Recursive Bayesian inference on stochastic differential equations

This thesis is concerned with recursive Bayesian estimation of non-linear dynamical systems, which can be modeled as discretely observed stochastic differential equations. The recursive real-time estimation algorithms for these continuous-discrete filtering problems are traditionally called optimal filters and the algorithms for recursively computing the estimates based on batches of observations are called optimal smoothers. In this thesis, new practical algorithms for approximate and asymptotically optimal continuous-discrete filtering and smoothing are presented. The mathematical approach of this thesis is probabilistic and the estimation algorithms are formulated in terms of Bayesian inference. This means that the unknown parameters, the unknown functions and the physical noise processes are treated as random processes in the same joint probability space. The Bayesian approach provides a consistent way of computing the optimal filtering and smoothing estimates, which are optimal given the model assumptions and a consistent way of analyzing their uncertainties. The formal equations of the optimal Bayesian continuous-discrete filtering and smoothing solutions are well known, but the exact analytical solutions are available only for linear Gaussian models and for a few other restricted special cases. The main contributions of this thesis are to show how the recently developed discrete-time unscented Kalman filter, particle filter, and the corresponding smoothers can be applied in the continuous-discrete setting. The equations for the continuous-time unscented Kalman-Bucy filter are also derived. The estimation performance of the new filters and smoothers is tested using simulated data. Continuous-discrete filtering based solutions are also presented to the problems of tracking an unknown number of targets, estimating the spread of an infectious disease and to prediction of an unknown time series.reviewe

Graphical models for visual object recognition and tracking

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 277-301).We develop statistical methods which allow effective visual detection, categorization, and tracking of objects in complex scenes. Such computer vision systems must be robust to wide variations in object appearance, the often small size of training databases, and ambiguities induced by articulated or partially occluded objects. Graphical models provide a powerful framework for encoding the statistical structure of visual scenes, and developing corresponding learning and inference algorithms. In this thesis, we describe several models which integrate graphical representations with nonparametric statistical methods. This approach leads to inference algorithms which tractably recover high-dimensional, continuous object pose variations, and learning procedures which transfer knowledge among related recognition tasks. Motivated by visual tracking problems, we first develop a nonparametric extension of the belief propagation (BP) algorithm. Using Monte Carlo methods, we provide general procedures for recursively updating particle-based approximations of continuous sufficient statistics. Efficient multiscale sampling methods then allow this nonparametric BP algorithm to be flexibly adapted to many different applications.(cont.) As a particular example, we consider a graphical model describing the hand's three-dimensional (3D) structure, kinematics, and dynamics. This graph encodes global hand pose via the 3D position and orientation of several rigid components, and thus exposes local structure in a high-dimensional articulated model. Applying nonparametric BP, we recover a hand tracking algorithm which is robust to outliers and local visual ambiguities. Via a set of latent occupancy masks, we also extend our approach to consistently infer occlusion events in a distributed fashion. In the second half of this thesis, we develop methods for learning hierarchical models of objects, the parts composing them, and the scenes surrounding them. Our approach couples topic models originally developed for text analysis with spatial transformations, and thus consistently accounts for geometric constraints. By building integrated scene models, we may discover contextual relationships, and better exploit partially labeled training images. We first consider images of isolated objects, and show that sharing parts among object categories improves accuracy when learning from few examples.(cont.) Turning to multiple object scenes, we propose nonparametric models which use Dirichlet processes to automatically learn the number of parts underlying each object category, and objects composing each scene. Adapting these transformed Dirichlet processes to images taken with a binocular stereo camera, we learn integrated, 3D models of object geometry and appearance. This leads to a Monte Carlo algorithm which automatically infers 3D scene structure from the predictable geometry of known object categories.by Erik B. Sudderth.Ph.D

Multiple-Target Tracking in Complex Scenarios

In this dissertation, we develop computationally efficient algorithms for multiple-target tracking: MTT) in complex scenarios. For each of these scenarios, we develop measurement and state-space models, and then exploit the structure in these models to propose efficient tracking algorithms. In addition, we address design issues such as sensor selection and resource allocation. First, we consider MTT when the targets themselves are moving in a time-varying multipath environment. We develop a sparse-measurement model that allows us to exploit the inherent joint delay-Doppler diversity offered by the environment. We then reformulate the problem of MTT as a block-support recovery problem using the sparse measurement model. We exploit the structure of the dictionary matrix to develop a computationally efficient block support recovery algorithm: and thereby a multiple-target tracking algorithm) under the assumption that the channel state describing the time-varying multipath environment is known. Further, we also derive an upper bound on the overall error probability of wrongly identifying the support of the sparse signal. We then relax the assumption that the channel state is known. We develop a new particle filter called the Multiple Rao-Blackwellized Particle Filter: MRBPF) to jointly estimate both the target and the channel states. We also compute the posterior Cramér-Rao bound: PCRB) on the estimates of the target and the channel states and use the PCRB to find a suitable subset of antennas to be used for transmission in each tracking interval, as well as the power transmitted by these antennas. Second, we consider the problem of tracking an unknown number and types of targets using a multi-modal sensor network. In a multi-modal sensor network, different quantities associated with the same state are measured using sensors of different kinds. Hence, an efficient method that can suitably combine the diverse information measured by each sensor is required. We first develop a Hierarchical Particle Filter: HPF) to estimate the unknown state from the multi-modal measurements for a special class of problems which can be modeled hierarchically. We then model our problem of tracking using a hierarchical model and then use the proposed HPF for joint initiation, termination and tracking of multiple targets. The multi-modal data consists of the measurements collected from a radar, an infrared camera and a human scout. We also propose a unified framework for multi-modal sensor management that comprises sensor selection: SS), resource allocation: RA) and data fusion: DF). Our approach is inspired by the trading behavior of economic agents in commercial markets. We model the sensors and the sensor manager as economic agents, and the interaction among them as a double sided market with both consumers and producers. We propose an iterative double auction mechanism for computing the equilibrium of such a market. We relate the equilibrium point to the solutions of SS, RA and DF. Third, we address MTT problem in the presence of data association ambiguity that arises due to clutter. Data association corresponds to the problem of assigning a measurement to each target. We treat the data association and state estimation as separate subproblems. We develop a game-theoretic framework to solve the data association, in which we model each tracker as a player and the set of measurements as strategies. We develop utility functions for each player, and then use a regret-based learning algorithm to find the correlated equilibrium of this game. The game-theoretic approach allows us to associate measurements to all the targets simultaneously. We then use particle filtering on the reduced dimensional state of each target, independently

