Fusion of Data from Quadcopter���s Inertial Measurement Unit Using Complementary Filter

A quadcopter is a helicopter with four rotors, which is mechanically simple device, but requires complex electrical control for each motor. Control system needs accurate information about quadcopter���s attitude in order to achieve stable flight. The goal of this bachelor���s thesis was to research how this information could be obtained. Literature review revealed that most of the quadcopters, whose source-code is available, use a complementary filter or some derivative of it to fuse data from a gyroscope, an accelerometer and often also a magnetometer. These sensors combined are called an Inertial Measurement Unit. This thesis focuses on calculating angles from each sensor���s data and fusing these with a complementary filter. On the basis of literature review and measurements using a quadcopter, the proposed filter provides sufficiently accurate attitude data for flight control system. However, a simple complementary filter has one significant drawback ��� it works reliably only when the quadcopter is hovering or moving at a constant speed. The reason is that an accelerometer can���t be used to measure angles accurately if linear acceleration is present. This problem can be fixed using some derivative of a complementary filter like an adaptive complementary filter or a Kalman filter, which are not covered in this thesis.

Rigid body dynamics and Kalman filtering

X-ray computed log tomography has always been applied for qualitative reconstructions. In most cases, a series of consecutive slices of the timber are scanned to estimate the 3D image reconstruction of the entire log. However, the unexpected movement of the timber under study influences the quality of image reconstruction since the position and orientation of some scanned slices can be incorrectly estimated. In addition, the reconstruction time remains a significant challenge for practical applications. The present study investigates the possibility to employ modern physics engines for the problem of estimating the position of a moving rigid body and its scanned slices which are subject to X-ray computed tomography. The current work includes implementations of the extended Kalman filter and an algebraic reconstruction method for fan-bean computer tomography. In addition, modern techniques such as NVidia PhysX and CUDA are used in current study. As the result, it is numerically shown that it is possible to apply the extended Kalman filter together with a real-time physics engine, known as PhysX, in order to determine the position of a moving object. It is shown that the position of the rigid body can be determined based only on reconstructions of its slices. However, the simulation of the body movement sometimes is subject to an error during Kalman filter employment as PhysX is not always able to continue simulating the movement properly because of incorrect state estimation.

