On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

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.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Automatic absolute orientation of scanned aerial photographs

Image orientation is a basic problem in Digital Photogrammetry. While interior and relative orientations were succesfully automated, the same can not be said about absolute orientation. This process can be automated by using an approach based on relational matching and a heuristic that uses the analytical relation between straight features in the object space and its homologous in the image space. A build-in self-diagnosis is also used in this method, that is based on the implementation of data snooping statistic test in the process of spatial resection, using the Iterated Extended Kalman Filtering (IEKF). The aim of this paper is to present the basic principles of the proposed approach and results based on real data.

Line based camera calibration in machine vision dynamic applications

The problem of dynamic camera calibration considering moving objects in close range environments using straight lines as references is addressed. A mathematical model for the correspondence of a straight line in the object and image spaces is discussed. This model is based on the equivalence between the vector normal to the interpretation plane in the image space and the vector normal to the rotated interpretation plane in the object space. In order to solve the dynamic camera calibration, Kalman Filtering is applied; an iterative process based on the recursive property of the Kalman Filter is defined, using the sequentially estimated camera orientation parameters to feedback the feature extraction process in the image. For the dynamic case, e.g. an image sequence of a moving object, a state prediction and a covariance matrix for the next instant is obtained using the available estimates and the system model. Filtered state estimates can be computed from these predicted estimates using the Kalman Filtering approach and based on the system model parameters with good quality, for each instant of an image sequence. The proposed approach was tested with simulated and real data. Experiments with real data were carried out in a controlled environment, considering a sequence of images of a moving cube in a linear trajectory over a flat surface.

Localización y seguimiento de aeronaves mediante sistemas de multilateración de área extensa

El continuo crecimiento de la demanda del transporte aéreo, junto con los nuevos escenarios de intervención militar, están obligando a una optimización en el uso del espacio aéreo. De este modo, la UE y los EEUU (a través de SESAR y NextGen respectivamente) han asentado las bases para una nueva gestión del tráfico aéreo (ATM). Con ello, se pretende aumentar la capacidad de aeropuertos y rutas aéreas, otorgando mayor flexibilidad al uso del espacio aéreo sin comprometer la seguridad de los usuarios. Desde un punto de vista puramente técnico, la clave de este cambio de modelo está en el conocimiento de la posición de cada aeronave en cada instante. En este sentido, la tendencia en ATM es el uso de ADS-B como fuente principal de posicionamiento. Sin embargo, debido a que este sistema está basado en la difusión de la posición obtenida a través de GPS, es necesario un sistema de seguimiento independiente. Actualmente, la intención es migrar del radar secundario de vigilancia (SSR) a la multilateración de área extensa (WAM), con el fin de mejorar la integridad de la posición para aplicaciones en ruta. Aprovechando el rápido despliegue de ADS-B, se pretende reutilizar sus estaciones base para WAM. Cada estación base que recibe el mensaje ADS-B de la aeronave envía conjuntamente la medida del tiempo de llegada (TOA) de dicho mensaje al centro de tráfico aéreo. La posición de la aeronave se obtiene mediante multilateración, cuya técnica consiste en utilizar las medidas de TOA de un mismo mensaje ADS-B obtenidas en las distintas estaciones base. El objetivo es estimar la posición de cada aeronave con la mayor precisión posible. Para poder diseñar el sistema que permite alcanzar este objetivo, son dos los aspectos básicos a estudiar. Por una parte, la identificación y posterior caracterización de los errores (tanto sistemáticos como aleatorios) que afectan a la medida de TOA. Por otra parte, es necesario el estudio de los sistemas de seguimiento, basados en versiones sofisticadas del filtro de Kalman (IMM, UKF). Una vez establecidos estos dos pilares, la presente tesis doctoral propone un sistema que permite efectuar el seguimiento de las aeronaves, corrigiendo los efectos de las principales distorsiones que afectan a la medida de TOA: la refracción troposférica y el error de sincronismo. La mejora en la precisión de la localización ha sido evaluada mediante simulación de escenarios hipotéticos. ABSTRACT The ever-growing demand in the air transportation and the new military intervention scenarios, are generating a need to optimize the use of the airspace. This way, the EU and the USA (through SESAR and NextGen respectively) have set the ground to overhaul the current air traffic management. The intention is to enhance the capacity of airports and air routes, providing greater flexibility in the use of airspace without jeopardizing the security of the end-users. From a technical perspective, the key for this change lies in the knowledge of the aircraft position. The trend in Air Traffic Management (ATM) is to rely on ADS-B as the main source for aircraft positioning. However, this system is based on the aircraft’s self-declaration of its own (often GPS-based) navigation solution. It is therefore necessary to have an independent surveillance system. Nowadays, the intention is to gradually migrate from Secondary Surveillance Radar (SSR) towards Wide Area Multilateration (WAM) in order to enhance surveillance integrity for en-route applications. Given the fast deployment of ADS-B, the aim is to use its base stations for WAM. Each station sends the Time of Arrival (TOA) of the received ADS-B messages to the air traffic center (ATC). The aircraft position is obtained through multilateration, using the TOA of the same message measured by each station. The aim is to accurately estimate the position of each aircraft. Knowledge from two key areas has to be gathered prior to designing such a system. It is necessary to identify and then characterize the errors (both systematic and random) affecting the TOA measurements. The second element is the study of tracking systems based on sophisticated versions of the Kalman filtering (e.g. IMM, UKF). Based on this knowledge, the main contribution of this Ph.D. is an aircraft tracking system that corrects the effects of the main errors involved in the TOA measurement: tropospheric refraction and synchronization issues. Performance gains in positioning accuracy have been assessed by simulating hypothetical WAM scenarios.