Sparse Bayesian information filters for localization and mapping

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008This thesis formulates an estimation framework for Simultaneous Localization and Mapping (SLAM) that addresses the problem of scalability in large environments. We describe an estimation-theoretic algorithm that achieves significant gains in computational efficiency while maintaining consistent estimates for the vehicle pose and the map of the environment. We specifically address the feature-based SLAM problem in which the robot represents the environment as a collection of landmarks. The thesis takes a Bayesian approach whereby we maintain a joint posterior over the vehicle pose and feature states, conditioned upon measurement data. We model the distribution as Gaussian and parametrize the posterior in the canonical form, in terms of the information (inverse covariance) matrix. When sparse, this representation is amenable to computationally efficient Bayesian SLAM filtering. However, while a large majority of the elements within the normalized information matrix are very small in magnitude, it is fully populated nonetheless. Recent feature-based SLAM filters achieve the scalability benefits of a sparse parametrization by explicitly pruning these weak links in an effort to enforce sparsity. We analyze one such algorithm, the Sparse Extended Information Filter (SEIF), which has laid much of the groundwork concerning the computational benefits of the sparse canonical form. The thesis performs a detailed analysis of the process by which the SEIF approximates the sparsity of the information matrix and reveals key insights into the consequences of different sparsification strategies. We demonstrate that the SEIF yields a sparse approximation to the posterior that is inconsistent, suffering from exaggerated confidence estimates. This overconfidence has detrimental effects on important aspects of the SLAM process and affects the higher level goal of producing accurate maps for subsequent localization and path planning. This thesis proposes an alternative scalable filter that maintains sparsity while preserving the consistency of the distribution. We leverage insights into the natural structure of the feature-based canonical parametrization and derive a method that actively maintains an exactly sparse posterior. Our algorithm exploits the structure of the parametrization to achieve gains in efficiency, with a computational cost that scales linearly with the size of the map. Unlike similar techniques that sacrifice consistency for improved scalability, our algorithm performs inference over a posterior that is conservative relative to the nominal Gaussian distribution. Consequently, we preserve the consistency of the pose and map estimates and avoid the effects of an overconfident posterior. We demonstrate our filter alongside the SEIF and the standard EKF both in simulation as well as on two real-world datasets. While we maintain the computational advantages of an exactly sparse representation, the results show convincingly that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the original Gaussian distribution as produced by the EKF, but at much less computational expense. The thesis concludes with an extension of our SLAM filter to a complex underwater environment. We describe a systems-level framework for localization and mapping relative to a ship hull with an Autonomous Underwater Vehicle (AUV) equipped with a forward-looking sonar. The approach utilizes our filter to fuse measurements of vehicle attitude and motion from onboard sensors with data from sonar images of the hull. We employ the system to perform three-dimensional, 6-DOF SLAM on a ship hull

Information metrics for localization and mapping

Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals

Information metrics for localization and mapping

Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals

Information metrics for localization and mapping

Aplicat embargament des de la defensa de la tesi fins al 12/2019Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals.Postprint (published version

Absolute Positioning Using the Earth\u27s Magnetic Anomaly Field

Achieving worldwide alternatives to GPS is a challenging engineering problem. Current GPS alternatives often suffer from limitations such as where and when the systems can operate. Navigation using the Earth\u27s magnetic anomaly field, which is globally available at all times, shows promise to overcome many of these limitations. We present a navigation filter which uses the Earth\u27s magnetic anomaly field as a navigation signal to aid an inertial navigation system (INS) in an aircraft. The filter utilizes highly-accurate optically pumped cesium (OPC) magnetometers to make scalar measurements of the Earth\u27s magnetic field and compare them to a map using a marginalized particle filter approach. We demonstrate navigation accuracy of 13 meters DRMS with a high quality magnetic anomaly map at low altitudes with real flight data. We conduct a simulation over the continental United States to predict accuracies with respect to variables like location and altitude. Finally, we address the problem of map availability by presenting a method for a self-building magnetic anomaly model