321 research outputs found

    Efficient Schur Parametrization and Modeling of p-Stationary Second-Order Time-Series for LPC Transmission

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    Following the results presented in [1], we present an efficient approach to the Schur parametrization/modeling of a subclass of second-order time-series which we term p-stationary time-series, yielding a uniform hierarchy of algorithms suitable for efficient implementations and being a good starting point for nonlinear generalizations to higher-order non-Gaussian nearstationary time-series

    Sequential Detection with Mutual Information Stopping Cost

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    This paper formulates and solves a sequential detection problem that involves the mutual information (stochastic observability) of a Gaussian process observed in noise with missing measurements. The main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices. This monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies.The sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound. We illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly-by and persistent-surveillance applications involving a GMTI (Ground Moving Target Indicator) radar

    Sparse Bayesian information filters for localization and mapping

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    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

    Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices

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    Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive Δ\Delta-Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat's local field potential activity in a complex sequence memory task.Comment: 49 pages, 15 figure

    Non-Gaussian Geostatistical Modeling using (skew) t Processes

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    We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with tt marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) tt process we study the second-order and geometrical properties and in the tt case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the tt process. Moreover we compare the performance of the optimal linear predictor of the tt process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australi
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