The Experts below are selected from a list of 29184 Experts worldwide ranked by ideXlab platform
Jouni Hartikainen - One of the best experts on this subject based on the ideXlab platform.
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Spatiotemporal learning via infinite-dimensional bayesian Filtering and smoothing: A look at gaussian process regression through Kalman Filtering
IEEE Signal Processing Magazine, 2013Co-Authors: Simo Särkkä, Arno Solin, Jouni HartikainenAbstract:Gaussian process-based machine learning is a powerful Bayesian paradigm for nonparametric nonlinear regression and classification. In this article, we discuss connections of Gaussian process regression with Kalman Filtering and present methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional state-space models. This formulation allows for use of computationally efficient infinite-dimensional Kalman Filtering and smoothing methods, or more general Bayesian Filtering and smoothing methods, which reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into linear time complexity. The implication of this is that the use of machine-learning models in signal processing becomes computationally feasible, and it opens the possibility to combine machine-learning techniques with signal processing methods.
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infinite dimensional Kalman Filtering approach to spatio temporal gaussian process regression
International Conference on Artificial Intelligence and Statistics, 2012Co-Authors: Simo Särkkä, Jouni HartikainenAbstract:We show how spatio-temporal Gaussian process (GP) regression problems (or the equivalent Kriging problems) can be formulated as infinite-dimensional Kalman Filtering and Rauch-Tung-Striebel (RTS) smoothing problems, and present a procedure for converting spatio-temporal covariance functions into infinite-dimensional stochastic differential equations (SDEs). The resulting infinitedimensional SDEs belong to the class of stochastic pseudo-differential equations and can be numerically treated using the methods developed for deterministic counterparts of the equations. The scaling of the computational cost in the proposed approach is linear in the number of time steps as opposed to the cubic scaling of the direct GP regression solution. We also show how separable covariance functions lead to a finite-dimensional Kalman Filtering and RTS smoothing problem, present analytical and numerical examples, and discuss numerical methods for computing the solutions.
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Kalman Filtering and smoothing solutions to temporal gaussian process regression models
International Workshop on Machine Learning for Signal Processing, 2010Co-Authors: Jouni Hartikainen, Simo SärkkäAbstract:In this paper, we show how temporal (i.e., time-series) Gaussian process regression models in machine learning can be reformulated as linear-Gaussian state space models, which can be solved exactly with classical Kalman Filtering theory. The result is an efficient non-parametric learning algorithm, whose computational complexity grows linearly with respect to number of observations. We show how the reformulation can be done for Matern family of covariance functions analytically and for squared exponential covariance function by applying spectral Taylor series approximation. Advantages of the proposed approach are illustrated with two numerical experiments.
Simo Särkkä - One of the best experts on this subject based on the ideXlab platform.
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Spatiotemporal learning via infinite-dimensional bayesian Filtering and smoothing: A look at gaussian process regression through Kalman Filtering
IEEE Signal Processing Magazine, 2013Co-Authors: Simo Särkkä, Arno Solin, Jouni HartikainenAbstract:Gaussian process-based machine learning is a powerful Bayesian paradigm for nonparametric nonlinear regression and classification. In this article, we discuss connections of Gaussian process regression with Kalman Filtering and present methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional state-space models. This formulation allows for use of computationally efficient infinite-dimensional Kalman Filtering and smoothing methods, or more general Bayesian Filtering and smoothing methods, which reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into linear time complexity. The implication of this is that the use of machine-learning models in signal processing becomes computationally feasible, and it opens the possibility to combine machine-learning techniques with signal processing methods.
