5,658 research outputs found

    GP-SUM. Gaussian Processes Filtering of non-Gaussian Beliefs

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    This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted sum of Gaussians. The key attribute of GP-SUM is that it does not rely on linearizations of the dynamic or observation models, or on unimodal Gaussian approximations of the belief, hence enables tracking complex state distributions. The algorithm can be seen as a combination of a sampling-based filter with a probabilistic Bayes filter. On the one hand, GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. On the other hand, it achieves effective sampling and accurate probabilistic propagation by relying on the GP form of the system, and the sum-of-Gaussian form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also demonstrate its use in a pushing task, predicting with experimental accuracy the naturally occurring non-Gaussian distributions.Comment: WAFR 2018, 16 pages, 7 figure

    Learning the dynamics and time-recursive boundary detection of deformable objects

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    We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

    Extended Object Tracking: Introduction, Overview and Applications

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    This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

    State space reparametrization for approximating nonlinear models in Bayesian state estimation

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    Recursive Bayesian state estimation is a powerful methodology which is useful for the integration of data about a process of interest while considering all the sources of uncertainty which are present in the observations and in modeling inaccuracies. However, in its general form it is intractable and approximations need to be made in order to use it in real life applications. The most widely used algorithm to perform recursive state estimation is the Kalman filter, which assumes that the probability distributions that it propagates are Gaussian and that the measurement and dynamical processes are linear. If these assumptions are satisfied, the Kalman filter is optimal. In most applications, however, this proves to be an oversimplification, due to which several techniques have arisen to handle model non-linearity and different types of distributions. In this thesis, a novel method for the estimation of distributions with nonlinear dynamical and measurement models is presented, which uses a reparametrization of the state space of the distributions in order to exploit the linear properties of the Kalman filter. This involves the mapping of the distribution into a different space, and a subsequent approximation as a Gaussian distribution. An analysis of the adequacy of this transformation is presented, which shows that it is a valid approach in a number of practically interesting filtering problems. The proposed approach is applied to the estimation of the state of Earth-orbiting objects, as it is a challenging estimation scenario which can benefit from the use of filter. Space situational awareness is increasingly important as near-Earth space becomes cluttered with satellites and debris. In this work, the sensors that are most commonly used to track objects in orbit, radars and telescopes, are modeled and a filter based on the previously discussed ideas is proposed. Finally, a multi-object estimation filter based on a recent estimation framework is presented which propagates high amounts of information while maintaining low computational complexity. This is important as there are many challenges to tracking large amounts of orbiting objects in a principled way using ground-based sensors, and naturally extends the single object filter described above to the multi-sensor, multi-object case

    SMCTC : sequential Monte Carlo in C++

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    Sequential Monte Carlo methods are a very general class of Monte Carlo methods for sampling from sequences of distributions. Simple examples of these algorithms are used very widely in the tracking and signal processing literature. Recent developments illustrate that these techniques have much more general applicability, and can be applied very effectively to statistical inference problems. Unfortunately, these methods are often perceived as being computationally expensive and difficult to implement. This article seeks to address both of these problems. A C++ template class library for the efficient and convenient implementation of very general Sequential Monte Carlo algorithms is presented. Two example applications are provided: a simple particle filter for illustrative purposes and a state-of-the-art algorithm for rare event estimation

    Advanced sequential Monte Carlo methods and their applications to sparse sensor network for detection and estimation

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    The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this thesis, we present an advanced SMC method and the study of its asymptotic behavior. We apply the proposed SMC method in a target tracking problem using different observation models. Specifically, a distributed SMC algorithm is developed for a wireless sensor network (WSN) that incorporates with an informative-sensor detection technique. The novel SMC algorithm is designed to surmount the degeneracy problem by employing a multilevel Markov chain Monte Carlo (MCMC) procedure constructed by engaging drift homotopy and likelihood bridging techniques. The observations are gathered only from the informative sensors, which are sensing useful observations of the nearby moving targets. The detection of those informative sensors, which are typically a small portion of the WSN, is taking place by using a sparsity-aware matrix decomposition technique. Simulation results showcase that our algorithm outperforms current popular tracking algorithms such as bootstrap filter and auxiliary particle filter in many scenarios
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