Accuracy, efficiency and stability analysis of Sparse-grid Quadrature Kalman Filter in Near space hypersonic vehicles

Chen, Hongmei; Cheng, Xianghong; Dai, Chenxi; Ran, Changyan

doi:10.1109/plans.2014.6851354

Cited by 5 publications

(15 citation statements)

References 20 publications

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“…In a sparse-grid UKF, the sigma points are propagated in the full state space but the number of these points is 2n SG , which is significantly smaller than the full state space dimension. The error covariance matrix is generated the same way as in the UKF for the reduced system (13). As a result, the error covariance is a n SG × n SG symmetric matrix.…”

Section: The Sparse-grid Ukfmentioning

confidence: 99%

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A Sparse-grid UKF For The State Estimation of PDEs

Kang¹,

King²,

Xu³

2017

2017 Proceedings of the Conference on Control and Its Applications

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Abstract-Unscented Kalman Filter (UKF) has been widely used in the estimation of dynamical systems defined by ordinary differential equations. For partial differential equations, their discretized systems often have very high dimensions, which result in covariance matrices that are computationally intractable. In this paper, we introduce sparse-grids and an associated reduced state space, called a surplus space, in which the covariance matrices have relatively small dimensions and the number of sigma points is significantly reduced. The covariance in the reduced space can be used to compute the correction term for the updating process of the UKF. The resulting sparse-grid UKF is illustrated using an example of shallow water equations.

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Section: The Sparse-grid Ukfmentioning

confidence: 99%

“…In [15], the authors propose to use sparse-grids for the integrations in a quasi Monte Carlo filter. In [13] is analyzed. It is numerically tested using an example of space vehicle navigation system.…”

Section: Introductionmentioning

confidence: 99%

A Sparse-grid UKF For The State Estimation of PDEs

Kang¹,

King²,

Xu³

2017

2017 Proceedings of the Conference on Control and Its Applications

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“…Nevertheless, for practical cases, such as problems regarding high-dimensional variables and strong nonlinearity or a black-box model, the accuracy of the traditional SGNI (e.g., the SGNI with traditional univariate integration points) for UP analysis needs improvement, especially in solving high-order moments such as skewness and kurtosis of the system response. Although studies [34] on the Kalman filter have provided univariate integration perspectives to improve the solving accuracy, it is limited in arbitrary distributions of input random variables, thereby affecting the practicability of the method.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty propagation analysis by an extended sparse grid technique

Jia

Jiang

et al. 2018

Front. Mech. Eng.

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In this paper, an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle, aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function (PDF) of the system response. The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis. Moreover, assisted by the Rosenblatt transformation, the various types of extended integration points are transformed into the extended Gauss-Hermite integration points, which makes the method suitable for any type of continuous distribution. Subsequently, within the sparse grid numerical integration framework, the statistical moments of the system response are obtained based on the transformed points. Furthermore, based on the maximum entropy principle, the obtained first four-order statistical moments are used to fit the PDF of the system response. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed method, which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

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“…A number of traditional nonlinear Bayesian estimations have been proposed in the literature, such as extended Kalman filter (EKF), unscented Kalman filter (UKF), Cubature Kalman Filtering (CKF) [16] and Gauss-Hermite quadrature filter (GHF) [17]. Recently, a novel estimation problem concerning Sparse-grid Quadrature Kalman Filtering (SGQKF) [18,19], has been proposed due to its high accuracy and low cost computation cost. And furthermore, nonlinear H1 filtering has been an active branch within the area of nonlinear filtering problems to deal with model uncertainty [20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

“…One consists of a nonlinear time-invariant system affected by parameter uncertainties [20][21][22][23]25,26] that are deterministic and typically known only to lie in some bounded set in the context of H1 nonlinear filtering. It has been demonstrated by means of examples that the H1 nonlinear filtering has the advantage of being superior than conventional nonlinear filtering to uncertainties of the underlying systems [19][20][21][22]. However, there is no provision in H1 nonlinear filtering to ensure that the variance of the state estimation error lies within acceptable bounds [21,24].…”

Section: Introductionmentioning

confidence: 99%