The Experts below are selected from a list of 5259 Experts worldwide ranked by ideXlab platform
Yang Cheng - One of the best experts on this subject based on the ideXlab platform.
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extension of the sparse grid Quadrature Filter
International Conference on Information Fusion, 2014Co-Authors: Yang Cheng, Yang Tian, John L CrassidisAbstract:The sparse grid Quadrature Filter is a point-based Gaussian Filter in which expectations of nonlinear functions of Gaussian random vectors are computed using the sparse grid Quadrature. The sparse grid Quadrature can be considered a generalization of the Unscented Transform in that the Unscented Transform is equivalent to the level-2 sparse grid Quadrature. A novel extension of the sparse grid Quadrature Filter is presented that directly transforms the points in time update and measurement update to eliminate repeated covariance decomposition based point generation and to relax the Gaussian assumption inherent in the sparse grid Quadrature Filter as well as the sigmapoint Filters. A tracking example is presented to demonstrate the performance of the novel Filter.
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high degree cubature kalman Filter
Automatica, 2013Co-Authors: Bin Jia, Ming Xin, Yang ChengAbstract:The cubature Kalman Filter (CKF), which is based on the third degree spherical-radial cubature rule, is numerically more stable than the unscented Kalman Filter (UKF) but less accurate than the Gauss-Hermite Quadrature Filter (GHQF). To improve the performance of the CKF, a new class of CKFs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed. The third-degree CKF is a special case of the class. The high-degree CKFs of the class can achieve the accuracy and stability performances close to those of the GHQF but at lower computational cost. A numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high-degree cubature rules to improve the performance. The target tracking simulation shows that the fifth-degree CKF can achieve higher accuracy than the extended Kalman Filter, the UKF, the third-degree CKF, and the particle Filter, and is computationally much more efficient than the GHQF.
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sparse grid Quadrature nonlinear Filtering
Automatica, 2012Co-Authors: Bin Jia, Ming Xin, Yang ChengAbstract:In this paper, a novel nonlinear Filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The Filter utilizes weighted sparse-grid Quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate Quadrature points with a range of accuracy levels are determined by the moment matching method. Then the univariate Quadrature point sets are extended to form a multi-dimensional grid using the sparse-grid theory. Compared with the conventional point-based methods, the estimation accuracy level of the SGQF can be flexibly controlled and the number of sparse-grid Quadrature points for the SGQF is a polynomial of the dimension of the system, which alleviates the curse of dimensionality for high dimensional problems. The Unscented Kalman Filter (UKF) is proven to be a subset of the SGQF at the level-2 accuracy. The performance of this Filter is demonstrated by an orbit estimation problem. The simulation results show that the SGQF achieves higher accuracy than the Extended Kalman Filter (EKF), the UKF, and the Cubature Kalman Filter (CKF). In addition, the SGQF is computationally much more efficient than the multi-dimensional Gauss-Hermite Quadrature Filter (GHQF) with the same performance.
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salient point Quadrature nonlinear Filtering
American Control Conference, 2011Co-Authors: Bin Jia, Ming Xin, Yang ChengAbstract:In this paper, a new nonlinear Filter named Salient Point Quadrature Filter (SPQF) using a sparse grid method is proposed. The Filter is derived using the so-called salient points to approximate the integrals in the Bayesian estimation algorithm. The univariate salient points are determined by the moment match method and then the sparse-grid theory is used to extend the univariate salient point sets to multi-dimensional cases. Compared with the other point-based methods, the estimation accuracy level of the new Filter can be flexibly controlled and the Filter algorithm is computationally more efficient since the number of salient points for SPQF increases polynomially with the dimension, which alleviates the curse of the dimensionality for high dimensional problems. Another contribution of this paper is to show that the Unscented Kalman Filter (UKF) is a subset of the SPQF with the accuracy level 2. The performance of this new Filter was demonstrated by the orbit determination problem. The simulation results show that the new Filter has better performance than the Extended Kalman Filter (EKF) and UKF.
