On Variational Ensemble Kalman Filtering

The Extended Kalman Filter (EKF) and four dimensional assimilation variational method (4D-VAR) are both advanced data assimilation methods. The EKF is impractical in large scale problems and 4D-VAR needs much effort in building the adjoint model. In this work we have formulated a data assimilation method that will tackle the above difficulties. The method will be later called the Variational Ensemble Kalman Filter (VEnKF). The method has been tested with the Lorenz95 model. Data has been simulated from the solution of the Lorenz95 equation with normally distributed noise. Two experiments have been conducted, first with full observations and the other one with partial observations. In each experiment we assimilate data with three-hour and six-hour time windows. Different ensemble sizes have been tested to examine the method. There is no strong difference between the results shown by the two time windows in either experiment. Experiment I gave similar results for all ensemble sizes tested while in experiment II, higher ensembles produce better results. In experiment I, a small ensemble size was enough to produce nice results while in experiment II the size had to be larger. Computational speed is not as good as we would want. The use of the Limited memory BFGS method instead of the current BFGS method might improve this. The method has proven succesful. Even if, it is unable to match the quality of analyses of EKF, it attains significant skill in forecasts ensuing from the analysis it has produced. It has two advantages over EKF; VEnKF does not require an adjoint model and it can be easily parallelized.

Estudo comparativo sobre filtragem de sinais instrumentais usando transformadas de Fourier e Wavelet

A comparative study of the Fourier (FT) and the wavelet transforms (WT) for instrumental signal denoising is presented. The basic principles of wavelet theory are described in a succinct and simplified manner. For illustration, FT and WT are used to filter UV-VIS and plasma emission spectra using MATLAB software for computation. Results show that FT and WT filters are comparable when the signal does not display sharp peaks (UV-VIS spectra), but the WT yields a better filtering when the filling factor of the signal is small (plasma spectra), since it causes low peak distortion.

Kalman Filtering in Online Paper Quality Assessment

Controlling the quality variables (such as basis weight, moisture etc.) is a vital part of making top quality paper or board. In this thesis, an advanced data assimilation tool is applied to the quality control system (QCS) of a paper or board machine. The functionality of the QCS is based on quality observations that are measured with a traversing scanner making a zigzag path. The basic idea is the following: The measured quality variable has to be separated into its machine direction (MD) and cross direction (CD) variations due to the fact that the QCS works separately in MD and CD. Traditionally this is done simply by assuming one scan of the zigzag path to be the CD profile and its mean value to be one point of the MD trend. In this thesis, a more advanced method is introduced. The fundamental idea is to use the signals’ frequency components to represent the variation in both CD and MD. To be able to get to the frequency domain, the Fourier transform is utilized. The frequency domain, that is, the Fourier components are then used as a state vector in a Kalman filter. The Kalman filter is a widely used data assimilation tool to combine noisy observations with a model. The observations here refer to the quality measurements and the model to the Fourier frequency components. By implementing the two dimensional Fourier transform into the Kalman filter, we get an advanced tool for the separation of CD and MD components in total variation or, to be more general, for data assimilation. A piece of a paper roll is analyzed and this tool is applied to model the dataset. As a result, it is clear that the Kalman filter algorithm is able to reconstruct the main features of the dataset from a zigzag path. Although the results are made with a very short sample of paper roll, it seems that this method has great potential to be used later on as a part of the quality control system.

Evolución de la NAIRU en la economía española: una estimación mediante el filtro de Kalman

La tasa de paro de inflación estable (NAIRU) describe aquella tasa de desempleo que se alcanza en el equilibrio entre las reivindicaciones salariales de los trabajadores y los objetivos de beneficio de las empresas. En este trabajo se desarrolla un enfoque teórico general que permite determinar el nivel de la NAIRU. Esta cuestión adquiere una especial trascendencia teórica y empírica si se tiene en cuenta que esta tasa de paro de equilibrio ha aumentado en la mayoría de países europeos. Sin embargo, esta tasa de paro de equilibrio no puede observarse directamente por lo que se recurre a su estimación econométrica a partir del filtro de Kalman. Para ilustrar la potencialidad del modelo desarrollado y la influencia de la determinadas variables relacionadas con la distribución de las rentas salariales, se analiza cual ha sido la evolución de la NAIRU para la economía española en el periodo 1964-2004.

Eficiência de um hidrociclone de geometria "rietema" para pré-filtragem de água para irrigação

O hidrociclone é um equipamento amplamente utilizado pela indústria em processos envolvendo separação sólido-líquido, porém ainda pouco utilizado na agricultura irrigada no Brasil. Neste trabalho, avaliou-se o desempenho deste equipamento como pré-filtrante de partículas sólidas, oriundas dos processos erosivos e do assoreamento dos recursos hídricos. Os testes foram realizados com um hidrociclone de geometria "Rietema", possuindo diâmetro de 19,2 cm na parte cilíndrica, operando com vazões variando entre 10 m³ h-1 e 27 m³ h-1. Os materiais particulados usados em suspensão foram: solo franco-argiloso e areia de rio. Os resultados mostraram que a perda de carga máxima média foi de 52 kPa e 47 kPa para as suspensões aquosas de areia e solo, respectivamente. Seu melhor desempenho ocorreu operando com suspensão aquosa de areia, apresentando eficiência total de 92,3% para a vazão de 26,9 m³ h-1. Concluiu-se que o equipamento avaliado é mais eficiente para remoção de partículas de areia, podendo ser utilizado como pré-filtro em sistemas de irrigação.

