3,159 research outputs found

    A Spectral Learning Approach to Range-Only SLAM

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    We present a novel spectral learning algorithm for simultaneous localization and mapping (SLAM) from range data with known correspondences. This algorithm is an instance of a general spectral system identification framework, from which it inherits several desirable properties, including statistical consistency and no local optima. Compared with popular batch optimization or multiple-hypothesis tracking (MHT) methods for range-only SLAM, our spectral approach offers guaranteed low computational requirements and good tracking performance. Compared with popular extended Kalman filter (EKF) or extended information filter (EIF) approaches, and many MHT ones, our approach does not need to linearize a transition or measurement model; such linearizations can cause severe errors in EKFs and EIFs, and to a lesser extent MHT, particularly for the highly non-Gaussian posteriors encountered in range-only SLAM. We provide a theoretical analysis of our method, including finite-sample error bounds. Finally, we demonstrate on a real-world robotic SLAM problem that our algorithm is not only theoretically justified, but works well in practice: in a comparison of multiple methods, the lowest errors come from a combination of our algorithm with batch optimization, but our method alone produces nearly as good a result at far lower computational cost

    Predictive-State Decoders: Encoding the Future into Recurrent Networks

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    Recurrent neural networks (RNNs) are a vital modeling technique that rely on internal states learned indirectly by optimization of a supervised, unsupervised, or reinforcement training loss. RNNs are used to model dynamic processes that are characterized by underlying latent states whose form is often unknown, precluding its analytic representation inside an RNN. In the Predictive-State Representation (PSR) literature, latent state processes are modeled by an internal state representation that directly models the distribution of future observations, and most recent work in this area has relied on explicitly representing and targeting sufficient statistics of this probability distribution. We seek to combine the advantages of RNNs and PSRs by augmenting existing state-of-the-art recurrent neural networks with Predictive-State Decoders (PSDs), which add supervision to the network's internal state representation to target predicting future observations. Predictive-State Decoders are simple to implement and easily incorporated into existing training pipelines via additional loss regularization. We demonstrate the effectiveness of PSDs with experimental results in three different domains: probabilistic filtering, Imitation Learning, and Reinforcement Learning. In each, our method improves statistical performance of state-of-the-art recurrent baselines and does so with fewer iterations and less data.Comment: NIPS 201

    Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows

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    In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold learning technique, with a linear Kalman filter and with concepts from Koopman operator theory. More concretely, using diffusion maps, we construct data-driven virtual state coordinates, which linearize the system model. Based on these coordinates, we devise a data-driven framework for state estimation using the Kalman filter. We demonstrate the strengths of our method with respect to both parametric and non-parametric algorithms in three tracking problems. In particular, applying the approach to actual recordings of hippocampal neural activity in rodents directly yields a representation of the position of the animals. We show that the proposed method outperforms competing non-parametric algorithms in the examined stochastic problem formulations. Additionally, we obtain results comparable to classical parametric algorithms, which, in contrast to our method, are equipped with model knowledge.Comment: 15 pages, 12 figures, submitted to IEEE TS

    Data-driven model reduction and transfer operator approximation

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    In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis (TICA), dynamic mode decomposition (DMD), and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods
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