The thesis outlines the development and application of a few novel dynamic state estimation based methods for estimation of parameters of vibrating engineering structures. The study investigates strategies for data fusion from multiple tests of possibly different types and different sensor quantities through the introduction of a common pseudo-time parameter. These strategies have been developed within the framework of Kalman and particle filtering techniques. The proposed methods are applied to a suite of problems that includes laboratory and field studies with a primary focus on finite element model updating of bridge structures and vehicle structure interaction problems. The study also describes how finite element models residing in commercially available softwares can be made to communicate with database of measurements via a particle filtering algorithm developed on the Matlab platform. The thesis is divided into six chapters and an appendix. A review of literature on problems of structural system identification with emphasis on methods on dynamic state estimation techniques is presented in Chapter 1. The problem of system parameter idenfification when measurements originate from multiple tests and multiple sensors is considered in Chapter 2. and solution based on Neumann expansion of the structural static/dynamic stiffness matrix and Kalman filtering is proposed to tackle this problem. The question of decoupling the problem of parameter estimation from state estimation is also discussed. The avoidance of linearization of the stiffness matrix and solution of the parameter problems by using Monte Carlo filters is examined in Chapter 3. This also enables treatment of nonlinear structural mechanics problems. The proposed method is assessed using synthetic and laboratory measurement data. The problem of interfacing structural models residing in professional finite element analysis software with measured data via particle filtering algorithm developed on Matlab platform is considered in Chapter 4. Illustrative examples now cover laboratory studies on a beam structure and also filed studies on an existing multi-span masonry railway arch bridge. Identification of parameters of systems with strong nonlinearities, such, as a rectangular rubber sheet with a concentric hole, is also investigated. Studies on parameter identification in beam moving oscillator problem are reported in Chapter 5. The efficacy of particle filtering strategy in identifying parameters of this class of time varying system is demonstrated. A resume of contributions made and a few suggestions for further research are provided in Chapter 6. The appendix contains details of development of interfaces among finite element software(NISA), data base of measurements and particle filtering algorithm (developed on Matlab platform).

The problem of object detection deals with determining whether an instance of a given class of object is present or not. There are robust, supervised learning based algorithms available for object detection in an image. These image object detectors (image-based object detectors) use characteristics learnt from the training samples to find object and non-object regions. The characteristics used are such that the detectors work under a variety of conditions and hence are very robust. Object detection in video can be performed by using such a detector on each frame of the video sequence. This approach checks for presence of an object around each pixel, at different scales. Such a frame-based approach completely ignores the temporal continuity inherent in the video. The detector declares presence of the object independent of what has happened in the past frames. Also, various visual cues such as motion and color, which give hints about the location of the object, are not used. The current work is aimed at building a generic framework for using a supervised learning based image object detector for video that exploits temporal continuity and the presence of various visual cues. We use temporal continuity and visual cues to speed up the detection and improve detection accuracy by considering past detection results. We propose a generic framework, based on Experiential Sampling [1], which considers temporal continuity and visual cues to focus on a relevant subset of each frame. We determine some key positions in each frame, called attention samples, and object detection is performed only at scales with these positions as centers. These key positions are statistical samples from a density function that is estimated based on various visual cues, past experience and temporal continuity. This density estimation is modeled as a Bayesian Filtering problem and is carried out using Sequential Monte Carlo methods (also known as Particle Filtering), where a density is represented by a weighted sample set. The experiential sampling framework is inspired by Neisser’s perceptual cycle [2] and Itti-Koch’s static visual attention model[3]. In this work, we first use Basic Experiential Sampling as presented in[1]for object detection in video and show its limitations. To overcome these limitations, we extend the framework to effectively combine top-down and bottom-up visual attention phenomena. We use learning based detector’s response, which is a top-down cue, along with visual cues to improve attention estimate. To effectively handle multiple objects, we maintain a minimum number of attention samples per object. We propose to use motion as an alert cue to reduce the delay in detecting new objects entering the field of view. We use an inhibition map to avoid revisiting already attended regions. Finally, we improve detection accuracy by using a particle filter based detection scheme [4], also known as Track Before Detect (TBD). In this scheme, we compute likelihood of presence of the object based on current and past frame data. This likelihood is shown to be approximately equal to the product of average sample weights over past frames. Our framework results in a significant reduction in overall computation required by the object detector, with an improvement in accuracy while retaining its robustness. This enables the use of learning based image object detectors in real time video applications which otherwise are computationally expensive. We demonstrate the usefulness of this framework for frontal face detection in video. We use Viola-Jones’ frontal face detector[5] and color and motion visual cues. We show results for various cases such as sequences with single object, multiple objects, distracting background, moving camera, changing illumination, objects entering/exiting the frame, crossing objects, objects with pose variation and sequences with scene change. The main contributions of the thesis are i) We give an experiential sampling formulation for object detection in video. Many concepts like attention point and attention density which are vague in[1] are precisely defined. ii) We combine detector’s response along with visual cues to estimate attention. This is inspired by a combination of top-down and bottom-up attention maps in visual attention models. To the best of our knowledge, this is used for the first time for object detection in video. iii) In case of multiple objects, we highlight the problem with sample based density representation and solve by maintaining a minimum number of attention samples per object. iv) For objects first detected by the learning based detector, we propose to use a TBD scheme for their subsequent detections along with the learning based detector. This improves accuracy compared to using the learning based detector alone. This thesis is organized as follows . Chapter 1: In this chapter we present a brief survey of related work and define our problem. . Chapter 2: We present an overview of biological models that have motivated our work. . Chapter 3: We give the experiential sampling formulation as in previous work [1], show results and discuss its limitations. . Chapter 4: In this chapter, which is on Enhanced Experiential Sampling, we suggest enhancements to overcome limitations of basic experiential sampling. We propose track-before-detect scheme to improve detection accuracy. . Chapter 5: We conclude the thesis and give possible directions for future work in this area. . Appendix A: A description of video database used in this thesis. . Appendix B: A list of commonly used abbreviations and notations.

