endast i cirka 20 sekunder. Med hjäp av frekvenspspekrumen i figurer 5.2, 5.4, 5.3 försöktes en oscillationsfrekvens och periodtid tas fram, detta erhölls endast för fläktsystemet då hjulsystemet inte gav en tydlig oscillationsfrekvens. Slutsatsen som drogs var att det inte går att stabilisera de individuella systemen separat och sedan kombinera dem. Detta på grund av att det leder till att det ena systemet riskerar att agera som en störsignal till det andra systemet.

This dissertation addresses attitude control and inertial navigation of autonomous underwater vehicles (AUVs). We present theoretical justification for using simplified models, derive system identification algorithms, and verify our results through extensive field trials. Although this research focuses on small AUVs with limited instrumentation, the results are useful for underwater vehicles of any size. For attitude control of aircraft systems, second-order equivalent pitch-axis models are common and extensively studied. However, similar analysis has not been performed for the pitch-axis motion of underwater vehicles. In this dissertation, we study the utility and the limitations of second-order approximate models for AUVs. We seek to improve the flight performance and shorten the time required to re-design a control algorithm when the shape, mass-distribution, and/or net buoyancy of an AUV/payload configuration changes. In comparison to commonly implemented AUV attitude controllers, which neglect roll motion and address pitch and yaw dynamics separately, we derive a novel linear time-varying model that explicitly displays the coupling between pitch and yaw motion due to nonzero roll angle and/or roll rate. The model facilitates an Hâ control design approach that explicitly addresses robustness against those coupling terms and significantly reduces the effect of pitch and yaw coupling. To improve AUV navigation, we investigate algorithms for calibrating a triaxial gyroscope using angular orientation measurements and formally define AUV trajectories that are persistently exciting and for which the calibration coefficients are uniformly observable. To improve AUV guidance, we propose a near real-time ocean current identification method that estimates a non-uniform flow-field using only sparse flow measurements. / Ph. D.

This thesis deals with theoretical description of fiber-optic angular velocity sensors, or gyroscopes, and further with design and construction of own sensor of this type. The theoretical part describes problematics of interferometric and resonant fiber-optic gyroscopes. Basic principles and physical limits are described for both types. The main focus is then put on analysis of possible conceptions of these sensors. Solutions using different optical configurations as well as various modulation and signal processing schemes are discussed. The practical part deals with design and construction of own interferometric fiber-optic gyroscope in closed-loop configuration. The gyroscope utilizes all-fiber components including piezoelectric phase modulator and unexpensive single-mode fiber, which are commonly used only for open-loop configurations. To realize closed-loop operation, special modulation scheme based on fully harmonic signal was develeped, which yields linear output within wide dynamic range. This type of modulation requires high level of synchronization achieved by using a field-programmable gate array module. The gyroscope utilizes powerful broadband fiber source, polarizer and Lyot depolarizer which ensure good reciprocity of whole architecture. The parameters of the sensor, obtained by measurement, are even comparable to some sensors using PM fiber, which is much more expensive.

Les gyroscopes laser à gaz constituent une solution technique de haute performances dans les problématiques de navigation inertielle. Néanmoins, pour de très faibles vitesses de rotation, les petites imperfections des miroirs de la cavité optique font que les deux faisceaux contra-propageant sont verrouillés en phase. En conséquence, les mesures en quadrature de leur différence de phase ne permettent plus de remonter directement aux vitesses de rotation à l'intérieur d'une zone autour de zéro, dite zone aveugle statique, ou, si l'on utilise une procédure d'activation mécanique, dite zone aveugle dynamique. Ce travail montre qu'il est néanmoins possible, en utilisant des méthodes issues du filtrage et de l'estimation, de remonter aux vitesses de rotation mêmes si ces dernières sont en zone aveugle. Pour cela, on part d'une modélisation physique de la dynamique que l'on simplifie par des techniques de perturbations singulières pour en déduire une généralisation des équations de Lamb. Il s'agit de quatre équations différentielles non-linéaires qui décrivent la dynamique des intensités et des phases des deux faisceaux contra-propageant. Une étude qualitative par perturbations régulières, stabilité exponentielle des points d'équilibre et applications de Poincaré permet de caractériser les zones aveugles statiques et dynamiques en fonction des imperfections dues aux miroirs. Il est alors possible d'estimer en ligne avec un observateur asymptotique fondé sur les moindre carrés récursifs ces imperfections en rajoutant aux deux mesures en quadrature celles des deux intensités. La connaissance précise de ces imperfections permet alors de les compenser dans la dynamique de la phase relative, et ainsi d'estimer les rotations en zone aveugle. Des simulations numériques détaillées illustrent l'intérêt de ces observateurs pour augmenter la précision des gyroscopes à gaz. / Gaz ring laser gyroscopes provide a high performance technical solution for inertial navigation. However, for very low rotational speeds, the mirrors imperfections of the optical cavity induce a locking phenomena between the phases of the two counter-propagating Laser beams. Hence, the measurements of the phase difference can no longer be used when the speed is within an area around zero, called lock-in zone, or,if a procedure of mechanical dithering is implemented, dithering lock-in zone. Nevertheless, this work shows that it is possible using filtering and estimation methods to measure the speed even within the lock-in zones. To achieve this result, we exploit a physical modeling of the dynamics that we simplify, using singular perturbation techniques, to obtain a generalization of Lamb's equations. There are four non-linear differential equations describing the dynamics of the intensities and phases of the two counter-propagating beams. A qualitative study by regular perturbation theory, exponential stability of the equilibrium points and Poincaré maps allows a characterisation of the lock-in zones according to the mirrors imperfections. It is then possible to estimate online, with an asymptotic observer based on recursive least squares, these imperfections by considering the additional measurements of the beam intensities. Accurate knowledge of these imperfections enables us to compensate them in the dynamic of the relative phase, and thus to estimate rotational speeds within the lock-in zones. Detailed numerical simulations illustrate the interest of those observers to increase the accuracy of gas ring laser gyroscopes.