Estimation of State Space Models and Stochastic Volatility

Ma th��se est compos��e de trois chapitres reli��s �� l'estimation des mod��les espace-��tat et volatilit�� stochastique. Dans le premi��re article, nous d��veloppons une proc��dure de lissage de l'��tat, avec efficacit�� computationnelle, dans un mod��le espace-��tat lin��aire et gaussien. Nous montrons comment exploiter la structure particuli��re des mod��les espace-��tat pour tirer les ��tats latents efficacement. Nous analysons l'efficacit�� computationnelle des m��thodes bas��es sur le filtre de Kalman, l'algorithme facteur de Cholesky et notre nouvelle m��thode utilisant le compte d'op��rations et d'exp��riences de calcul. Nous montrons que pour de nombreux cas importants, notre m��thode est plus efficace. Les gains sont particuli��rement grands pour les cas o�� la dimension des variables observ��es est grande ou dans les cas o�� il faut faire des tirages r��p��t��s des ��tats pour les m��mes valeurs de param��tres. Comme application, on consid��re un mod��le multivari�� de Poisson avec le temps des intensit��s variables, lequel est utilis�� pour analyser le compte de donn��es des transactions sur les march��s financi��res. Dans le deuxi��me chapitre, nous proposons une nouvelle technique pour analyser des mod��les multivari��s �� volatilit�� stochastique. La m��thode propos��e est bas��e sur le tirage efficace de la volatilit�� de son densit�� conditionnelle sachant les param��tres et les donn��es. Notre m��thodologie s'applique aux mod��les avec plusieurs types de d��pendance dans la coupe transversale. Nous pouvons modeler des matrices de corr��lation conditionnelles variant dans le temps en incorporant des facteurs dans l'��quation de rendements, o�� les facteurs sont des processus de volatilit�� stochastique ind��pendants. Nous pouvons incorporer des copules pour permettre la d��pendance conditionnelle des rendements sachant la volatilit��, permettant avoir diff��rent lois marginaux de Student avec des degr��s de libert�� sp��cifiques pour capturer l'h��t��rog��n��it�� des rendements. On tire la volatilit�� comme un bloc dans la dimension du temps et un �� la fois dans la dimension de la coupe transversale. Nous appliquons la m��thode introduite par McCausland (2012) pour obtenir une bonne approximation de la distribution conditionnelle �� posteriori de la volatilit�� d'un rendement sachant les volatilit��s d'autres rendements, les param��tres et les corr��lations dynamiques. Le mod��le est ��valu�� en utilisant des donn��es r��elles pour dix taux de change. Nous rapportons des r��sultats pour des mod��les univari��s de volatilit�� stochastique et deux mod��les multivari��s. Dans le troisi��me chapitre, nous ��valuons l'information contribu��e par des variations de volatilite r��alis��e �� l'��valuation et pr��vision de la volatilit�� quand des prix sont mesur��s avec et sans erreur. Nous utilisons de mod��les de volatilit�� stochastique. Nous consid��rons le point de vue d'un investisseur pour qui la volatilit�� est une variable latent inconnu et la volatilit�� r��alis��e est une quantit�� d'��chantillon qui contient des informations sur lui. Nous employons des m��thodes bay��siennes de Monte Carlo par cha��ne de Markov pour estimer les mod��les, qui permettent la formulation, non seulement des densit��s a posteriori de la volatilit��, mais aussi les densit��s pr��dictives de la volatilit�� future. Nous comparons les pr��visions de volatilit�� et les taux de succ��s des pr��visions qui emploient et n'emploient pas l'information contenue dans la volatilit�� r��alis��e. Cette approche se distingue de celles existantes dans la litt��rature empirique en ce sens que ces derni��res se limitent le plus souvent �� documenter la capacit�� de la volatilit�� r��alis��e �� se pr��voir �� elle-m��me. Nous pr��sentons des applications empiriques en utilisant les rendements journaliers des indices et de taux de change. Les diff��rents mod��les concurrents sont appliqu��s �� la seconde moiti�� de 2008, une p��riode marquante dans la r��cente crise financi��re.

D��veloppement et validation d'un mod��le de simulation num��rique personnalis�� �� une athl��te de plongeon

Les entra��neurs en sports acrobatiques disposent de peu d���outils permettant d���am��liorer leur compr��hension des saltos vrill��s et la performance des athl��tes. L���objectif de ce m��moire ��tait de d��velopper un environnement graphique de simulation num��rique r��aliste et utile des acrobaties a��riennes. Un mod��le compos�� de 17 segments et de 42 degr��s de libert�� a ��t�� d��velopp�� et personnalis�� �� une athl��te de plongeon. Un syst��me opto��lectronique ��chantillonn�� �� 300 Hz a permis l���acquisition de huit plongeons en situation r��elle d���entra��nement. La cin��matique articulaire reconstruite avec un filtre de Kalman ��tendu a ��t�� utilis��e comme entr��e du mod��le. Des erreurs quadratiques moyennes de 20�� (salto) et de 9�� (vrille) entre les performances simul��es et r��elles ont permis de valider le mod��le. Enfin, une formation bas��e sur le simulateur a ��t�� offerte �� 14 entra��neurs en sports acrobatiques. Une augmentation moyenne de 11 % des r��sultats aux questionnaires post-test a permis de constater le potentiel p��dagogique de l���outil pour la formation.