As robotic systems move from well-controlled settings to increasingly unstructured environments, they are required to operate in highly dynamic and cluttered scenarios. Finding an object, estimating its pose, and tracking its pose over time within such scenarios are challenging problems. Although various approaches have been developed to tackle these problems, the scope of objects addressed and the robustness of solutions remain limited. In this thesis, we target a robust object perception using visual sensory information, which spans from the traditional monocular camera to the more recently emerged RGB-D sensor, in unstructured environments. Toward this goal, we address four critical challenges to robust 6-DOF object pose estimation and tracking that current state-of-the-art approaches have, as yet, failed to solve. The first challenge is how to increase the scope of objects by allowing visual perception to handle both textured and textureless objects. A large number of 3D object models are widely available in online object model databases, and these object models provide significant prior information including geometric shapes and photometric appearances. We note that using both geometric and photometric attributes available from these models enables us to handle both textured and textureless objects. This thesis presents our efforts to broaden the spectrum of objects to be handled by combining geometric and photometric features. The second challenge is how to dependably estimate and track the pose of an object despite the clutter in backgrounds. Difficulties in object perception rise with the degree of clutter. Background clutter is likely to lead to false measurements, and false measurements tend to result in inaccurate pose estimates. To tackle significant clutter in backgrounds, we present two multiple pose hypotheses frameworks: a particle filtering framework for tracking and a voting framework for pose estimation. Handling of object discontinuities during tracking, such as severe occlusions, disappearances, and blurring, presents another important challenge. In an ideal scenario, a tracked object is visible throughout the entirety of tracking. However, when an object happens to be occluded by other objects or disappears due to the motions of the object or the camera, difficulties ensue. Because the continuous tracking of an object is critical to robotic manipulation, we propose to devise a method to measure tracking quality and to re-initialize tracking as necessary. The final challenge we address is performing these tasks within real-time constraints. Our particle filtering and voting frameworks, while time-consuming, are composed of repetitive, simple and independent computations. Inspired by that observation, we propose to run massively parallelized frameworks on a GPU for those robotic perception tasks which must operate within strict time constraints.

