The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Robert J Elliott - One of the best experts on this subject based on the ideXlab platform.
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discrete time Nonlinear Filtering algorithms using gauss hermite quadrature
Proceedings of the IEEE, 2007Co-Authors: Ienkaran Arasaratnam, Simon Haykin, Robert J ElliottAbstract:In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for Nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression (SLR) through a set of Gauss-Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, Nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other Nonlinear Filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve Nonlinear non- Gaussian Filtering problems.
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discrete time Nonlinear Filtering algorithms using gauss hermite quadrature new computationally efficient methods are proposed for more accurately analyzing and modeling dynamic processes that are Nonlinear and subject to non gaussian noise
Proceedings of the IEEE, 2007Co-Authors: Ienkaran Arasaratnam, Simon Haykin, Robert J ElliottAbstract:In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for Nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression (SLR) through a set of Gauss-Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, Nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other Nonlinear Filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve Nonlinear non- Gaussian Filtering problems.
Stephen S.-t. Yau - One of the best experts on this subject based on the ideXlab platform.
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hermite spectral method to 1 d forward kolmogorov equation and its application to Nonlinear Filtering problems
IEEE Transactions on Automatic Control, 2013Co-Authors: Xue Luo, Stephen S.-t. YauAbstract:In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It greatly improves the resolution of HSM. The convergence rate of HSM to FKE is analyzed in the suitable function space and has been verified by the numerical simulation. As an important application and our primary motivation to study the HSM to FKE, we work on the implementation of the Nonlinear Filtering (NLF) problems with a real-time algorithm developed by S.-T. Yau and the second author in 2008. The HSM to FKE is served as the off-line computation in this algorithm. The translating factor of the generalized Hermite functions and the moving-window technique are introduced to deal with the drifting of the posterior conditional density function of the states in the on-line experiments. Two numerical experiments of NLF problems are carried out to illustrate the feasibility of our algorithm. Moreover, our algorithm surpasses the particle filters as a real-time solver to NLF.
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hermite spectral method to 1d forward kolmogorov equation and its application to Nonlinear Filtering problems
arXiv: Optimization and Control, 2013Co-Authors: Xue Luo, Stephen S.-t. YauAbstract:In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It greatly improves the resolution of HSM. The convergence rate of HSM to FKE is analyzed in the suitable function space and has been verified by the numerical simulation. As an important application and our primary motivation to study the HSM to FKE, we work on the implementation of the Nonlinear Filtering (NLF) problem with a real-time algorithm developed in [17]. The HSM to FKE is served as the off-line computation in this algorithm. The translating factor of the generalized Hermite functions and the moving-window technique are introduced to deal with the drifting of the posterior conditional density function of the states in the on-line experiments. Two numerical experiments of NLF problems are carried out to illustrate the feasibility of our algorithm. Moreover, our algorithm surpasses the particle filter as a real-time solver to NLF.
Kaiqi Xiong - One of the best experts on this subject based on the ideXlab platform.
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performance evaluation of ukf based Nonlinear Filtering
Automatica, 2006Co-Authors: Kaiqi Xiong, H Y Zhang, C W ChanAbstract:The performance of the modified unscented Kalman filter (UKF) for Nonlinear stochastic discrete-time system with linear measurement equation is investigated. It is proved that under certain conditions, the estimation error of the UKF remains bounded. Furthermore, it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm. Error behavior of the UKF is then derived in terms of mean square error (MSE), and the Cramer-Rao lower bound (CRLB) is introduced as a performance measure. The modified UKF is found to approach the CRLB if the difference between the real noise covariance matrix and the selected one is small enough. These results are verified by using Monte Carlo simulations on two example systems.
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Gaussian filters for Nonlinear Filtering problems
IEEE Transactions on Automatic Control, 2000Co-Authors: Kazufumi Ito, Kaiqi XiongAbstract:We develop and analyze real-time and accurate filters for Nonlinear Filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gaussian distributions. A new update rule of weights for Gaussian sum filters is proposed. Our numerical tests demonstrate that new filters significantly improve the extended Kalman filter with no additional cost, and the new Gaussian sum filter has a nearly optimal performance.
Ienkaran Arasaratnam - One of the best experts on this subject based on the ideXlab platform.
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discrete time Nonlinear Filtering algorithms using gauss hermite quadrature
Proceedings of the IEEE, 2007Co-Authors: Ienkaran Arasaratnam, Simon Haykin, Robert J ElliottAbstract:In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for Nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression (SLR) through a set of Gauss-Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, Nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other Nonlinear Filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve Nonlinear non- Gaussian Filtering problems.
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discrete time Nonlinear Filtering algorithms using gauss hermite quadrature new computationally efficient methods are proposed for more accurately analyzing and modeling dynamic processes that are Nonlinear and subject to non gaussian noise
Proceedings of the IEEE, 2007Co-Authors: Ienkaran Arasaratnam, Simon Haykin, Robert J ElliottAbstract:In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for Nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression (SLR) through a set of Gauss-Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, Nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other Nonlinear Filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve Nonlinear non- Gaussian Filtering problems.
Xue Luo - One of the best experts on this subject based on the ideXlab platform.
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hermite spectral method to 1 d forward kolmogorov equation and its application to Nonlinear Filtering problems
IEEE Transactions on Automatic Control, 2013Co-Authors: Xue Luo, Stephen S.-t. YauAbstract:In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It greatly improves the resolution of HSM. The convergence rate of HSM to FKE is analyzed in the suitable function space and has been verified by the numerical simulation. As an important application and our primary motivation to study the HSM to FKE, we work on the implementation of the Nonlinear Filtering (NLF) problems with a real-time algorithm developed by S.-T. Yau and the second author in 2008. The HSM to FKE is served as the off-line computation in this algorithm. The translating factor of the generalized Hermite functions and the moving-window technique are introduced to deal with the drifting of the posterior conditional density function of the states in the on-line experiments. Two numerical experiments of NLF problems are carried out to illustrate the feasibility of our algorithm. Moreover, our algorithm surpasses the particle filters as a real-time solver to NLF.
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hermite spectral method to 1d forward kolmogorov equation and its application to Nonlinear Filtering problems
arXiv: Optimization and Control, 2013Co-Authors: Xue Luo, Stephen S.-t. YauAbstract:In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It greatly improves the resolution of HSM. The convergence rate of HSM to FKE is analyzed in the suitable function space and has been verified by the numerical simulation. As an important application and our primary motivation to study the HSM to FKE, we work on the implementation of the Nonlinear Filtering (NLF) problem with a real-time algorithm developed in [17]. The HSM to FKE is served as the off-line computation in this algorithm. The translating factor of the generalized Hermite functions and the moving-window technique are introduced to deal with the drifting of the posterior conditional density function of the states in the on-line experiments. Two numerical experiments of NLF problems are carried out to illustrate the feasibility of our algorithm. Moreover, our algorithm surpasses the particle filter as a real-time solver to NLF.