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infinite dimensional Kalman Filtering approach to spatio temporal gaussian process regression
International Conference on Artificial Intelligence and Statistics, 2012Co-Authors: Simo Särkkä, Jouni HartikainenAbstract:We show how spatio-temporal Gaussian process (GP) regression problems (or the equivalent Kriging problems) can be formulated as infinite-dimensional Kalman Filtering and Rauch-Tung-Striebel (RTS) smoothing problems, and present a procedure for converting spatio-temporal covariance functions into infinite-dimensional stochastic differential equations (SDEs). The resulting infinitedimensional SDEs belong to the class of stochastic pseudo-differential equations and can be numerically treated using the methods developed for deterministic counterparts of the equations. The scaling of the computational cost in the proposed approach is linear in the number of time steps as opposed to the cubic scaling of the direct GP regression solution. We also show how separable covariance functions lead to a finite-dimensional Kalman Filtering and RTS smoothing problem, present analytical and numerical examples, and discuss numerical methods for computing the solutions.
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Kalman Filtering and smoothing solutions to temporal gaussian process regression models
International Workshop on Machine Learning for Signal Processing, 2010Co-Authors: Jouni Hartikainen, Simo SärkkäAbstract:In this paper, we show how temporal (i.e., time-series) Gaussian process regression models in machine learning can be reformulated as linear-Gaussian state space models, which can be solved exactly with classical Kalman Filtering theory. The result is an efficient non-parametric learning algorithm, whose computational complexity grows linearly with respect to number of observations. We show how the reformulation can be done for Matern family of covariance functions analytically and for squared exponential covariance function by applying spectral Taylor series approximation. Advantages of the proposed approach are illustrated with two numerical experiments.
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recursive noise adaptive Kalman Filtering by variational bayesian approximations
IEEE Transactions on Automatic Control, 2009Co-Authors: Simo Särkkä, Aapo NummenmaaAbstract:This article considers the application of variational Bayesian methods to joint recursive estimation of the dynamic state and the time-varying measurement noise parameters in linear state space models. The proposed adaptive Kalman Filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately. The result is a recursive algorithm, where on each step the state is estimated with Kalman filter and the sufficient statistics of the noise variances are estimated with a fixed-point iteration. The performance of the algorithm is demonstrated with simulated data.
Yunmin Zhu - One of the best experts on this subject based on the ideXlab platform.
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optimal distributed Kalman Filtering fusion with singular covariances of Filtering errors and measurement noises
IEEE Transactions on Automatic Control, 2014Co-Authors: Enbin Song, Yunmin ZhuAbstract:In this paper, we present the globally optimal distributed Kalman Filtering fusion with singular covariances of Filtering errors and measurement noises. The following facts motivate us to consider the problem. First, the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms. However, it can not be guaranteed to exist in practice. For example, when state estimation for a given dynamic system is subject to state equality constraints, the estimation error covariance matrices must be singular. Second, the proposed fused state estimate is still exactly the same as the centralized Kalman Filtering using all sensor raw measurements. Moreover, the existing performance analysis results on the distributed Kalman Filtering fusion for the multisensor system with feedback are also extended to the singular covariance matrices of Filtering error. The final numerical examples support the theoretical results and show an advantage of less computational burden.
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Novel Data Association Algorithm Based on Integrated Random Coefficient Matrices Kalman Filtering
IEEE Transactions on Aerospace and Electronic Systems, 2012Co-Authors: Yingting Luo, Yunmin Zhu, Xiaojing Shen, Enbin SongAbstract:We present a novel data association algorithm based on an integrated random coefficient matrices Kalman Filtering (DAIRKF) for the multiple targets and sensors tracking association problem. The basic idea of this algorithm is to integrate all targets and measurements which need to be associated to a new whole system. Then the random coefficient matrices Kalman Filtering is applied to this integrated dynamic system to derive the estimates of these target states. Since this algorithm violates some independence conditions for the optimality of the random coefficient matrices Kalman Filtering, it is suboptimal in the mean square error (MSE) sense. Nevertheless, in some degree, there is still a correct theoretical basis in DAIRKF and the idea of this algorithm is significantly different from that of joint probabilistic data association (JPDA). Moreover, we can extend the single-sensor DAIRKF algorithm to a multisensor DAIRKF (MSDAIRKF) algorithm with high survivability in poor environment. The computation burden of MSDAIRKF grows linearly as the number of sensors increases. Numerical examples show that the new algorithm works significantly better than JPDA in many cases.
