Orbit determination has long relied on the use of the Kalman filter, or specifically the extended Kalman filter, as a means of accurately navigating spacecraft. With the advent of cheaper, more powerful computers more accurate techniques such as the particle filter have been utilized. These Bayesian types of filters have in more recent years found their way to other applications. Dr. Furfaro and B. Gaudet have demonstrated the ability of the particle filter to accurately estimate the angular velocity, homogenous density, and rotation angle of a non-uniformly rotating ellipsoid shaped asteroid. This paper extends that work by utilizing a particle filter to accurately estimate the angular velocity and homogenous density of an ellipsoidal asteroid while simultaneously determining the location and mass of a mass concentration modeled as a point mass embedded within the asteroid. This work shows that by taking measurements in several locations around the asteroid, the asteroid's rotation state and mass distribution can be discerned.

Vehicles losing their GPS signal is a considerable issue for autonomous vehicles and can be a danger to people in their vicinity. To circumvent this issue, a particle filter localization technique using pre-generated offline Open Street Map (OSM) maps was investigated in a software simulation of Scania’s heavy-duty trucks. The localization technique runs in real-time and provides a way to localize the vehicle safely if the starting position is known. Access to global localization was limited, and the particle filter still succeeded in localizing the vehicle in the vicinity of the correct road segment by creating a graph of the map information and matching the trajectory to the vehicle’s sensor data. The mean error of the Particle filter localization technique in optimal conditions is 16m, which is 20% less than an optimally tuned dead reckoning solution. The mean error is about 50% larger compared to a Global Positioning System. The final product shows potential for expansion but requires more investigation to allow for real-world deployment. / Att fordon kan mista sin GPS-signal är ett stort problem för autonoma fordon och kan vara en fara för människor i dess närhet. För att undvika detta problem föreslås en icke-global lokaliseringsteknik som använder Open Street Maps-kartor (OSM) och ett partikelfilter för att lokalisera fordonet i en mjukvarusimulation. Implementering körs i realtid och anger fordonets position med en tillräcklig träffsäkerhet för att det inte ska utgöra någon fara om dess startposition är känd. Globala lokaliseringsmöjligheter var begränsade, och partikelfiltret lyckades lokalisera fordonet till rätt vägsegment genom att konstruera en graf över den kartinformation den läst in och para ihop fordonets nuvarande färdväg med denna. Resultatet ger en lösning som optimalt har ett medelfel på 16m, vilket är 20% mindre än medelfelet jämfört med optimiserad dödräkning. Lösningen har ca 50% större medelfel än positionering med GPS. Slutresultatet visar en potential att användas i verkliga situationer, men kräver mer undersökningar.

<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.

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Depuis les années 2000, un progrès significatif est enregistré dans les travaux de recherche qui proposent l’apprentissage de détecteurs d’objets sur des grandes bases de données étiquetées manuellement et disponibles publiquement. Cependant, lorsqu’un détecteur générique d’objets est appliqué sur des images issues d’une scène spécifique les performances de détection diminuent considérablement. Cette diminution peut être expliquée par les différences entre les échantillons de test et ceux d’apprentissage au niveau des points de vues prises par la(les) caméra(s), de la résolution, de l’éclairage et du fond des images. De plus, l’évolution de la capacité de stockage des systèmes informatiques, la démocratisation de la "vidéo-surveillance" et le développement d’outils d’analyse automatique des données vidéos encouragent la recherche dans le domaine du trafic routier. Les buts ultimes sont l’évaluation des demandes de gestion du trafic actuelles et futures, le développement des infrastructures routières en se basant sur les besoins réels, l’intervention pour une maintenance à temps et la surveillance des routes en continu. Par ailleurs, l’analyse de trafic est une problématique dans laquelle plusieurs verrous scientifiques restent à lever. Ces derniers sont dus à une grande variété dans la fluidité de trafic, aux différents types d’usagers, ainsi qu’aux multiples conditions météorologiques et lumineuses. Ainsi le développement d’outils automatiques et temps réel pour l’analyse vidéo de trafic routier est devenu indispensable. Ces outils doivent permettre la récupération d’informations riches sur le trafic à partir de la séquence vidéo et doivent être précis et faciles à utiliser. C’est dans ce contexte que s’insèrent nos travaux de thèse qui proposent d’utiliser les connaissances antérieurement acquises et de les combiner avec des informations provenant de la nouvelle scène pour spécialiser un détecteur d’objet aux nouvelles situations de la scène cible. Dans cette thèse, nous proposons de spécialiser automatiquement un classifieur/détecteur générique d’objets à une scène de trafic routier surveillée par une caméra fixe. Nous présentons principalement deux contributions. La première est une formalisation originale de transfert d’apprentissage transductif à base d’un filtre séquentiel de type Monte Carlo pour la spécialisation automatique d’un classifieur. Cette formalisation approxime itérativement la distribution cible inconnue au départ, comme étant un ensemble d’échantillons de la base spécialisée à la scène cible. Les échantillons de cette dernière sont sélectionnés à la fois à partir de la base source et de la scène cible moyennant une pondération qui utilise certaines informations a priori sur la scène. La base spécialisée obtenue permet d’entraîner un classifieur spécialisé à la scène cible sans