This paper deals with the application of SLAM algorithms on experimental four wheel vehicle Car4. The first part shows the basic functioning of SLAM including a description of the extended Kalman filter, which is one of its main components. Then there is a brief list of software tools available to solve this problem in the environment of MATLAB and an overview of sensors used in this work. The second part presents methodology and results of the testing of individual sensors and their combinations to calculate odometry and scan the surrounding space. It also shows the process of applying SLAM algorithms on Car4 vehicle using the selected sensors and the results of testing of the entire system in practice.

Aktive Magnetlager ermöglichen berührungsfreies Lagern und begrenztes Bewegen von Rotoren. Die für einen stabilen Betrieb notwendige Lageregelung erfordert genaue und schnelle Messsysteme. Die bisher verwendeten Messsysteme erfordern zusätzlichen Bauraum. In dieser Arbeit wird ein integriertes, kapazitives Messsystem für Radiallager vorgestellt, durch das die axiale Baulänge des Rotors reduziert und Dislokationseffekte vermieden werden können. Es wurde dadurch eine höhere Regelungsdynamik erreicht. Außerdem wurde ein erweitertes Kalman-Filter mit nichtlinearer Kraftberechnung implementiert, um die Lageregelung mit verrauschten Messsignalen stabil betreiben zu können. Die Verbesserung der Lageregelung durch das integrierte Messsystem und das Kalman-Filter werden anhand von Versuchsergebnissen verdeutlicht.

Die Dissertation beschreibt Verfahren zur Fusion von Sensordaten am Beispiel eines PreCrash-Systems für Kraftfahrzeuge. Ein PreCrash-System erkennt mit Hilfe von Sensoren, die das Fahrzeugumfeld überwachen, (unvermeidliche) Unfälle wenige hundert Millisekunden vor Beginn des Zusammenstoßes und stellt verschiedene Informationen zur Verfügung, die bei der Aktivierung von Sicherheitseinrichtungen wie Gurtstraffer oder Airbags hilfreich sind. Neben guten Erkennungsleistungen spielt bei einem solchen System vor allem die Eignung für den Einsatz im automobilen Umfeld mit all seinen Anforderungen eine große Rolle. Dies bedeutet zum Beispiel Robustheit gegenüber schwierigen Wetterbedingungen, geringe Anforderungen an die Rechenleistung und auch die Erkennung eines Sensorausfalls. Ebenso stellt die Vielfalt möglicher Objekte mit ihren unterschiedlichen Reflexionseigenschaften und teilweise sehr hohen Relativgeschwindigkeiten eine besondere Herausforderung für ein umfelderkennendes System dar. Nach einführenden Betrachtungen zum Stand der Technik und der Zielstellung, unterschiedliche Sensorik zur Verbesserung der Detektionsleistungen und damit der Robustheit des Gesamtsystems zu fusionieren, beinhaltet die Arbeit eine Beschreibung der Funktionalität "PreCrash", Angaben zu Voraussetzungen und speziellen Umgebungsbedingungen im Fahrzeugbereich, die Einfluss auf die Verfahrensauswahl ausüben und eine Beschreibung der verwendeten Sensorik. Signalverarbeitungsverfahren zur Realisierung eines PreCrash-Systems sind sowohl auf Basis eines Einzelsensorsystems als auch auf Grundlage eines Multisensorsystems ausführlich dokumentiert. Ansätze zur Sensordatenfusion werden gesondert dargestellt und auch Nebenaspekte wie die Erkennung von Sensorausfällen berücksichtigt. Die Arbeit enthält Ergebnisse, die die Erkennungsleistungen mehrerer implementierter Verfahren aufzeigen und die auf realen, mit Hilfe eines Versuchsfahrzeuges aufgenommener Daten basieren.