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anisotropic sparse gauss hermite Quadrature Filter
AIAA Guidance Navigation and Control Conference, 2011Co-Authors: Bin Jia, Ming Xin, Yang ChengAbstract:In this paper, a new nonlinear Filter based on the anisotropic sparse Gauss-Hermite Quadrature (ASGHQ) is proposed. The sparse Gauss-Hermite Quadrature (SGHQ) has been recently proposed and used in the nonlinear Filtering to overcome the curse-of-dimensionality problem in the conventional Gauss-Hermite Quadrature (GHQ). SGHQ is more efficient to use since the number of SGHQ points increases polynomially with dimension whereas the number of GHQ points increases exponentially with dimension. In this paper, we propose to use ASGHQ to design a new nonlinear Filter as an extension of SGHQ. The advantage of ASGHQ is that the design of Quadrature incorporates the information of the system which is neglected by GHQ or SGHQ. As a result, the Quadrature points in the Filter algorithm can be further reduced and thus, this new nonlinear Filter is particularly useful for high dimensional nonlinear Filtering problems. In addition, the accuracy of ASGHQ is analyzed. The performance of this new Filter is demonstrated by the application to the attitude estimation problem, which demonstrates much better performance than the extended Kalman Filter (EKF), unscented Kalman Filter (UKF) and more efficient than the Filters based on SGHQ and GHQ.
Bin Jia - One of the best experts on this subject based on the ideXlab platform.
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refined nonlinear gaussian Quadrature Filter
Advances in Computing and Communications, 2019Co-Authors: Bin Jia, Ming XinAbstract:Gaussian Filters have been widely used in various applications due to their simplicity and effectiveness. For nonlinear estimation problems, Gaussian Filters are usually developed from numerical Quadrature rules to approximate the Gaussian weighted integrals in nonlinear Filtering algorithms. However, the Gaussian assumption may not be viable after propagation of Quadrature through nonlinear dynamics, which leads to degraded Quadrature and inaccurate update of mean and covariance. In this paper, we propose a new refined nonlinear Gaussian Quadrature Filter in which the predicted probability density function (PDF) is not assumed Gaussian. A set of Monte Carlo samples are first propagated through nonlinear dynamics. The statistic moments can be directly obtained from the propagated Monte Carlo samples. The refined Quadrature points and weights are generated from the moments' information using the arbitrary polynomial chaos method. Since the refined Quadrature points contain higher order statistic information of the propagated PDF, they have the potential to better represent the uncertainty and provide a more accurate estimate. Numerical examples show the effectiveness of the proposed Filter.
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nonlinearity based adaptive sparse grid Quadrature Filter
Advances in Computing and Communications, 2015Co-Authors: Tao Sun, Ming Xin, Bin JiaAbstract:The recently emerging sparse-grid Quadrature Filter (SGQF) has been shown to outperform the unscented Kalman Filter owing to its higher levels of estimation accuracy It can achieve the close performance to the Gauss Hermite Quadrature Filter without suffering the curse-of-dimensionality problem. However, the computation efficiency of the SGQF can be further improved by exploring the inherent system structure. In this paper, a new adaptive sparse-grid Quadrature Filter (ASGQF) is proposed. The accuracy levels of the sparse-grid Quadrature (SGQ) are adaptively selected based on the nonlinearity of the stochastic system such that a higher level of SGQ is used only when the nonlinearity measure is high, which reduces the unnecessary computation complexity. A global measure and a local measure of nonlinearity are used and compared. In a target tracking example, the ASGQF with the adaptive mixture of low level SGQ and high level SGQ is shown to achieve close performance to the sole higher level SGQF and demands much less computation load.