Augmented state Kalman filtering for AUV navigation

Addresses the problem of estimating the motion of an autonomous underwater vehicle (AUV), while it constructs a visual map ("mosaic" image) of the ocean floor. The vehicle is equipped with a down-looking camera which is used to compute its motion with respect to the seafloor. As the mosaic increases in size, a systematic bias is introduced in the alignment of the images which form the mosaic. Therefore, this accumulative error produces a drift in the estimation of the position of the vehicle. When the arbitrary trajectory of the AUV crosses over itself, it is possible to reduce this propagation of image alignment errors within the mosaic. A Kalman filter with augmented state is proposed to optimally estimate both the visual map and the vehicle position

Data assimilation for marine monitoring and prediction: The MERCATOR operational assimilation systems and the MERSEA developments

During the past 15 years, a number of initiatives have been undertaken at national level to develop ocean forecasting systems operating at regional and/or global scales. The co-ordination between these efforts has been organized internationally through the Global Ocean Data Assimilation Experiment (GODAE). The French MERCATOR project is one of the leading participants in GODAE. The MERCATOR systems routinely assimilate a variety of observations such as multi-satellite altimeter data, sea-surface temperature and in situ temperature and salinity profiles, focusing on high-resolution scales of the ocean dynamics. The assimilation strategy in MERCATOR is based on a hierarchy of methods of increasing sophistication including optimal interpolation, Kalman filtering and variational methods, which are progressively deployed through the Syst`eme d���Assimilation MERCATOR (SAM) series. SAM-1 is based on a reduced-order optimal interpolation which can be operated using ���altimetry-only��� or ���multi-data��� set-ups; it relies on the concept of separability, assuming that the correlations can be separated into a product of horizontal and vertical contributions. The second release, SAM-2, is being developed to include new features from the singular evolutive extended Kalman (SEEK) filter, such as three-dimensional, multivariate error modes and adaptivity schemes. The third one, SAM-3, considers variational methods such as the incremental four-dimensional variational algorithm. Most operational forecasting systems evaluated during GODAE are based on least-squares statistical estimation assuming Gaussian errors. In the framework of the EU MERSEA (Marine EnviRonment and Security for the European Area) project, research is being conducted to prepare the next-generation operational ocean monitoring and forecasting systems. The research effort will explore nonlinear assimilation formulations to overcome limitations of the current systems. This paper provides an overview of the developments conducted in MERSEA with the SEEK filter, the Ensemble Kalman filter and the sequential importance re-sampling filter.

Estimating discharge from inundation imagery

Remote sensing from space-borne platforms is often seen as an appealing method of monitoring components of the hydrological cycle, including river discharge, due to its spatial coverage. However, data from these platforms is often less than ideal because the geophysical properties of interest are rarely measured directly and the measurements that are taken can be subject to significant errors. This study assimilated water levels derived from a TerraSAR-X synthetic aperture radar image and digital aerial photography with simulations from a two dimensional hydraulic model to estimate discharge, inundation extent, depths and velocities at the confluence of the rivers Severn and Avon, UK. An ensemble Kalman filter was used to assimilate spot heights water levels derived by intersecting shorelines from the imagery with a digital elevation model. Discharge was estimated from the ensemble of simulations using state augmentation and then compared with gauge data. Assimilating the real data reduced the error between analyzed mean water levels and levels from three gauging stations to less than 0.3 m, which is less than typically found in post event water marks data from the field at these scales. Measurement bias was evident, but the method still provided a means of improving estimates of discharge for high flows where gauge data are unavailable or of poor quality. Posterior estimates of discharge had standard deviations between 63.3 m3s-1 and 52.7 m3s-1, which were below 15% of the gauged flows along the reach. Therefore, assuming a roughness uncertainty of 0.03-0.05 and no model structural errors discharge could be estimated by the EnKF with accuracy similar to that arguably expected from gauging stations during flood events. Quality control prior to assimilation, where measurements were rejected for being in areas of high topographic slope or close to tall vegetation and trees, was found to be essential. The study demonstrates the potential, but also the significant limitations of currently available imagery to reduce discharge uncertainty in un-gauged or poorly gauged basins when combined with model simulations in a data assimilation framework.