Sistema com aeração, decantação e filtragem para a melhoria da qualidade de água em irrigação localizada

A qualidade da água é muito importante para irrigação por gotejamento, pois ela escoa por pequenos bocais dos emissores, podendo ocorrer obstrução devido à deposição dos sólidos em suspensão. Portanto, antes da instalação do projeto, devem-se avaliar parâmetros de qualidade da água, para adotar medidas preventivas, evitando o risco de entupimento do sistema. Este trabalho teve como objetivo avaliar um sistema composto por aeradores com aspersores, sobre leito de pedra, para a precipitação dos íons Fe+2e Mn+2 em tanque de decantação, e um conjunto de filtragem composto por três filtros de areia e um de disco, em sistema de irrigação localizada. O trabalho foi realizado na Fazenda Alvorada, no município de Nova Granada - SP, no período de março a outubro de 2008. Foram realizadas determinações de variáveis físicas e químicas da água, ao longo do sistema de aeração, decantação e filtragem, o qual foi eficiente para a melhoria da qualidade de água, reduzindo os níveis de risco de entupimento de severo para médio e de médio para baixo. Oxigênio dissolvido, condutividade elétrica, pH, Fe+2e Fe+3 não diferenciaram a qualidade de água entre os pontos do sistema de tratamento, porém a turbidez, sólidos dissolvidos, sólidos em suspensão, ferro total e manganês total reduziram-se significativamente pelo uso do sistema proposto, melhorando a qualidade da água.

Estimation of aircraft aerodynamic derivatives using Extended Kalman Filter

Design of flight control laws, verification of performance predictions, and the implementation of flight simulations are tasks that require a mathematical model of the aircraft dynamics. The dynamical models are characterized by coefficients (aerodynamic derivatives) whose values must be determined from flight tests. This work outlines the use of the Extended Kalman Filter (EKF) in obtaining the aerodynamic derivatives of an aircraft. The EKF shows several advantages over the more traditional least-square method (LS). Among these the most important are: there are no restrictions on linearity or in the form which the parameters appears in the mathematical model describing the system, and it is not required that these parameters be time invariant. The EKF uses the statistical properties of the process and the observation noise, to produce estimates based on the mean square error of the estimates themselves. Differently, the LS minimizes a cost function based on the plant output behavior. Results for the estimation of some longitudinal aerodynamic derivatives from simulated data are presented.

Kalman filter for computational market dynamics

Kalman filter is a recursive mathematical power tool that plays an increasingly vital role in innumerable fields of study. The filter has been put to service in a multitude of studies involving both time series modelling and financial time series modelling. Modelling time series data in Computational Market Dynamics (CMD) can be accomplished using the Jablonska-Capasso-Morale (JCM) model. Maximum likelihood approach has always been utilised to estimate the parameters of the JCM model. The purpose of this study is to discover if the Kalman filter can be effectively utilized in CMD. Ensemble Kalman filter (EnKF), with 50 ensemble members, applied to US sugar prices spanning the period of January, 1960 to February, 2012 was employed for this work. The real data and Kalman filter trajectories showed no significant discrepancies, hence indicating satisfactory performance of the technique. Since only US sugar prices were utilized, it would be interesting to discover the nature of results if other data sets are employed.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Variational Ensemble Kalman Filtering in Hydrology

The current thesis manuscript studies the suitability of a recent data assimilation method, the Variational Ensemble Kalman Filter (VEnKF), to real-life fluid dynamic problems in hydrology. VEnKF combines a variational formulation of the data assimilation problem based on minimizing an energy functional with an Ensemble Kalman filter approximation to the Hessian matrix that also serves as an approximation to the inverse of the error covariance matrix. One of the significant features of VEnKF is the very frequent re-sampling of the ensemble: resampling is done at every observation step. This unusual feature is further exacerbated by observation interpolation that is seen beneficial for numerical stability. In this case the ensemble is resampled every time step of the numerical model. VEnKF is implemented in several configurations to data from a real laboratory-scale dam break problem modelled with the shallow water equations. It is also tried in a two-layer Quasi- Geostrophic atmospheric flow problem. In both cases VEnKF proves to be an efficient and accurate data assimilation method that renders the analysis more realistic than the numerical model alone. It also proves to be robust against filter instability by its adaptive nature.

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.

Algoritmos de filtrado de Kalman para estados de sistemas estocásticos sobre observaciones discretas y continuas

Tesis (Maestro en Ciencias de la Ingeniería Eléctrica con Especialidad en Control) - Universidad Autónoma de Nuevo León, 1999

Instantaneous us estimation of oscillating phasors with Taylor ? - Kalman-Fourier filters.

Tesis (Doctor en Ingeniería Eléctrica) UANL, 2011.

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