35,870 research outputs found

    Doubly Robust Smoothing of Dynamical Processes via Outlier Sparsity Constraints

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    Coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice. In this context, the present paper develops novel fixed-lag and fixed-interval smoothing algorithms that are robust to outliers simultaneously present in the measurements {\it and} in the state dynamics. Outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least-squares criterion that is regularized with the 1\ell_1-norm of the outliers in order to effect sparsity control. The resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers, are expressed in closed form per iteration, and are provably convergent. Additional attractive features of the novel doubly robust smoother include: i) ability to handle both types of outliers; ii) universality to unknown nominal noise and outlier distributions; iii) flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions; and iv) improved performance relative to competing alternatives at comparable complexity, as corroborated via simulated tests.Comment: Submitted to IEEE Trans. on Signal Processin

    Robust Singular Smoothers For Tracking Using Low-Fidelity Data

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    Tracking underwater autonomous platforms is often difficult because of noisy, biased, and discretized input data. Classic filters and smoothers based on standard assumptions of Gaussian white noise break down when presented with any of these challenges. Robust models (such as the Huber loss) and constraints (e.g. maximum velocity) are used to attenuate these issues. Here, we consider robust smoothing with singular covariance, which covers bias and correlated noise, as well as many specific model types, such as those used in navigation. In particular, we show how to combine singular covariance models with robust losses and state-space constraints in a unified framework that can handle very low-fidelity data. A noisy, biased, and discretized navigation dataset from a submerged, low-cost inertial measurement unit (IMU) package, with ultra short baseline (USBL) data for ground truth, provides an opportunity to stress-test the proposed framework with promising results. We show how robust modeling elements improve our ability to analyze the data, and present batch processing results for 10 minutes of data with three different frequencies of available USBL position fixes (gaps of 30 seconds, 1 minute, and 2 minutes). The results suggest that the framework can be extended to real-time tracking using robust windowed estimation.Comment: 9 pages, 9 figures, to be included in Robotics: Science and Systems 201

    Robust Filtering and Smoothing with Gaussian Processes

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    We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of "system identification" is more robust than finding point estimates of a parametric function representation. In this article, we present a principled algorithm for robust analytic smoothing in GP dynamic systems, which are increasingly used in robotics and control. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail.Comment: 7 pages, 1 figure, draft version of paper accepted at IEEE Transactions on Automatic Contro

    Semiparametric Bayesian models for human brain mapping

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    Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility

    Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation

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    In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering and smoothing algorithms are equivalent to a particular algorithm for solving this problem. Once this equivalence is established, we present extensions of Kalman smoothing to systems with nonlinear process and measurement models, systems with linear and nonlinear inequality constraints, systems with outliers in the measurements or sudden changes in the state, and systems where the sparsity of the state sequence must be accounted for. All extensions preserve the computational efficiency of the classic algorithms, and most of the extensions are illustrated with numerical examples, which are part of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure

    Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models

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    We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including on-line and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods
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