intervention humaine. La deuxième contribution consiste à proposer deux stratégies d’observation pour l’étape mise à jour du filtre SMC. Ces stratégies sont à la base d’un ensemble d’indices spatio-temporels spécifiques à la scène de vidéo-surveillance. Elles sont utilisées pour la pondération des échantillons cibles. Les différentes expérimentations réalisées ont montré que l’approche de spécialisation proposée est performante et générique. Nous avons pu y intégrer de multiples stratégies d’observation. Elle peut être aussi appliquée à tout type de classifieur. De plus, nous avons implémenté dans le logiciel OD SOFT de Logiroad les possibilités de chargement et d’utilisation d’un détecteur fourni par notre approche. Nous avons montré également les avantages des détecteurs spécialisés en comparant leurs résultats avec celui de la méthode Vu-mètre de Logiroad. / Since 2000, a significant progress has been recorded in research work which has proposed to learn object detectors using large manually labeled and publicly available databases. However, when a generic object detector is applied on images of a specific scene, the detection performances will decrease considerably. This decrease may be explained by the differences between the test samples and the learning ones at viewpoints taken by camera(s), resolution, illumination and background images. In addition, the storage capacity evolution of computer systems, the "video surveillance" democratization and the development of automatic video-data analysis tools have encouraged research into the road-traffic domain. The ultimate aims are the management evaluation of current and future trafic requests, the road infrastructures development based on real necessities, the intervention of maintenance task in time and the continuous road surveillance. Moreover, traffic analysis is a problematicness where several scientific locks should be lifted. These latter are due to a great variety of traffic fluidity, various types of users, as well multiple weather and lighting conditions. Thus, developing automatic and real-time tools to analyse road-traffic videos has become an indispensable task. These tools should allow retrieving rich data concerning the traffic from the video sequence and they must be precise and easy to use. This is the context of our thesis work which proposes to use previous knowledges and to combine it with information extracted from the new scene to specialize an object detector to the new situations of the target scene. In this thesis, we propose to automatically specialize a generic object classifier/detector to a road traffic scene surveilled by a fixed camera. We mainly present two contributions. The first one is an original formalization of Transductive Transfer Learning based on a sequential Monte Carlo filter for automatic classifier specialization. This formalization approximates iteratively the previously unknown target distribution as a set of samples composing the specialized dataset of the target scene. The samples of this dataset are selected from both source dataset and target scene further to a weighting step using some prior information on the scene. The obtained specialized dataset allows training a specialized classifier to the target scene without human intervention. The second contribution consists in proposing two observation strategies to be used in the SMC filter’s update step. These strategies are based on a set of specific spatio-temporal cues of the video surveillance scene. They are used to weight the target samples. The different experiments carried out have shown that the proposed specialization approach is efficient and generic. We have been able to integrate multiple observation strategies. It can also be applied to any classifier / detector. In addition, we have implemented into the Logiroad OD SOFT software the loading and utilizing possibilities of a detector provided by our approach. We have also shown the advantages of the specialized detectors by comparing their results to the result of Logiroad’s Vu-meter method.

The focus of the thesis is on the development of a few stochastic search schemes for inverse problems and their applications in medical imaging. After the introduction in Chapter 1 that motivates and puts in perspective the work done in later chapters, the main body of the thesis may be viewed as composed of two parts: while the first part concerns the development of stochastic search algorithms for inverse problems (Chapters 2 and 3), the second part elucidates on the applicability of search schemes to inverse problems of interest in tomographic imaging (Chapters 4 and 5). The chapter-wise contributions of the thesis are summarized below. Chapter 2 proposes a Monte Carlo stochastic filtering algorithm for the recursive estimation of diffusive processes in linear/nonlinear dynamical systems that modulate the instantaneous rates of Poisson measurements. The same scheme is applicable when the set of partial and noisy measurements are of a diffusive nature. A key aspect of our development here is the filter-update scheme, derived from an ensemble approximation of the time-discretized nonlinear Kushner Stratonovich equation, that is modified to account for Poisson-type measurements. Specifically, the additive update through a gain-like correction term, empirically approximated from the innovation integral in the filtering equation, eliminates the problem of particle collapse encountered in many conventional particle filters that adopt weight-based updates. