We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction. / CNDM / CADICS

Dans la vie de tous les jours, nous assistons à des chorégraphies surprenantes dans les déplacements de foules de piétons. Les mécanismes qui sont à la base de la dynamique des foules humaines restent peu connus. Un des modes d’observation des piétons consiste à réaliser des mesures en conditions réelles (exemple : aéroport, gare, etc.). La trajectoire empruntée, la vitesse et l’accélération sont les données de base pour une telle analyse. C’est dans ce contexte que se placent nos travaux qui combinent étroitement observations en milieu naturel et expérimentations contrôlées. Nous avons proposé un système pour le suivi de plusieurs piétons dans un environnement fermé, à l’aide d’un réseau de télémètres lasers à balayage. Nous avons fait avancer l’état de l’art sur quatre plans.Premièrement, nous avons introduit une méthode de fusion automatique des données, permettant de discriminer les objets statiques (murs, poteaux, etc.) et aussi d’augmenter le taux de détection.Deuxièmement, nous avons proposé une méthode de détection non paramétrique basée sur la modélisation de la marche. L’algorithme estime la position du piéton, que celui-ci soit immobile ou en mouvement.Finalement, notre suivi repose sur la méthode Rao-Blackwell Monte Carlo Association de Données, avec la particularité de suivre un nombre variable de piétons.L’algorithme a été évalué quantitativement par des expériences de comportement social à différents niveaux de densité. Ces expériences ont eu lieu dans une école, près de 300 piétons ont été suivis dont une trentaine simultanément. / In everyday life, we witness surprising choreographies in the movements of crowds of pedestrians. The mechanisms that underlie the dynamics of human crowd dynamics remain poorly understood. One of the ways of observing pedestrians consists in taking measurements in real conditions (e. g. airport, station, etc.). The trajectory, speed and acceleration are the basic data for such an analysis. It is in this context that our work is placed, which closely combines observations in the natural environment with controlled experiments. We proposed a system for tracking multiple pedestrians in a closed environment using a network of scanning laser rangefinders. We have advanced the state of the art on four levels: first, we have introduced an automatic data fusion method to discriminate static objects (walls, poles, etc.) and also to increase the detection rate; second, we have proposed a non-parametric detection method based on walking modeling. The algorithm estimates the position of the pedestrian, whether stationary or moving, and finally, our monitoring is based on the Rao-Blackwell Monte Carlo Association Data Method, with the particularity of tracking a variable number of pedestrians, which was quantitatively evaluated by experiments in social behaviour at different levels of density. These experiments took place in a school, nearly 300 pedestrians were followed, about thirty of them simultaneously.

<p>In this thesis Sequential Monte Carlo filters, or particle filters, applied to aircraft navigation is considered. This report consists of two parts. The first part is an illustration of the theory behind this thesis project. The second and most important part evaluates the algorithm by using real flight data.</p><p>Navigation is about determining one's own position, orientation and velocity. The sensor fusion studied combines data from an inertial navigation system (INS) with measurements of the ground elevation below in order to form a terrain aided positioning system (TAP). The ground elevation measurements are compared with a height database. The height database is highly non-linear, which is why a marginalized particle filter (MPF) is used for the sensor fusion.</p><p>Tests have shown that the MPF delivers a stable and good estimate of the position, as long as it receives good data. A comparison with Saab's NINS algorithm showed that the two algorithms perform quite similar, although NINS performs better when data is lacking.</p>

In this thesis Sequential Monte Carlo filters, or particle filters, applied to aircraft navigation is considered. This report consists of two parts. The first part is an illustration of the theory behind this thesis project. The second and most important part evaluates the algorithm by using real flight data. Navigation is about determining one's own position, orientation and velocity. The sensor fusion studied combines data from an inertial navigation system (INS) with measurements of the ground elevation below in order to form a terrain aided positioning system (TAP). The ground elevation measurements are compared with a height database. The height database is highly non-linear, which is why a marginalized particle filter (MPF) is used for the sensor fusion. Tests have shown that the MPF delivers a stable and good estimate of the position, as long as it receives good data. A comparison with Saab's NINS algorithm showed that the two algorithms perform quite similar, although NINS performs better when data is lacking.