ABSTRACT IMPLEMENTATION OF NORTHFINDING TECHNIQUES Oguz, Pinar MS, Department of Electrical and Electronics Engineering Supervisor: Assoc. Prof. Dr. T.Engin Tuncer June 2006, 131 pages The fundamental problem of navigation is to find the initial north angle of the body with respect to the reference frame. Determination of the north angle of the body frame is required in spacecraft, aircraft, sea-craft, land-craft and missile control and guidance. This thesis discusses implementation and comparison of four northfinding techniques. These are GPS (Global Positioning System) based with integer search, GPS based with Kalman filter, accelerometer based and IMU (Inertial Measurement Unit) based techniques. The north angle is determined by the processing of difference measurements of the GPS carrier phase between two antennas at GPS based northfinding techniques. Carrier phase ambiguity resolution is the main problem in GPS based techniques. Since, GPS receiver measures only the fractional part of the carrier phase. Therefore, integer part remains unknown. Two distinct ideas are applied to solve carrier phase ambiguities in two techniques. One of them is integer search on single phase difference. Suitable integer sets are checked on the cost function which is constructed from the single phase difference between two antennas. The other technique uses integer estimator and attitude estimator with Kalman filter rely on double difference phase measurements which are obtained from carrier phase differences of two antennas and two satellites at one instant. To test the GPS based techniques, a realistic GPS emulator is implemented. GPS emulator provides typical GPS raw navigation data including satellite positions, pseudoranges and carrier phases. Accelerometer based northfinding technique is composed of a vertically placed linear accelerometer on a rotating platform. The north angle is found by Coriolis acceleration due to Earth and platform rotation. Implementation problems of this technique in practice are discussed. IMU based northfinding technique has inertial sensor components such as gyroscopes and accelerometers to sense the Earth rotation rate and gravitational force respectively. The north angle is found by the processing of these inertial sensors output. Real set-up is established to test the IMU based technique.

This diploma thesis deals with theoretical analysis, design and practical solution of flight statements electronic sensor. This device is primarily intended for measuring telemetry data during aerobatic flights. Theoretical part contains fundamentals of GPS and inertial navigation systems. Design of the device is divided into three parts - design of block structure, construction and software for the measuring device. The final realization is made with respect to minimal system requirements and to possible future extensibility for wider usage spectrum.

This master thesis deals with measurement and modeling of MEMS inertial sensors. This paper describes basic principles of inertial sensors along with their most often errors. The next part shows results from inertial sensor market analysis, which enabling a selection of sensors to be measured. The following two chapters present methods for inertial sensor modeling and testing. The biggest part of text is dedicated to presentation of measurement results showing us static measurement of Allan variance, Earth rotation, temperature dependent bias and dynamic measurement of gyroscope sensitivity testing over temperature. In the last part of the thesis is presented a design of sensor error model by autocorrelation function and Allan variance and also an evaluation of achieved results.

Distance and the associated parameters can be measured by specific sensors mobile device. Introduction The work focuses on the description of the sensors and the effects on their accuracy. To measure the distance, there is a number of good practices, which were described and demonstrated the application implemented source code for the Android platform. The project works with a total of three sensors, namely accelerometer, magnetometer and camera. The main objective of this work is the definition and application of methods for measuring distance using the appropriate sensors.

This document deals with issues of testing semiconductor inertial sensors like gyroscopes and accelerometers, but also other sensors like magnetometers, inclinometers and others for aviation navigation purposes where strict requirements cover every system. The goal of this thesis is to create modular test platform for testing wide variety of sensors in different combinations under variable circumstances. The development covers mechanical design, electrical design – hardware and also control algorithm – software.