منابع مشابه
Gauss-Hermite interval quadrature rule
The existence and uniqueness of the Gaussian interval quadrature formula with respect to the Hermite weight function on R is proved. Similar results have been recently obtained for the Jacobi weight on [−1, 1] and for the generalized Laguerre weight on [0,+∞). Numerical construction of the Gauss–Hermite interval quadrature rule is also investigated, and a suitable algorithm is proposed. A few n...
متن کاملA note on multivariate Gauss-Hermite quadrature
The nodes xi and weights wi are uniquely determined by the choice of the domain D and the weighting kernel ψ(x). In fact, one may go as far as to say that the choice of the domain and the kernel defines a quadrature. In particular, the location of the nodes xi are given by the roots of the polynomial of order m in the sequence of orthonormal polynomials {πj} generated by the metric 〈πj|πk〉 := ∫...
متن کاملMultimodal Nonlinear Filtering Using Gauss-Hermite Quadrature
In filtering problems the (posterior) state distribution p(x) is recursively estimated given observations y and state dynamics. For nonlinear observation functions, the state distribution can becomemultimodal. Common Solutions are 1.Unimodal Gaussian filter using linearization of obs. function. 2. “Bank of filters” using multiple independent unimodal filters. We present a variational approach f...
متن کاملSimplified Gauss Hermite Filter Based on Sparse Grid Gauss Hermite Quadrature
In order to improve estimation accuracy of nonliear system with linear measurement model, simplified gauss hermite filter based on sparse grid gauss hermite quadrature (SGHF) is proposed. Comparing to conventional Gauss-Hermite filter (GHF) based on tensor product gauss quadrature rule, simplified SGHF not only maintains GHF’s advantage of precission controllable, high estimation accuracy, but ...
متن کاملUnscented Kalman filter revisited - Hermite-Gauss Quadrature approach
Kalman filter is a frequently used tool for linear state estimation due to its simplicity and optimality. It can further be used for fusion of information obtained from multiple sensors. Kalman filtering is also often applied to nonlinear systems. As the direct application of bayesian functional recursion is computationally not feasible, approaches commonly taken use either a local approximatio...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1999
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(99)00054-0