Title: Ensemble Kalman filter on high and infinite dimensional spaces Author: Mgr. Ivan Kasanický Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Daniel Hlubinka, Ph.D., Department of Probability and Mathematical Statistics Consultant: prof. RNDr. Jan Mandel, CSc., Department of Mathematical and Statistical Sciences, University of Colorado Denver Abstract: The ensemble Kalman filter (EnKF) is a recursive filter, which is used in a data assimilation to produce sequential estimates of states of a hidden dynamical system. The evolution of the system is usually governed by a set of di↵erential equations, so one concrete state of the system is, in fact, an element of an infinite dimensional space. In the presented thesis we show that the EnKF is well defined on a infinite dimensional separable Hilbert space if a data noise is a weak random variable with a covariance bounded from below. We also show that this condition is su cient for the 3DVAR and the Bayesian filtering to be well posed. Additionally, we extend the already known fact that the EnKF converges to the Kalman filter in a finite dimension, and prove that a similar statement holds even in a infinite dimension. The EnKF su↵ers from a low rank approximation of a state covariance, so a covariance localization is required in...

This master thesis studied methods for tracking and localising a moving target from an autonomous seeker drone. Feasible methods for automatic control of the seeker drone and different antenna configurations were explored as well. Two different tracking filters and two different controllers were tested for this purpose. The algorithm was developed in Python and MATLAB. The evaluation of the filters and controllers was done both theoretically with simulations but also practically with flight tests. Performance and robustness were measured by examining the estimated target position and the smoothness of the seeker path. Both filters performed satisfactorily, the same conclusion could be made for the automatic controllers as well. Regardless of the sufficient results, for future work there are several aspects which can be improved. The communication with the drone’s motors, the noise models and one of the automatic controllers are all examples of areas which canbe improved further.

With the growing popularity of business analytics, companies experience an increasing need of reliable data. Although the availability of behavioural data showing what the consumers do has increased, the access to data showing consumer mentality, what the con- sumers actually think, remain heavily dependent on tracking surveys. This thesis inves- tigates the performance of a Dynamic Factor Model using respondent-level data gathered through repeated cross-sectional surveys. Through Monte Carlo simulations, the model was shown to improve the accuracy of brand tracking estimates by double digit percent- ages, or equivalently reducing the required amount of data by more than a factor 2, while maintaining the same level of accuracy. Furthermore, the study showed clear indications that even greater performance benefits are possible.

No description available.

The Global Positioning System (GPS) and an Inertial Navigation System (INS)are two basic navigation systems. Due to their complementary characters in manyaspects, a GPS/INS integrated navigation system has been a hot research topic inthe recent decade. Both advantages and disadvantages of each individual systemare analyzed. The Micro Electrical Mechanical Sensors (MEMS) successfully solved theproblems of price, size and weight with the traditional INS. Therefore they arecommonly applied in GPS/INS integrated systems. The biggest problem ofMEMS is the large sensor errors, which rapidly degrade the navigationperformance in an exponential speed. By means of different methods, i.e.autoregressive model, Gauss-Markov process, Power Spectral Density and AllanVariance, we analyze the stochastic errors within the MEMS sensors. Real testson a MEMS based inertial measurement unit for each method are carried out. Theresults show that different methods give similar estimates of stochastic errorsources. These error coefficients can be used further in the Kalman filter for betternavigation performance and in the Doppler frequency estimate for fasteracquisition after the GPS signal outage. Three levels of GPS/IMU integration structures, i.e. loose, tight and ultra tightGPS/IMU navigation, are introduced with a brief analysis of each character. Theloose integration principles are given with detailed equations as well as the basicINS navigation principles. The Extended Kalman Filter (EKF) is introduced as the basic data fusionalgorithm, which is also the core of the whole navigation system to be presented.The kinematic constraints of land vehicle navigation, i.e. velocity constraint andheight constraint, are presented. These physical constraints can be used asadditional information to further reduce the navigation errors. The theoreticalanalysis of the Kalman filter with constraints are given to show the improvementon the navigation performance. As for the outliers in practical applications, theequivalent weight is introduced to adaptively reduce the influence on positioningaccuracy. A detailed implementation process of the GPS/IMU integration system is given.Based on the system model, we show the propagation of position standard errorswith the tight integration structure under different scenarios. Even less than 4observable satellites can contribute to the integrated system. Especially 2 satellitescan maintain the orientation errors at a reasonable level due to the benefit of thetight integration. A real test with loose integration structure is carried out, and theEKF performance as well as the physical constraints are analyzed in detail. Also atest with random outliers at the resolution level is carried out to show theeffectiveness of the equivalent weight. Finally some suggestions on future researchare proposed. / <p>QC 20111006</p>