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optimal distributed Kalman Filtering fusion algorithm without invertibility of estimation error and sensor noise covariances
IEEE Signal Processing Letters, 2012Co-Authors: Enbin Song, Yingting Luo, Yunmin ZhuAbstract:Although the globally optimal distributed Kalman Filtering fusion has been proposed and studied for more than twenty years, the invertibility of estimation error and measurement noise covariances has been always a restrictive assumption to derive a globally optimal distributed Kalman Filtering fusion equivalent to the centralized Kalman Filtering fusion. This letter proposes an optimal distributed Kalman Filtering fusion algorithm for general dynamic systems without invertibility of estimation error and measurement noise covariances. The new algorithm uses the convex combination fusion, whose fusion weights are recursively given. Computer experiments show that the performance of this fusion algorithm is very likely to be equivalent to that of the centralized Kalman Filtering fusion. In practice, the new fusion algorithm can be applied to any distributed Kalman Filtering fusion, such as the equality constrained distributed Kalman Filtering fusion.
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globally optimal multisensor distributed random parameter matrices Kalman Filtering fusion with applications
Sensors, 2008Co-Authors: Yingting Luo, Yunmin Zhu, Enbin Song, Jie Zhou, Dandan Luo, Donghua WangAbstract:This paper proposes a new distributed Kalman Filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman Filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman Filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman Filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.
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brief paper optimal Kalman Filtering fusion with cross correlated sensor noises
Automatica, 2007Co-Authors: Enbin Song, Yunmin Zhu, Jie Zhou, Zhisheng YouAbstract:When there is no feedback from the fusion center to local sensors, we present a distributed Kalman Filtering fusion formula for linear dynamic systems with sensor noises cross-correlated, and prove that under a mild condition the fused state estimate is equivalent to the centralized Kalman Filtering using all sensor measurements, therefore, it achieves the best performance. Then, for the same dynamic system, when there is feedback, a modified Kalman Filtering fusion with feedback for distributed recursive state estimators is proposed, and prove that the fusion formula with feedback is, as the fusion without feedback, still exactly equivalent to the corresponding centralized Kalman Filtering fusion formula; the various P matrices in the feedback Kalman Filtering at both local filters and the fusion center are still the covariance matrices of tracking errors; the feedback does reduce the covariance of each local tracking error.
Enbin Song - One of the best experts on this subject based on the ideXlab platform.
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optimal distributed Kalman Filtering fusion with singular covariances of Filtering errors and measurement noises
IEEE Transactions on Automatic Control, 2014Co-Authors: Enbin Song, Yunmin ZhuAbstract:In this paper, we present the globally optimal distributed Kalman Filtering fusion with singular covariances of Filtering errors and measurement noises. The following facts motivate us to consider the problem. First, the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms. However, it can not be guaranteed to exist in practice. For example, when state estimation for a given dynamic system is subject to state equality constraints, the estimation error covariance matrices must be singular. Second, the proposed fused state estimate is still exactly the same as the centralized Kalman Filtering using all sensor raw measurements. Moreover, the existing performance analysis results on the distributed Kalman Filtering fusion for the multisensor system with feedback are also extended to the singular covariance matrices of Filtering error. The final numerical examples support the theoretical results and show an advantage of less computational burden.