Recursive linear estimation for general discrete-time descriptor systems

This paper considers the optimal linear estimates recursion problem for discrete-time linear systems in its more general formulation. The system is allowed to be in descriptor form, rectangular, time-variant, and with the dynamical and measurement noises correlated. We propose a new expression for the filter recursive equations which presents an interesting simple and symmetric structure. Convergence of the associated Riccati recursion and stability properties of the steady-state filter are provided. (C) 2010 Elsevier Ltd. All rights reserved.

A SON Enhanced Algorithm for Observed Time Differences Based Geolocation in Real 3G Networks

Conferência - 16th International Symposium on Wireless Personal Multimedia Communications (WPMC)- Jun 24-27, 2013

Use of negative information in positioning and tracking algorithms

To avoid additional hardware deployment, indoor localization systems have to be designed in such a way that they rely on existing infrastructure only. Besides the processing of measurements between nodes, localization procedure can include the information of all available environment information. In order to enhance the performance of Wi-Fi based localization systems, the innovative solution presented in this paper considers also the negative information. An indoor tracking method inspired by Kalman filtering is also proposed.

Complementary filter design with three frequency bands: robot attitude estimation

This paper extents the by now classic sensor fusion complementary filter (CF) design, involving two sensors, to the case where three sensors that provide measurements in different bands are available. This paper shows that the use of classical CF techniques to tackle a generic three sensors fusion problem, based solely on their frequency domain characteristics, leads to a minimal realization, stable, sub-optimal solution, denoted as Complementary Filters3 (CF3). Then, a new approach for the estimation problem at hand is used, based on optimal linear Kalman filtering techniques. Moreover, the solution is shown to preserve the complementary property, i.e. the sum of the three transfer functions of the respective sensors add up to one, both in continuous and discrete time domains. This new class of filters are denoted as Complementary Kalman Filters3 (CKF3). The attitude estimation of a mobile robot is addressed, based on data from a rate gyroscope, a digital compass, and odometry. The experimental results obtained are reported.

6D Visual Odometry with Dense Probabilistic Egomotion Estimation

Proceedings of the International Conference on Computer Vision Theory and Applications, 361-365, 2013, Barcelona, Spain

Adaptive modeling and high quality spectral estimation for speech enhancement

In this work an adaptive modeling and spectral estimation scheme based on a dual Discrete Kalman Filtering (DKF) is proposed for speech enhancement. Both speech and noise signals are modeled by an autoregressive structure which provides an underlying time frame dependency and improves time-frequency resolution. The model parameters are arranged to obtain a combined state-space model and are also used to calculate instantaneous power spectral density estimates. The speech enhancement is performed by a dual discrete Kalman filter that simultaneously gives estimates for the models and the signals. This approach is particularly useful as a pre-processing module for parametric based speech recognition systems that rely on spectral time dependent models. The system performance has been evaluated by a set of human listeners and by spectral distances. In both cases the use of this pre-processing module has led to improved results.

Recursive neuro fuzzy techniques for online identification and control

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Specialisation in Europe and asymmetric shocks: potential risks of EMU

Most optimistic views, based on Optimum Currency Areas (OCA) literature, have concluded that the probability of asymmetric shocks to occur at anational level will tend to diminish in the Economic and Monetary Union (EMU)as a result of the intensification of the integration process during the most recent years. Therefore, since Economic Geography Theories predict a higherspecialisation of regions, it is expected that asymmetric shocks will increase.Previous studies have examined to what extent asymmetric shocks have been relevant in the past using, mainly, static measures of asymmetries such as the correlation coefficients between series of shocks previously calculated from astructural VAR model (Bayoumi and Eichengreen, 1992).In this paper, we study the evolution of manufacturing specific asymmetries in Europe from a dynamic point of view (applying the modelproposed by Haldane and Hall, 1991) in order to obtain new evidence about potential risks of EMU.

Specialisation in Europe and asymmetric shocks: potential risks of EMU

Most optimistic views, based on Optimum Currency Areas (OCA) literature, have concluded that the probability of asymmetric shocks to occur at anational level will tend to diminish in the Economic and Monetary Union (EMU)as a result of the intensification of the integration process during the most recent years. Therefore, since Economic Geography Theories predict a higherspecialisation of regions, it is expected that asymmetric shocks will increase.Previous studies have examined to what extent asymmetric shocks have been relevant in the past using, mainly, static measures of asymmetries such as the correlation coefficients between series of shocks previously calculated from astructural VAR model (Bayoumi and Eichengreen, 1992).In this paper, we study the evolution of manufacturing specific asymmetries in Europe from a dynamic point of view (applying the modelproposed by Haldane and Hall, 1991) in order to obtain new evidence about potential risks of EMU.