The project explores the possibilities on how to improve the accuracy of GPS velocity data by using sensor fusion with an extended Kalman filter. The proposed solution in this project is a sensor fusion between the GPS and IMU of the system, where the extended Kalman filter was used to estimate the velocity from the sensor data. The hardware used for the data acquisition to the proposed solution was a Pixhawk 4 (PX4), which has an IMU consisting of accelerometers, gyroscopes and magnetometers. The PX4:s corresponding GPS module was also used to collect accurate velocity data. The data was logged using Simulink and later processed with MATLAB. The sensor fusion using the extended Kalman filter gave good estimates upon constant acceleration but had problems with estimating over varying acceleration. This was initially planned to be solved using smoothing filters, which is an essential part of the fusion process, but was never implemented due to time constraints. The constructed filter acts as a foundation towards future improvement. Other methods such as unscented Kalman filter, particle filter and neural network could also be explored to improve the estimation of the velocity due to these filters being known to have better performance. However, most of these alternatives need more computing power and are generally harder to implement compared to the extended Kalman filter. This project would be beneficial to QTAGG, since increasing the velocity resolution and accuracy of the system can provide possibilities of better optimization. It is also a commonly implemented solution where there are many state of the art implementations available.

[pt] A evolução dos conhecimentos em Finanças nas últimas três décadas foi rápido e vertiginoso. Hoje os mercados financeiros oferecem produtos sofisticados para investidores e empresas, e por outro lado, tais agentes demandam instrumentos confiáveis para atender suas necessidades em busca de maiores retornos e menores riscos. Todo esse desenvolvimento baseia-se fundamentalmente em metodologias de apreçamento de ativos. Grande parte deste conhecimento é oriundo dos trabalhos pioneiros de Black e Scholes (1973) e Merton (1973). Em síntese, estes trabalhos apoiaram-se em processos estocásticos para preços de ativos para apreçar um derivativo. A natureza do processo estocástico de evolução dos preços é o ponto central para a derivação dos modelos de apreçamento. A análise do comportamento dos preços das commodities possui duas grandes vertentes na literatura. A primeira trata os preços como decorrência de modelos de equilíbrio entre a oferta e a demanda. Estes modelos prosperaram pouco em termos de pesquisa. A outra vertente trata da análise da evolução dos preços baseando-se na série histórica propriamente dita. Esta linha de pesquisa está mais presente na literatura. Esta tese concentra-se nesta abordagem. As commodities possuem características particulares principalmente porque a formação de preços ocorre, via de regra, em mercados futuros. Isto faz com que muitos fatos estilizados não possam ser descritos por modelos de um fator (ou uma variável estocástica). Os fatores (variáveis estocásticas) ou variáveis de estado em muitas situações não são observáveis e necessitam ser estimados. Os modelos de preços futuros, escritos como função das variáveis de estado, recebe o nome de equação de observação. Quando as variáveis de estado são Gaussianas e a equação de observação é linear nos estados, o problema pode ser estimado pelo filtro de Kalman clássico. Se ocorrer a não linearidade, esta dificuldade pode ser contornada pelo filtro de Kalman estendido. Quando o problema é não Gaussiano a literatura usa outras metodologias (freqüentemente aproximações) que não o filtro de Kalman. Esta tese trata de processos estocásticos para preços de commodities propondo extensões aos modelos existentes na literatura. A derivação dos modelos é feita com o uso da transformada de Duffie e Kan (1996) em ambiente de não arbitragem. Algumas das extensões incluem modelos não Gaussianos. Esta tese investiga a estimação destes modelos pela metodologia denominada filtro de partículas. O filtro de partículas é um procedimento recursivo para integração, dentro da classe dos métodos seqüenciais de MonteCarlo. A proposta de