A marginalised particle filter with variational inference for non‐linear state‐space models with Gaussian mixture noise

This work proposes a marginalised particle filter with variational inference for non‐linear state‐space models (SSMs) with Gaussian mixture noise. A latent variable indicating the component of the Gaussian mixture considered at each time instant is introduced to specify the measurement mode of the SSM. The resulting joint posterior distribution of the state vector, the mode variable and the parameters of the Gaussian mixture noise is marginalised with respect to the noise variables. The marginalised posterior distribution of the state and mode is then approximated by using an appropriate marginalised particle filter. The noise parameters conditionally on each particle system of the state and mode variable are finally updated by using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state‐of‐the‐art approaches in the context of positioning in urban canyons using global navigation satellite systems

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

Conjugate priors for Bayesian object tracking

Object tracking refers to the problem of using noisy sensor measurements to determine the location and characteristics of objects of interest in clutter. Nowadays, object tracking has found applications in numerous research venues as well as application areas, including air traffic control, maritime navigation, remote sensing, intelligent video surveillance, and more recently environmental perception, which is a key enabling technology in autonomous vehicles. This thesis studies conjugate priors for Bayesian object tracking with focus on multi-object tracking (MOT) based on sets of trajectories. Finite Set Statistics provides an elegant Bayesian formulation of MOT in terms of the theory of random finite sets (RFSs). Conjugate priors are also of great interest as they provide families of distributions that are suitable to work with when seeking accurate approximations to the true posterior distributions. Many RFS-based MOT approaches are only concerned with multi-object filtering without attempting to estimate object trajectories. An appealing approach to building tracks is by computing the multi-object densities on sets of trajectories. This leads to the development of trajectory filters, e.g., filters based on Poisson multi-Bernoulli mixture (PMBM) conjugate priors.In this thesis, [Paper A] and [Paper B] consider the problem of point object tracking where an object generates at most one measurement per scan. In [Paper A], it is shown that the trajectory MBM filter is the solution to the MOT problem for standard point object models with multi-Bernoulli birth. In addition, the multi-scan implementations of trajectory PMBM and MBM filters are presented. In [Paper B], a solution for recovering full trajectory information, via the calculation of the posterior of the set of trajectories from a sequence of multi-object filtering densities and the multi-object dynamic model, is presented. [Paper C] and [Paper D] consider the problem of ex- tended object tracking where an object may generate multiple measurements per scan. In [Paper C], the extended object PMBM filter for sets of objects is generalized to sets of trajectories. In [Paper D], a learning-based extended ob- ject tracking algorithm using a hierarchical truncated Gaussian measurement model tailored for automotive radar measurements is presented

Uncertainty-aware 3D Object-Level Mapping with Deep Shape Priors

3D object-level mapping is a fundamental problem in robotics, which is especially challenging when object CAD models are unavailable during inference. In this work, we propose a framework that can reconstruct high-quality object-level maps for unknown objects. Our approach takes multiple RGB-D images as input and outputs dense 3D shapes and 9-DoF poses (including 3 scale parameters) for detected objects. The core idea of our approach is to leverage a learnt generative model for shape categories as a prior and to formulate a probabilistic, uncertainty-aware optimization framework for 3D reconstruction. We derive a probabilistic formulation that propagates shape and pose uncertainty through two novel loss functions. Unlike current state-of-the-art approaches, we explicitly model the uncertainty of the object shapes and poses during our optimization, resulting in a high-quality object-level mapping system. Moreover, the resulting shape and pose uncertainties, which we demonstrate can accurately reflect the true errors of our object maps, can also be useful for downstream robotics tasks such as active vision. We perform extensive evaluations on indoor and outdoor real-world datasets, achieving achieves substantial improvements over state-of-the-art methods. Our code will be available at https://github.com/TRAILab/UncertainShapePose.Comment: Manuscript submitted to ICRA 202

Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced. © 2013 Elsevier Inc. All rights reserved

Latent parameter estimation in fusion networks using separable likelihoods

Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional solutions to the problem pose difficulties in scaling with the number of sensors due to the joint multi-sensor filtering involved when evaluating the parameter likelihood. In this article, we propose a separable pseudo-likelihood which is a more accurate approximation compared to a previously proposed alternative under typical operating conditions. In addition, we consider using separable likelihoods in the presence of many objects and ambiguity in associating measurements with objects that originated them. To this end, we use a state space model with a hypothesis based parameterisation, and, develop an empirical Bayesian perspective in order to evaluate separable likelihoods on this model using local filtering. Bayesian inference with this likelihood is carried out using belief propagation on the associated pairwise Markov random field. We specify a particle algorithm for latent parameter estimation in a linear Gaussian state space model and demonstrate its efficacy for network self-calibration using measurements from non-cooperative targets in comparison with alternatives.Comment: accepted with minor revisions, IEEE Transactions on Signal and Information Processing Over Network

A survey on active simultaneous localization and mapping: state of the art and new frontiers

Active simultaneous localization and mapping (SLAM) is the problem of planning and controlling the motion of a robot to build the most accurate and complete model of the surrounding environment. Since the first foundational work in active perception appeared, more than three decades ago, this field has received increasing attention across different scientific communities. This has brought about many different approaches and formulations, and makes a review of the current trends necessary and extremely valuable for both new and experienced researchers. In this article, we survey the state of the art in active SLAM and take an in-depth look at the open challenges that still require attention to meet the needs of modern applications. After providing a historical perspective, we present a unified problem formulation and review the well-established modular solution scheme, which decouples the problem into three stages that identify, select, and execute potential navigation actions. We then analyze alternative approaches, including belief-space planning and deep reinforcement learning techniques, and review related work on multirobot coordination. This article concludes with a discussion of new research directions, addressing reproducible research, active spatial perception, and practical applications, among other topics