This thesis analyzes the process of deblurring of degraded images generated by space-variant nonlinear image systems with Gaussian observation noise. The restoration of blurred images is performed by using two methods / a modified version of the Optimum Decoding Based Smoothing Algorithm and the Bootstrap Filter Algorithm which is a version of Particle Filtering methods. A computer software called MATLAB is used for performing the simulations of image estimation. The results of some simulations for various observation and image models are presented.

In high range-resolution (HRR) radar systems, the returns from a single target may fall in multiple adjacent range bins which individually vary in amplitude. A target following this representation is commonly referred to as an extended target and results in more information about the target. However, extracting this information from the radar returns is challenging due to several complexities. These complexities include the single dimensional nature of the radar measurements, complexities associated with the scattering of electromagnetic waves, and complex environments in which radar systems are required to operate. There are several applications of HRR radar systems which extract target information with varying levels of success. A commonly used application is that of imaging referred to as synthetic aperture radar (SAR) and inverse SAR (ISAR) imaging. These techniques combine multiple single dimension measurements in order to obtain a single two dimensional image. These techniques rely on rotational motion between the target and the radar occurring during the collection of the single dimension measurements. In the case of ISAR, the radar is stationary while motion is induced by the target. There are several difficulties associated with the unknown motion of the target when standard Doppler processing techniques are used to synthesise ISAR images. In this dissertation, a non-standard Dop-pler approach, based on Bayesian inference techniques, was considered to address the difficulties. The target and observations were modelled with a non-linear state space model. Several different Bayesian techniques were implemented to infer the hidden states of the model, which coincide with the unknown characteristics of the target. A simulation platform was designed in order to analyse the performance of the implemented techniques. The implemented techniques were capable of successfully tracking a randomly generated target in a controlled environment. The influence of varying several parameters, related to the characteristics of the target and the implemented techniques, was explored. Finally, a comparison was made between standard Doppler processing and the Bayesian methods proposed. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Electrical, Electronic and Computer Engineering / unrestricted

Les modèles de chaînes de Markov cachées ou plus généralement ceux de Feynman-Kac sont aujourd'hui très largement utilisés. Ils permettent de modéliser une grande diversité de séries temporelles (en finance, biologie, traitement du signal, ...) La complexité croissante de ces modèles a conduit au développement d'approximations via différentes méthodes de Monte-Carlo, dont le Markov Chain Monte-Carlo (MCMC) et le Sequential Monte-Carlo (SMC). Les méthodes de SMC appliquées au filtrage et au lissage particulaires font l'objet de cette thèse. Elles consistent à approcher la loi d'intérêt à l'aide d'une population de particules définies séquentiellement. Différents algorithmes ont déjà été développés et étudiés dans la littérature. Nous raffinons certains de ces résultats dans le cas du Forward Filtering Backward Smoothing et du Forward Filtering Backward Simulation grâce à des inégalités de déviation exponentielle et à des contrôles non asymptotiques de l'erreur moyenne. Nous proposons également un nouvel algorithme de lissage consistant à améliorer une population de particules par des itérations MCMC, et permettant d'estimer la variance de l'estimateur sans aucune autre simulation. Une partie du travail présenté dans cette thèse concerne également les possibilités de mise en parallèle du calcul des estimateurs particulaires. Nous proposons ainsi différentes interactions entre plusieurs populations de particules. Enfin nous illustrons l'utilisation des chaînes de Markov cachées dans la modélisation de données financières en développant un algorithme utilisant l'Expectation-Maximization pour calibrer les paramètres du modèle exponentiel d'Ornstein-Uhlenbeck multi-échelles / Hidden Markov chain models or more generally Feynman-Kac models are now widely used. They allow the modelling of a variety of time series (in finance, biology, signal processing, ...) Their increasing complexity gave birth to approximations using Monte-Carlo methods, among which Markov Chain Monte-Carlo (MCMC) and Sequential Monte-Carlo (SMC). SMC methods applied to particle filtering and smoothing are dealt with in this thesis. These methods consist in approximating the law of interest through a particle population sequentially defined. Different algorithms have already been developed and studied in the literature. We make some of these results more precise in the particular of the Forward Filtering Backward Smoothing and Forward Filtering Backward Simulation by showing exponential deviation inequalities and by giving non-asymptotic upper bounds to the mean error. We also introduce a new smoothing algorithm improving a particle population through MCMC iterations and allowing to estimate the estimator variance without further simulation. Part of the work presented in this thesis is devoted to the parallel computing of particle estimators. We study different interaction schemes between several particle populations. Finally, we also illustrate the use of hidden Markov chains in the modelling of financial data through an algorithm using Expectation-Maximization to calibrate the exponential Ornstein-Uhlenbeck multiscale stochastic volatility model