utilização desta metodologia decorre do fato de que ela dispensa as condições de linearidade e Gaussianidade. Dentre as contribuições desta tese destacam-se as extensões dos processos estocásticos aplicáveis para quaisquer commodities e as análises de modelos não Gaussianos através da metodologia do filtro de partículas. Além disso, a pesquisa apresenta: (i) conclusões acerca dos modelos de dois fatores aplicados à série de preços da commodity petróleo; (ii) a análise da viabilidade do filtro de partículas mostrando que o erro obtido é próximo daquele do filtro de Kalman para problemas Gaussianos e a resposta obtida da estimação paramétrica é coerente com diversos trabalhos da literatura; (iii) análise da viabilidade operacional de implementação do filtro de partículas em termos do tempo computacional despendido nos processos de filtragem e estimação paramétrica. A tese conclui que o filtro de partículas, apesar ser computacionalmente intenso, é viável na prática face ao imenso desenvolvimento computacional. Ainda mais, por ser uma metodologia aplicável a problemas complexos de inferência, sua utilização em modelos cada vez mais sofisticados é muito promissora. / [en] The evolution of the ideas in Finance has been huge in the last decades. Nowadays the financial markets offer investors sophisticated products. And investors in turn demand reliable financial instruments to meet their needs in search for greater returns and lower risks. This development is based mainly on asset pricing methodologies. The greatest part of this knowledge comes from the seminal works of Black and Scholes (1973) and Merton (1973). To summarize, their works are based on the assumption of a specific stochastic process that governs asset prices. And then a derivative of this underlying asset can be priced. The nature of the stochastic process that describes the evolution of prices is the key point for deriving pricing formulae. The analysis of the behavior of commodity prices has two approaches. The first approach considers prices as a consequence of the equilibrium between supply and demand. These models have not received enough attention in literature. The second approach, which has received more attention, is based on the analysis of price time series. The commodities have particular features because they are most of the times negotiated in future markets. The consequence is that the one factor models badly describe their stylized facts. The factors (stochastic variables) are known as state variables which most of the times are non observables, and need to be estimated. When state variables are Gaussians and the observation equation is linear in states, the classical Kalman filter can be used to access these variables. If non linearity is present extended Kalman filter is used, but when state variables are non Gaussian the literature does not use filtering processes. This thesis analyses the stochastic processes of commodities proposing extensions to the existing models. The derivation of models is based on Duffie and Kan (1996) transform, in a non arbitrage environment. Some extensions are non Gaussian. This thesis investigates the estimation of these models using particle filter methodology. The particle filter is a recursive procedure for integration in the sequential Monte-Carlo methods. The advantage of this methodology is that it does not require linear or Gaussian conditions. The contributions of this research are the extensions of stochastic processes that can be used for any commodity and the use of particle filter as an estimation methodology in Finance. Furthermore the thesis presents: (i) the conclusions about two factor models applied to oil prices; (ii) the analysis of the use of particle filter verifying that errors in both, Kalman filter and particle filter are close and that parameters estimation is in accordance with the literature; (iii) the analysis of the implementation of particle filter showing that it is viable considering the computational time of filtering and parameters estimation. The thesis concludes that the particle filter is viable, although time consuming, due to the hardware development. And more, since particle filter is useful for complex inference problems, its application to sophisticated models is promising.