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performance comparison between extended kalman Filter and sparse grid Quadrature Filter for spacecraft attitude estimation using low grade attitude sensors
AIAA Infotech@Aerospace (I@A) Conference, 2013Co-Authors: Quang M Lam, Ming Xin, Bin JiaAbstract:Attitude Determination Subsystem (ADS) is essential to the spacecraft pointing control and highly relies on the onboard sensors’ quality and Filtering techniques. For high quality gyros, it is quite doable to achieve precision ADS using the 6 state EKF. However, for low grade low cost Micro-Electro-Mechanical System (MEMS) gyros and Complementary Metal-Oxide Semiconductor (CMOS) star tracker (ST), especially in higher slew rates type of missions, the 6 state EKF may not be the right or adequate structure to achieve precision attitude estimation capability because MEMS Scale Factor Errors (SFE) and Mis-Alignment Errors (MAE) at high rate will become a dominant error source contaminating gyros' measured rate vector. As a result, SFE and MAE errors may need to be estimated on-line along with the gyro bias errors for real-time error removal and correction to address the high rate slew operating conditions. This paper looks into the emerging Sparse Grid Quadrature Filter (SGQF), a nonlinear point-based Gaussian approximation Filtering technique, as an alternative to potentially replace the EKF from the accuracy and robustness standpoints. The study is intended to determine the pros and cons of each Filtering scheme and perform a simulation based evaluation of both Filters for a possible precision ADS solution using low cost MEMS gyros and CMOS star tracker.
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high degree cubature kalman Filter
Automatica, 2013Co-Authors: Bin Jia, Ming Xin, Yang ChengAbstract:The cubature Kalman Filter (CKF), which is based on the third degree spherical-radial cubature rule, is numerically more stable than the unscented Kalman Filter (UKF) but less accurate than the Gauss-Hermite Quadrature Filter (GHQF). To improve the performance of the CKF, a new class of CKFs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed. The third-degree CKF is a special case of the class. The high-degree CKFs of the class can achieve the accuracy and stability performances close to those of the GHQF but at lower computational cost. A numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high-degree cubature rules to improve the performance. The target tracking simulation shows that the fifth-degree CKF can achieve higher accuracy than the extended Kalman Filter, the UKF, the third-degree CKF, and the particle Filter, and is computationally much more efficient than the GHQF.
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Vision-Based Spacecraft Relative Navigation Using Sparse-Grid Quadrature Filter
IEEE Transactions on Control Systems Technology, 2013Co-Authors: Bin Jia, Ming XinAbstract:In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse-grid Quadrature Filter. The relative navigation provides the estimates of the relative orbit and relative attitude as well as the gyro biases. It is a challenging problem because of its high nonlinearity and dimensionality. The extended Kalman Filter (EKF) and the unscented Kalman Filter (UKF) have been used in the past to solve this problem. However, these Filters are not accurate enough in the presence of large initial uncertainties or high nonlinearities. Moreover, although other Filters, such as the Gauss-Hermite Quadrature Filter and the particle Filter, can be more accurate than the EKF and UKF, they are hard to use in this high-dimensional estimation problem since a large number of Quadrature points or particles are required and therefore the computation complexity is prohibitive. It is shown in this paper that the new sparse-grid Quadrature Filter can achieve much higher estimation accuracy than EKF, UKF, and the cubature Kalman Filter without excessive computation load.
Ming Xin - One of the best experts on this subject based on the ideXlab platform.
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refined nonlinear gaussian Quadrature Filter
Advances in Computing and Communications, 2019Co-Authors: Bin Jia, Ming XinAbstract:Gaussian Filters have been widely used in various applications due to their simplicity and effectiveness. For nonlinear estimation problems, Gaussian Filters are usually developed from numerical Quadrature rules to approximate the Gaussian weighted integrals in nonlinear Filtering algorithms. However, the Gaussian assumption may not be viable after propagation of Quadrature through nonlinear dynamics, which leads to degraded Quadrature and inaccurate update of mean and covariance. In this paper, we propose a new refined nonlinear Gaussian Quadrature Filter in which the predicted probability density function (PDF) is not assumed Gaussian. A set of Monte Carlo samples are first propagated through nonlinear dynamics. The statistic moments can be directly obtained from the propagated Monte Carlo samples. The refined Quadrature points and weights are generated from the moments' information using the arbitrary polynomial chaos method. Since the refined Quadrature points contain higher order statistic information of the propagated PDF, they have the potential to better represent the uncertainty and provide a more accurate estimate. Numerical examples show the effectiveness of the proposed Filter.