Extended Kalman filtering for robotic proximity sensing

The authors address the problems in using a fiber-optic proximity sensor to detect robot end-effector positioning errors in performing a contact task when uncertainties about target position exist. An extended Kalman filter approach is employed to solve the nonlinear filtering problem. Some experimental results are given.

A Gaussian-mixture ensemble transform filter

We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions. Copyright �� 2011 Royal Meteorological Society

A novel ensemble method for retrieving properties of warm cloud in 3-D using ground-based scanning radar and zenith radiances

We present a novel method for retrieving high-resolution, three-dimensional (3-D) nonprecipitating cloud fields in both overcast and broken-cloud situations. The method uses scanning cloud radar and multiwavelength zenith radiances to obtain gridded 3-D liquid water content (LWC) and effective radius (re) and 2-D column mean droplet number concentration (Nd). By using an adaption of the ensemble Kalman filter, radiances are used to constrain the optical properties of the clouds using a forward model that employs full 3-D radiative transfer while also providing full error statistics given the uncertainty in the observations. To evaluate the new method, we first perform retrievals using synthetic measurements from a challenging cumulus cloud field produced by a large-eddy simulation snapshot. Uncertainty due to measurement error in overhead clouds is estimated at 20% in LWC and 6% in re, but the true error can be greater due to uncertainties in the assumed droplet size distribution and radiative transfer. Over the entire domain, LWC and re are retrieved with average error 0.05���0.08 g m-3 and ~2 ��m, respectively, depending on the number of radiance channels used. The method is then evaluated using real data from the Atmospheric Radiation Measurement program Mobile Facility at the Azores. Two case studies are considered, one stratocumulus and one cumulus. Where available, the liquid water path retrieved directly above the observation site was found to be in good agreement with independent values obtained from microwave radiometer measurements, with an error of 20 g m-2.

An Ensemble Kalman Smoother for Nonlinear Dynamics

It is for mally proved that the general smoother for nonlinear dynamics can be for mulated as a sequential method, that is, obser vations can be assimilated sequentially during a for ward integration. The general filter can be derived from the smoother and it is shown that the general smoother and filter solutions at the final time become identical, as is expected from linear theor y. Then, a new smoother algorithm based on ensemble statistics is presented and examined in an example with the Lorenz equations. The new smoother can be computed as a sequential algorithm using only for ward-in-time model integrations. It bears a strong resemblance with the ensemble Kalman filter . The difference is that ever y time a new dataset is available during the for ward integration, an analysis is computed for all previous times up to this time. Thus, the first guess for the smoother is the ensemble Kalman filter solution, and the smoother estimate provides an improvement of this, as one would expect a smoother to do. The method is demonstrated in this paper in an intercomparison with the ensemble Kalman filter and the ensemble smoother introduced by van Leeuwen and Evensen, and it is shown to be superior in an application with the Lorenz equations. Finally , a discussion is given regarding the properties of the analysis schemes when strongly non-Gaussian distributions are used. It is shown that in these cases more sophisticated analysis schemes based on Bayesian statistics must be used.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

Aplicando estrat��gias simult��neas de momento e valor no mercado brasileiro

A teoria de Finan��as Comportamentais surge como uma nova abordagem ao mercado financeiro, argumentando que alguns eventos podem ser mais bem explicados se as restri����es da racionalidade do investidor s��o relaxadas. Conceitos de psicologia e limites �� arbitragem s��o usados para modelar as inefici��ncias, criando a id��ia de ser poss��vel ganhar sistematicamente do mercado. Este trabalho prop��e um novo modelo, simplista na sua implementa����o, para aproveitar os retornos anormais advindos de estrat��gias de momentum e revers��o �� m��dia simultaneamente. A id��ia de um efeito momentum de longo prazo mais forte que o de curto prazo �� introduzida, mas os resultados emp��ricos mostram que a din��mica do mercado brasileiro rejeita este conceito. O modelo falha em conseguir retornos positivos e livres de risco.