Cette thèse s’intéresse au problème de l’inférence bayésienne dans les modèles probabilistes dynamiques. Plus précisément nous nous focalisons sur les méthodes de Monte Carlo pour l’intégration. Nous revisitons tout d’abord le mécanisme d’échantillonnage d’importance avec rééchantillonnage, puis son extension au cadre dynamique connue sous le nom de filtrage particulaire, pour enfin conclure nos travaux par une application à la poursuite multi-cibles.En premier lieu nous partons du problème de l’estimation d’un moment suivant une loi de probabilité, connue à une constante près, par une méthode de Monte Carlo. Tout d’abord,nous proposons un nouvel estimateur apparenté à l’estimateur d’échantillonnage d’importance normalisé mais utilisant deux lois de proposition différentes au lieu d’une seule. Ensuite,nous revisitons le mécanisme d’échantillonnage d’importance avec rééchantillonnage dans son ensemble afin de produire des tirages Monte Carlo indépendants, contrairement au mécanisme usuel, et nous construisons ainsi deux nouveaux estimateurs.Dans un second temps nous nous intéressons à l’aspect dynamique lié au problème d’inférence bayésienne séquentielle. Nous adaptons alors dans ce contexte notre nouvelle technique de rééchantillonnage indépendant développée précédemment dans un cadre statique.Ceci produit le mécanisme de filtrage particulaire avec rééchantillonnage indépendant, que nous interprétons comme cas particulier de filtrage particulaire auxiliaire. En raison du coût supplémentaire en tirages requis par cette technique, nous proposons ensuite une procédure de rééchantillonnage semi-indépendant permettant de le contrôler.En dernier lieu, nous considérons une application de poursuite multi-cibles dans un réseau de capteurs utilisant un nouveau modèle bayésien, et analysons empiriquement les résultats donnés dans cette application par notre nouvel algorithme de filtrage particulaire ainsi qu’un algorithme de Monte Carlo par Chaînes de Markov séquentiel / This thesis deals with integration calculus in the context of Bayesian inference and Bayesian statistical filtering. More precisely, we focus on Monte Carlo integration methods. We first revisit the importance sampling with resampling mechanism, then its extension to the dynamic setting known as particle filtering, and finally conclude our work with a multi-target tracking application. Firstly, we consider the problem of estimating some moment of a probability density, known up to a constant, via Monte Carlo methodology. We start by proposing a new estimator affiliated with the normalized importance sampling estimator but using two proposition densities rather than a single one. We then revisit the importance sampling with resampling mechanism as a whole in order to produce Monte Carlo samples that are independent, contrary to the classical mechanism, which enables us to develop two new estimators. Secondly, we consider the dynamic aspect in the framework of sequential Bayesian inference. We thus adapt to this framework our new independent resampling technique, previously developed in a static setting. This yields the particle filtering with independent resampling mechanism, which we reinterpret as a special case of auxiliary particle filtering. Because of the increased cost required by this technique, we next propose a semi independent resampling procedure which enables to control this additional cost. Lastly, we consider an application of multi-target tracking within a sensor network using a new Bayesian model, and empirically analyze the results from our new particle filtering algorithm as well as a sequential Markov Chain Monte Carlo algorithm