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth, first with application to filtering problems with diffusive or Poisson-type measurements and then to an automatic control problem wherein the exterminations of the associated cost functional is achieved simply by an appropriate redefinition of the innovation process. The aim of one of the numerical examples in Chapter 2 is to minimize the structural response of a duffing oscillator under external forcing. We pose this problem of active control within a filtering framework wherein the goal is to estimate the control force that minimizes an appropriately chosen performance index. We employ the proposed filtering algorithm to estimate the control force and the oscillator displacements and velocities that are minimized as a result of the application of the control force. While Fig. 1 shows the time histories of the uncontrolled and controlled displacements and velocities of the oscillator, a plot of the estimated control force against the external force applied is given in Fig. 2. (a) (b) Fig. 1. A plot of the time histories of the uncontrolled and controlled (a) displacements and (b) velocities. Fig. 2. A plot of the time histories of the external force and the estimated control force Stochastic filtering, despite its numerous applications, amounts only to a directed search and is best suited for inverse problems and optimization problems with unimodal solutions. In view of general optimization problems involving multimodal objective functions with a priori unknown optima, filtering, similar to a regularized Gauss-Newton (GN) method, may only serve as a local (or quasi-local) search. In Chapter 3, therefore, we propose a stochastic search (SS) scheme that whilst maintaining the basic structure of a filtered martingale problem, also incorporates randomization techniques such as scrambling and blending, which are meant to aid in avoiding the so-called local traps. The key contribution of this chapter is the introduction of yet another technique, termed as the state space splitting (3S) which is a paradigm based on the principle of divide-and-conquer. The 3S technique, incorporated within the optimization scheme, offers a better assimilation of measurements and is found to outperform filtering in the context of quantitative photoacoustic tomography (PAT) to recover the optical absorption field from sparsely available PAT data using a bare minimum ensemble. Other than that, the proposed scheme is numerically shown to be better than or at least as good as CMA-ES (covariance matrix adaptation evolution strategies), one of the best performing optimization schemes in minimizing a set of benchmark functions. Table 1 gives the comparative performance of the proposed scheme and CMA-ES in minimizing a set of 40-dimensional functions (F1-F20), all of which have their global minimum at 0, using an ensemble size of 20. Here, 10 5 is the tolerance limit to be attained for the objective function value and MAX is the maximum number of iterations permissible to the optimization scheme to arrive at the global minimum. Table 1. Performance of the SS scheme and Chapter 4 gathers numerical and experimental evidence to support our conjecture in the previous chapters that even a quasi-local search (afforded, for instance, by the filtered martingale problem) is generally superior to a regularized GN method in solving inverse problems. Specifically, in this chapter, we solve the inverse problems of ultrasound modulated optical tomography (UMOT) and diffraction tomography (DT). In UMOT, we perform a spatially resolved recovery of the mean-squared displacements, p r of the scattering centres in a diffusive object by measuring the modulation depth in the decaying autocorrelation of the incident coherent light. This modulation is induced by the input ultrasound focussed to a specific region referred to as the region of interest (ROI) in the object. Since the ultrasound-induced displacements are a measure of the material stiffness, in principle, UMOT can be applied for the early diagnosis of cancer in soft tissues. In DT, on the other hand, we recover the real refractive index distribution, n r of an optical fiber from experimentally acquired transmitted intensity of light traversing through it. In both cases, the filtering step encoded within the optimization scheme recovers superior reconstruction images vis-à-vis the GN method in terms of quantitative accuracies. Fig. 3 gives a comparative cross-sectional plot through the centre of the reference and reconstructed p r images in UMOT when the ROI is at the centre of the object. Here, the anomaly is presented as an increase in the displacements and is at the centre of the ROI. Fig. 4 shows the comparative cross-sectional plot of the reference and reconstructed refractive index distributions, n r of the optical fiber in DT. Fig. 3. Cross-sectional plot through the center of the reference and reconstructed p r images. Fig. 4. Cross-sectional plot through the center of the reference and reconstructed n r distributions. In Chapter 5, the SS scheme is applied to our main application, viz. photoacoustic tomography (PAT) for the recovery of the absorbed energy map, the optical absorption coefficient and the chromophore concentrations in soft tissues. Nevertheless, the main contribution of this chapter is to provide a single-step method for the recovery of the optical absorption field from both simulated and experimental time-domain PAT data. A single-step direct recovery is shown to yield better reconstruction than the generally adopted two-step method for quantitative PAT. Such a quantitative reconstruction maybe converted to a functional image through a linear map. Alternatively, one could also perform a one-step recovery of the chromophore concentrations from the boundary pressure, as shown using simulated data in this chapter. Being a Monte Carlo scheme, the SS scheme is highly parallelizable and the availability of such a machine-ready inversion scheme should finally enable PAT to emerge as a clinical tool in medical diagnostics. Given below in Fig. 5 is a comparison of the optical absorption map of the Shepp-Logan phantom with the reconstruction obtained as a result of a direct (1-step) recovery. Fig. 5. The (a) exact and (b) reconstructed optical absorption maps of the Shepp-Logan phantom. The x- and y-axes are in m and the colormap is in mm-1. Chapter 6 concludes the work with a brief summary of the results obtained and suggestions for future exploration of some of the schemes and applications described in this thesis.