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nonlinearity based adaptive sparse grid Quadrature Filter
Advances in Computing and Communications, 2015Co-Authors: Tao Sun, Ming Xin, Bin JiaAbstract:The recently emerging sparse-grid Quadrature Filter (SGQF) has been shown to outperform the unscented Kalman Filter owing to its higher levels of estimation accuracy It can achieve the close performance to the Gauss Hermite Quadrature Filter without suffering the curse-of-dimensionality problem. However, the computation efficiency of the SGQF can be further improved by exploring the inherent system structure. In this paper, a new adaptive sparse-grid Quadrature Filter (ASGQF) is proposed. The accuracy levels of the sparse-grid Quadrature (SGQ) are adaptively selected based on the nonlinearity of the stochastic system such that a higher level of SGQ is used only when the nonlinearity measure is high, which reduces the unnecessary computation complexity. A global measure and a local measure of nonlinearity are used and compared. In a target tracking example, the ASGQF with the adaptive mixture of low level SGQ and high level SGQ is shown to achieve close performance to the sole higher level SGQF and demands much less computation load.
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performance comparison between extended kalman Filter and sparse grid Quadrature Filter for spacecraft attitude estimation using low grade attitude sensors
AIAA Infotech@Aerospace (I@A) Conference, 2013Co-Authors: Quang M Lam, Ming Xin, Bin JiaAbstract:Attitude Determination Subsystem (ADS) is essential to the spacecraft pointing control and highly relies on the onboard sensors’ quality and Filtering techniques. For high quality gyros, it is quite doable to achieve precision ADS using the 6 state EKF. However, for low grade low cost Micro-Electro-Mechanical System (MEMS) gyros and Complementary Metal-Oxide Semiconductor (CMOS) star tracker (ST), especially in higher slew rates type of missions, the 6 state EKF may not be the right or adequate structure to achieve precision attitude estimation capability because MEMS Scale Factor Errors (SFE) and Mis-Alignment Errors (MAE) at high rate will become a dominant error source contaminating gyros' measured rate vector. As a result, SFE and MAE errors may need to be estimated on-line along with the gyro bias errors for real-time error removal and correction to address the high rate slew operating conditions. This paper looks into the emerging Sparse Grid Quadrature Filter (SGQF), a nonlinear point-based Gaussian approximation Filtering technique, as an alternative to potentially replace the EKF from the accuracy and robustness standpoints. The study is intended to determine the pros and cons of each Filtering scheme and perform a simulation based evaluation of both Filters for a possible precision ADS solution using low cost MEMS gyros and CMOS star tracker.
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high degree cubature kalman Filter
Automatica, 2013Co-Authors: Bin Jia, Ming Xin, Yang ChengAbstract:The cubature Kalman Filter (CKF), which is based on the third degree spherical-radial cubature rule, is numerically more stable than the unscented Kalman Filter (UKF) but less accurate than the Gauss-Hermite Quadrature Filter (GHQF). To improve the performance of the CKF, a new class of CKFs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed. The third-degree CKF is a special case of the class. The high-degree CKFs of the class can achieve the accuracy and stability performances close to those of the GHQF but at lower computational cost. A numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high-degree cubature rules to improve the performance. The target tracking simulation shows that the fifth-degree CKF can achieve higher accuracy than the extended Kalman Filter, the UKF, the third-degree CKF, and the particle Filter, and is computationally much more efficient than the GHQF.
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Vision-Based Spacecraft Relative Navigation Using Sparse-Grid Quadrature Filter
IEEE Transactions on Control Systems Technology, 2013Co-Authors: Bin Jia, Ming XinAbstract:In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse-grid Quadrature Filter. The relative navigation provides the estimates of the relative orbit and relative attitude as well as the gyro biases. It is a challenging problem because of its high nonlinearity and dimensionality. The extended Kalman Filter (EKF) and the unscented Kalman Filter (UKF) have been used in the past to solve this problem. However, these Filters are not accurate enough in the presence of large initial uncertainties or high nonlinearities. Moreover, although other Filters, such as the Gauss-Hermite Quadrature Filter and the particle Filter, can be more accurate than the EKF and UKF, they are hard to use in this high-dimensional estimation problem since a large number of Quadrature points or particles are required and therefore the computation complexity is prohibitive. It is shown in this paper that the new sparse-grid Quadrature Filter can achieve much higher estimation accuracy than EKF, UKF, and the cubature Kalman Filter without excessive computation load.