Mathematical models are used in engineering and the sciences to estimate properties of systems of interest, increasing our understanding of the surrounding world and driving technological innovation. Unfortunately, as the systems of interest grow in complexity, so to do the models necessary to accurately describe them. Analytic solutions for problems with such models are provably intractable, motivating the use of approximate yet still accurate estimation techniques. Particle filtering methods have emerged as a popular tool in the presence of such models, spreading from its origins in signal processing to a diverse set of fields throughout engineering and the sciences including medical research, economics, robotics, and geophysics. In groundwater hydrology, a key component of aquifer assessment is the determination of the properties which permit water resource managers to estimate aquifer drawdown and safe yield. Presented is a particle filtering approach to estimate aquifer properties from transient data sets, leveraging recently published analytically-derived models for confined aquifers. The approach is examined experimentally through validation against three common aquifer testing problems: determination of (i) transmissivity and storage coefficient from non-leaky confined aquifer performance tests, (ii) transmissivity, storage coefficient, and vertical hydraulic conductivity of a confining unit from leaky confined aquifer performance tests, and (iii) transmissivity and storage coefficient from non-leaky confined aquifer performance tests with noisy data and boundary effects. The first two problems are well-addressed and the presented approach compares favorably to the results obtained from other published methods. The third problem, which the presented method can tackle more naturally than previously-published methods, underscores the flexibility of particle filtering and, in turn, the promise such methods offer for a myriad of other geoscience problems

This thesis discusses the use of Kalman filtering for noise reduction in a 3-D gesture- based computer music controller known as the Radio Drum and for real-time tempo tracking of rhythmic and melodic musical performances. The Radio Drum noise reduction Kalman filter is designed based on previous research in the field of target tracking for radar applications and prior knowledge of a drummer’s expected gestures throughout a performance. In this case we are seeking to improve the position estimates of a drum stick in order to enhance the expressivity and control of the instrument by the performer. Our approach to tempo tracking is novel in that a multi- modal approach combining gesture sensors and audio in a late fusion stage lead to higher accuracy in the tempo estimates.

To navigate successfully in a previously unexplored environment, a mobile robot must be able to estimate the spatial relationships of the objects of interest accurately. A Simultaneous Localization and Mapping (SLAM) sys- tem employs its sensors to build incrementally a map of its surroundings and to localize itself in the map simultaneously. The aim of this research project is to develop a SLAM system suitable for self propelled household lawnmowers. The proposed bearing-only SLAM system requires only an omnidirec- tional camera and some inexpensive landmarks. The main advantage of an omnidirectional camera is the panoramic view of all the landmarks in the scene. Placing landmarks in a lawn field to define the working domain is much easier and more flexible than installing the perimeter wire required by existing autonomous lawnmowers. The common approach of existing bearing-only SLAM methods relies on a motion model for predicting the robot’s pose and a sensor model for updating the pose. In the motion model, the error on the estimates of object positions is cumulated due mainly to the wheel slippage. Quantifying accu- rately the uncertainty of object positions is a fundamental requirement. In bearing-only SLAM, the Probability Density Function (PDF) of landmark position should be uniform along the observed bearing. Existing methods that approximate the PDF with a Gaussian estimation do not satisfy this uniformity requirement. This thesis introduces both geometric and proba- bilistic methods to address the above problems. The main novel contribu- tions of this thesis are: 1. A bearing-only SLAM method not requiring odometry. The proposed method relies solely on the sensor model (landmark bearings only) without relying on the motion model (odometry). The uncertainty of the estimated landmark positions depends on the vision error only, instead of the combination of both odometry and vision errors. 2. The transformation of the spatial uncertainty of objects. This thesis introduces a novel method for translating the spatial un- certainty of objects estimated from a moving frame attached to the robot into the global frame attached to the static landmarks in the environment. 3. The characterization of an improved PDF for representing landmark position in bearing-only SLAM. The proposed PDF is expressed in polar coordinates, and the marginal probability on range is constrained to be uniform. Compared to the PDF estimated from a mixture of Gaussians, the PDF developed here has far fewer parameters and can be easily adopted in a probabilistic framework, such as a particle filtering system. The main advantages of our proposed bearing-only SLAM system are its lower production cost and flexibility of use. The proposed system can be adopted in other domestic robots as well, such as vacuum cleaners or robotic toys when terrain is essentially 2D.