Made available in DSpace on 2014-06-12T17:35:07Z (GMT). No. of bitstreams: 2 arquivo3632_1.pdf: 1762777 bytes, checksum: e94374ad230aa9afab9b590aa9caa2bd (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Ao longo dos anos, modelos Bayesianos vêm recebendo atenção especial da academia e em aplicações principalmente por possibilitarem uma combinação matemática entre corpos de evidência subjetiva e empírica. A metodologia de integração de Monte Carlo via cadeias de Markov é uma das principais classes de algoritmos para computar estimativas marginais a partir de modelos Bayesianos. Entre os métodos de integração de Monte Carlo via cadeias de Markov, o algoritmo de Metropolis-Hastings merece destaque. Em resumo, para o conjunto de d variáveis (ou componentes) do modelo Bayesiano, X = (X1, X2, , Xd), tal algoritmo elabora uma cadeia de Markov onde cada estado visitado é uma realização de X, x = (x1, x2, , xd), amostrada das distribuições de probabilidades condicionais das variáveis do modelo, f(xi| x1, x2, , xi-1, xi+1, , xd). Quando a simulação é governada por distribuições cuja amostragem direta é viável, o algoritmo de Metropolis-Hastings converge para o método de Gibbs e técnicas de redução de variância tais como Rao-Blackwellization podem ser adotadas. Caso contrário, diante de distribuições cuja amostragem direta é inviável, Rao-Blackwellization é possível a partir do método de griddy-Gibbs, que recorre a funções aproximadas. Esta tese propõe uma variante de griddy-Gibbs que pode ser também classificada como uma extensão do algoritmo de Metropolis-Hastings (diferentemente do método de griddy-Gibbs tradicional que descarta a possibilidade de se rejeitar os valores amostrados ao longo das simulações). Além disso, algoritmos de integração numérica adaptativos e técnicas de agrupamento, tais como o método adaptativo de Simpson e centroidal Voronoi tessellations, são adotados. Casos de estudo apontam o algoritmo proposto como uma boa alternativa a métodos existentes, promovendo estimativas mais precisas sob um menor consumo de recursos computacionais em muitas situações

<p>Navigation is about knowing your own position, orientation and velocity relative to some geographic entities. The sensor fusion considered in this thesis combines data from a dead reckoning system, inertial navigation system (INS), and measurements of the ground elevation. The very fast dynamics of aircraft navigation makes it difficult to estimate the true states. Instead the algorithm studied will estimate the errors of the INS and compensate for them. A height database is used along with the measurements. The height database is highly non-linear why a Rao-Blackwellized particle filter is used for the sensor fusion. This integrated navigation system only uses data from its own sensors and from the height database, which means that it is independent of information from outside the aircraft. </p><p>This report will describe the algorithm and illustrate the theory used. The main purpose is to evaluate the algorithm using real flight data, why the result chapter is the most important.</p>

Navigation is about knowing your own position, orientation and velocity relative to some geographic entities. The sensor fusion considered in this thesis combines data from a dead reckoning system, inertial navigation system (INS), and measurements of the ground elevation. The very fast dynamics of aircraft navigation makes it difficult to estimate the true states. Instead the algorithm studied will estimate the errors of the INS and compensate for them. A height database is used along with the measurements. The height database is highly non-linear why a Rao-Blackwellized particle filter is used for the sensor fusion. This integrated navigation system only uses data from its own sensors and from the height database, which means that it is independent of information from outside the aircraft. This report will describe the algorithm and illustrate the theory used. The main purpose is to evaluate the algorithm using real flight data, why the result chapter is the most important.

With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages. Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.

<p>With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages.</p><p>Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.</p>