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Novel Data Association Algorithm Based on Integrated Random Coefficient Matrices Kalman Filtering
IEEE Transactions on Aerospace and Electronic Systems, 2012Co-Authors: Yingting Luo, Yunmin Zhu, Xiaojing Shen, Enbin SongAbstract:We present a novel data association algorithm based on an integrated random coefficient matrices Kalman Filtering (DAIRKF) for the multiple targets and sensors tracking association problem. The basic idea of this algorithm is to integrate all targets and measurements which need to be associated to a new whole system. Then the random coefficient matrices Kalman Filtering is applied to this integrated dynamic system to derive the estimates of these target states. Since this algorithm violates some independence conditions for the optimality of the random coefficient matrices Kalman Filtering, it is suboptimal in the mean square error (MSE) sense. Nevertheless, in some degree, there is still a correct theoretical basis in DAIRKF and the idea of this algorithm is significantly different from that of joint probabilistic data association (JPDA). Moreover, we can extend the single-sensor DAIRKF algorithm to a multisensor DAIRKF (MSDAIRKF) algorithm with high survivability in poor environment. The computation burden of MSDAIRKF grows linearly as the number of sensors increases. Numerical examples show that the new algorithm works significantly better than JPDA in many cases.
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optimal distributed Kalman Filtering fusion algorithm without invertibility of estimation error and sensor noise covariances
IEEE Signal Processing Letters, 2012Co-Authors: Enbin Song, Yingting Luo, Yunmin ZhuAbstract:Although the globally optimal distributed Kalman Filtering fusion has been proposed and studied for more than twenty years, the invertibility of estimation error and measurement noise covariances has been always a restrictive assumption to derive a globally optimal distributed Kalman Filtering fusion equivalent to the centralized Kalman Filtering fusion. This letter proposes an optimal distributed Kalman Filtering fusion algorithm for general dynamic systems without invertibility of estimation error and measurement noise covariances. The new algorithm uses the convex combination fusion, whose fusion weights are recursively given. Computer experiments show that the performance of this fusion algorithm is very likely to be equivalent to that of the centralized Kalman Filtering fusion. In practice, the new fusion algorithm can be applied to any distributed Kalman Filtering fusion, such as the equality constrained distributed Kalman Filtering fusion.
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globally optimal multisensor distributed random parameter matrices Kalman Filtering fusion with applications
Sensors, 2008Co-Authors: Yingting Luo, Yunmin Zhu, Enbin Song, Jie Zhou, Dandan Luo, Donghua WangAbstract:This paper proposes a new distributed Kalman Filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman Filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman Filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman Filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.
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brief paper optimal Kalman Filtering fusion with cross correlated sensor noises
Automatica, 2007Co-Authors: Enbin Song, Yunmin Zhu, Jie Zhou, Zhisheng YouAbstract:When there is no feedback from the fusion center to local sensors, we present a distributed Kalman Filtering fusion formula for linear dynamic systems with sensor noises cross-correlated, and prove that under a mild condition the fused state estimate is equivalent to the centralized Kalman Filtering using all sensor measurements, therefore, it achieves the best performance. Then, for the same dynamic system, when there is feedback, a modified Kalman Filtering fusion with feedback for distributed recursive state estimators is proposed, and prove that the fusion formula with feedback is, as the fusion without feedback, still exactly equivalent to the corresponding centralized Kalman Filtering fusion formula; the various P matrices in the feedback Kalman Filtering at both local filters and the fusion center are still the covariance matrices of tracking errors; the feedback does reduce the covariance of each local tracking error.
K P Schwarz - One of the best experts on this subject based on the ideXlab platform.
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adaptive Kalman Filtering for ins gps
Journal of Geodesy, 1999Co-Authors: Ahmed Mohamed, K P SchwarzAbstract:After reviewing the two main approaches of adaptive Kalman Filtering, namely, innovation-based adaptive estimation (IAE) and multiple-model-based adaptive estimation (MMAE), the detailed development of an innovation-based adaptive Kalman filter for an integrated inertial navigation system/global positioning system (INS/GPS) is given. The developed adaptive Kalman filter is based on the maximum likelihood criterion for the proper choice of the filter weight and hence the filter gain factors. Results from two kinematic field tests in which the INS/GPS was compared to highly precise reference data are presented. Results show that the adaptive Kalman filter outperforms the conventional Kalman filter by tuning either the system noise variance–covariance (V–C) matrix `Q' or the update measurement noise V–C matrix `R' or both of them.