R A Minasian - One of the best experts on this subject based on the ideXlab platform.
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microwave photonic Quadrature Filter based on an all optical programmable hilbert transformer
Optics Letters, 2011Co-Authors: Thomas X H Huang, R A MinasianAbstract:A microwave photonic Quadrature Filter, new to our knowledge, based on an all-optical Hilbert transformer is presented. It is based on mapping of a Hilbert transform transfer function between the optical and electrical domains, using a programmable Fourier-domain optical processor and high-speed photodiodes. The technique enables the realization of an extremely wide operating bandwidth, tunable programmable bandwidth, and a highly precise amplitude and phase response. Experimental results demonstrate a microwave Quadrature Filter from 10 to 20 GHz, which achieves an amplitude imbalance of less than ±0.23 dB and a phase imbalance of less than ±0.5°.
Jian Wei Yang - One of the best experts on this subject based on the ideXlab platform.
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shift unitary transform for constructing two dimensional wavelet Filters
Journal of Applied Mathematics, 2011Co-Authors: Fei Li, Jian Wei YangAbstract:Due to the difficulty for constructing two-dimensional wavelet Filters, the commonly used wavelet Filters are tensor-product of one-dimensional wavelet Filters. In some applications, more perfect reconstruction Filters should be provided. In this paper, we introduce a transformation which is referred to as Shift Unitary Transform (SUT) of Conjugate Quadrature Filter (CQF). In terms of this transformation, we propose a parametrization method for constructing two-dimensional orthogonal wavelet Filters. It is proved that tensor-product wavelet Filters are only special cases of this parametrization method. To show this, we introduce the SUT of one-dimensional CQF and present a complete parametrization of one-dimensional wavelet system. As a result, more ways are provided to randomly generate two-dimensional perfect reconstruction Filters.
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image ownership verification via unitary transform of conjugate Quadrature Filter
International Conference on Intelligent Computing, 2006Co-Authors: Jian Wei Yang, Wensheng Chen, Xinxiang Zhang, Bin FangAbstract:A wavelet-based watermarking system is described for ownership verification of digital images. The wavelet Filters used in this system are constructed by unitary transform of two-dimensional conjugate Quadrature Filter (CQF). Tensor-product wavelet Filters are only special cases of this construction. This construction provides more ways to randomly generate perfect reconstruction Filters, and will increase the difficulty for counterfeiters to gain the exact knowledge of our watermark. Furthermore, the watermark is inserted into several middle-frequency sub-bands and the existence of the watermark is asserted if any one of the correlation values is greater than a pre-determined threshold. Experimental results show that the proposed algorithm achieves invisibility, blind, and robustness to noising, sharpening, cropping etc.
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image ownership verification via unitary transform of conjugate Quadrature Filter
International Conference on Intelligent Computing, 2006Co-Authors: Jian Wei Yang, Wensheng Chen, Xinxiang Zhang, Bin FangAbstract:A wavelet-based watermarking system is described for ownership verification of digital images. The wavelet Filters used in this system are constructed by unitary transform of two-dimensional conjugate Quadrature Filter (CQF). Tensor-product wavelet Filters are only special cases of this construction. This construction provides more ways to randomly generate perfect reconstruction Filters, and will increase the difficulty for counterfeiters to gain the exact knowledge of our watermark. Furthermore, the watermark is inserted into several middle-frequency sub-bands and the existence of the watermark is asserted if any one of the correlation values is greater than a pre-determined threshold. Experimental results show that the proposed algorithm achieves invisibility, blind, and robustness to noising, sharpening, cropping etc.