Essays on regulatory risk issues

Most studies around that try to verify the existence of regulatory risk look mainly at developed countries. Looking at regulatory risk in emerging market regulated sectors is no less important to improving and increasing investment in those markets. This thesis comprises three papers comprising regulatory risk issues. In the first Paper I check whether CAPM betas capture information on regulatory risk by using a two-step procedure. In the first step I run Kalman Filter estimates and then use these estimated betas as inputs in a Random-Effect panel data model. I find evidence of regulatory risk in electricity, telecommunications and all regulated sectors in Brazil. I find further evidence that regulatory changes in the country either do not reduce or even increase the betas of the regulated sectors, going in the opposite direction to the buffering hypothesis as proposed by Peltzman (1976). In the second Paper I check whether CAPM alphas say something about regulatory risk. I investigate a methodology similar to those used by some regulatory agencies around the world like the Brazilian Electricity Regulatory Agency (ANEEL) that incorporates a specific component of regulatory risk in setting tariffs for regulated sectors. I find using SUR estimates negative and significant alphas for all regulated sectors especially the electricity and telecommunications sectors. This runs in the face of theory that predicts alphas that are not statistically different from zero. I suspect that the significant alphas are related to misspecifications in the traditional CAPM that fail to capture true regulatory risk factors. On of the reasons is that CAPM does not consider factors that are proven to have significant effects on asset pricing, such as Fama and French size (ME) and price-to-book value (ME/BE). In the third Paper, I use two additional factors as controls in the estimation of alphas, and the results are similar. Nevertheless, I find evidence that the negative alphas may be the result of the regulated sectors premiums associated with the three Fama and French factors, particularly the market risk premium. When taken together, ME and ME/BE regulated sectors diminish the statistical significance of market factors premiums, especially for the electricity sector. This show how important is the inclusion of these factors, which unfortunately is scarce in emerging markets like Brazil.

Efeitos da baixa liquidez em posi����es compradas em rela����o ��s posi����es vendidas sobre o desempenho de fundos long short em situa����o de crise sist��mica (2008)

Diversos estudos sobre investimentos em A����es e Fundos de Investimentos no Brasil, mais especificamente sobre Fundos Multimercados Long-Short, focam em sua neutralidade em rela����o ao Ibovespa bem como na performance de seus gestores e de suas respectivas estrat��gias, como Penna (2007) e Gomes e Cresto (2010). Com ��nfase na compara����o entre a liquidez da posi����o comprada e a da posi����o vendida em a����es, foi verificado o comportamento de fundos long-short em situa����es normais e de crise, do per��odo que vai de 2007 a 2009. Foram encontrados fortes ind��cios de que houve perda maior em momentos de estresse por parte de fundos que carregavam a����es menos l��quidas em suas carteiras na posi����o comprada em rela����o a posi����o vendida, apesar do n��mero reduzido de fundos estudados e tamb��m de ter sido utilizado periodicidade mensal. Encontrou-se um retorno m��dio em 2008 de 11,1% para uma carteira formada por fundos com a����es mais l��quidas na posi����o comprada do que na posi����o vendida e 5,4% para uma carteira com posi����o inversa. Uma an��lise de risco-retorno feita com o ��ndice de Sharpe (IS) corrobora o estudo, pois a carteira composta por fundos com posi����o mais l��quida na posi����o vendida apresentou IS de -1,5368, bem inferior ao IS de -0,3374 da carteira de posi����o inversa (mais l��quida na posi����o comprada). Foi tamb��m utilizado o Modelo ��ndice, como em Bodie, Kane e Marcus (2005), para verificar se esses fundos, separados em carteiras divididas entre mais l��quidos na posi����o comprada do que na posi����o vendida e vice-versa, tinham desempenho melhor que o mercado (IBOVESPA) de maneira sistem��tica (alpha=��) e a exposi����o dessas carteiras ao risco de mercado (Beta = ��), al��m do Modelo de Fatores. As regress��es realizadas para os modelos citados encontram coeficientes e respectivas infer��ncias estat��sticas que respaldam a hip��tese acima, apesar de baixo n��mero de observa����es utilizado.